Satellite Geodesy Lecture Notes MSU 2015.pptx

MIDLANDS STATE
UNIVERSITY
FACULTY OF SCIENCE
DEPARTMENT OF SURVEYING
AND GEOMATICS
SVG302 GPS
LECTURE NOTES
LECTURER: D NJIKE

CHAPTER 1
INTRODUCTION TO SATELLITE GEODESY
Geodesy – is the science of the measurement and mapping of the earth’s
surface (Helmert, 1880) {classical definition}.
– includes the determination of the earth’s external gravity field as
well as the surface of the ocean floor (Torge, 1991)
Satellite – an artificial body placed in orbit round the earth or another planet in
order to collect information or for communication.
- a celestial body orbiting the earth or another planet.
Satellite Geodesy – comprises the observational and computational
techniques which allow the solution of geodetic problems
by the use of precise measurement to, from or between
artificial mostly near-earth satellites
- is the measurement of the form and dimensions of the Earth,
the location of objects on its surface and the figure of the
Earth's gravity field by means of artificial satellite techniques
- geodesy by means of artificial satellites.

Objectives of satellite geodesy
1. Determination of precise global, regional and local 3-D positions (e.g.
establishment of geodetic control
2. Determination of the earth’s gravity field and linear functions of this field
(e.g. precise geoid)
3. Measurement and modelling of geodynamical phenomena (e.g. polar
motion, earth rotation, crustal deformation)
Historical Developments of Satellite Geodesy
1957 – Launch of SPUTNIK 1
1958 - Earth Flattening from satellite data (f = 1/298.3)
1958 – LaUnch of EXPLORER IB

Cont’d
1959- Third Zonal Harmonic (Pear shape of the earth)
1959 – Theory of the Motion of Artificial satellites
1960 – Launch of TRANSIT-1B
1960 – Launch of ECHO-1
1960 –Theory of satellite orbits
1962 – Launch of ANNA-1B
1962 – Geodetic connection between France and Algeria
1964 – basic geodetic problems had been successfully tackled namely:
• Determination of a precise numerical value of the earth flattening
• Determination of the general shape of global geoid
• Determination of connections between most important geodetic datums
(to +50m)

Phases of development
1. 1958 – 1970
Development of basic methods for satellite observation, computational and analysis of
satellite orbits
2. 1970 – 1980
Scientific projects phase
New observation techniques were developed and refined – laser ranging to satellites and
to the moon and satellite altimetry
TRANSIT system was used for geodetic Doppler positioning
3. 1980 – onwards
Operational use of satellite techniques in geodesy, geodynamics and land surveying.
Two aspects:
a) Satellites methods are increasingly used by surveying community replacing the
conventional methods
b) Increased observation accuracy

Applications of Satellite Geodesy
Global Geodesy
• General shape of the earth’s figure and gravity field
• Dimensions of a mean earth ellipsoid
• Establishment of a global terrestrial reference frame
• Detailed geoid as a reference surface on land and at sea
• Connection between different geodetic datums
• Connection of national datums with a global datum
Geodetic Control
• Establishment of geodetic control for national networks
• Installation of 3-D homogeneous networks
• Analysis and improvements of existing terrestrial networks
• Establishment of geodetic connections between islands or with the mainland
• Densification of existing networks up to short interstation distances

Cont’d
Geodynamics
• Control points for crustal motion
• Polar motion, earth rotation
• Solid earth tides
Applied and Plane Geodesy
• Detailed plane surveying (cadastral, engineering, GIS, mapping etc,)
• Installation of special networks and control for engineering tasks
• Terrestrial control points in Photogrammetry and Remote Sensing
• Position and orientation of Photogrammetric cameras
• Control points for Cartography during expedition

Cont’d
Navigation and Marine Geodesy
• Precise navigation of land, sea and air vehicles
• Precise positioning for marine mapping exploration, hydrography,
oceanography, marine geology and geophysics
• Connections of tide gauges (unification of height systems)
Related Fields
• Position and velocity determination for geophysical observations
(gravimetric, magnetic, seismic survey) also at sea and in the air
• Determination of ice motion in glaciology

CHAPTER 2
FUNDAMENTALS OF COORDINATE SYSTEMS
Well defined and reproducible reference coordinate system are essentials for
description of satellite motion, modelling of observables, and the
representation and interpretation of results
• Reference coordinate systems in satellite geodesy are global and geocentric
by nature
• Terrestrial measurements are by nature local in character
• Relationship between both systems must be known with sufficient
accuracy
• Since relative position and orientation change with time, the recording
modelling of the observation time plays an important role
• The establishment of precise transformation formulas between systems is
one of the most important tasks in satellite geodesy

Cartesian Coordinate systems and Coordinate Transformations
In a Cartesian coordinate system with the axes x, y, z the position of a
point P is determined by its position vector:

Cartesian Coordinate systems and Coordinate Transformations
• The transformation to a second Cartesian coordinate system with
identical origin and the axes xI, yI, zI, which is generated from the first
one by a rotation around the z-axis by the angle y , can be realized
through the matrix operation

The representation is valid for a right-handed coordinate system.
When viewed towards the origin, a counter-clockwise rotation is
positive. Any coordinate transformation can be realized through
a combination of rotations. The complete transformation is

• The mathematical properties of rotation matrices are described using
linear algebra. The following rules are of importance:

• The relation between the position vectors in two arbitrarily rotated
coordinate systems is then
• In satellite geodesy the rotation angles are often very small, thus
allowing the use of the linearized form for R. With cos α ∼= 1 and
sin α ∼= α (in radians), neglecting higher order terms, it follows that

• To describe satellite motion, observables and models it is
necessary to have a well-defined and reproducible reference
coordinate system.
• Since the accuracy in satellite systems and the precision
requirements are tight, these reference systems have to be
accurate as well.
• It is important to note the difference between Reference
System and Reference Frame, two different concepts.
• The first one is understood as a theoretical definition,
including models and standards for its implementation. The
second one is its practical implementation through
observations and a set of reference coordinates, e.g. a set of
fundamental stars, for a Celestial Reference Frame, or
fiducial stations, for a Terrestrial Reference Frame.
Coordinate Systems

• The International Celestial Reference System (ICRS) was
proposed by the International Earth Rotation and Reference
Systems Service (IERS) and formally accepted by the
International Astronomical Union (IAU) in 1997.
• A realization of the ICRS is the International Celestial
Reference Frame (ICRF).
• On the other hand, IERS is in charge of defining, realizing
and promoting the International Terrestrial Reference
System (ITRS).
• Realizations of ITRS are the International Terrestrial
Reference Frames (ITRFs), being the ITRF2005 the current
reference realization of ITRS.
Coordinate Systems

• also known as Earth Centred Inertial (ECI) (Strictly
speaking this is a quasi-inertial system because of the
annual motion of the Earth around the Sun, and thus it
is subjected to a certain acceleration, but can be
thought of as inertial over short periods of time).
• mainly used for the description of satellite motion.
• the CRS has its origin in the Earth's centre of mass or
Geocentre,
• its fundamental plane is the mean Equator plane
(containing the Geocentre) of the epoch J2000.0,
• the principal axis x is pointing to the mean Vernal
equinox of epoch J2000.0.
Coordinate Systems
Conventional Celestial Reference System

Coordinate Systems

• The three axis defining this coordinate are shown in
Figure 1 above.
• xCRS axis: Its origin is the Geocentre, the Earth's centre of
mass, and its direction is towards the mean equinox at
J2000.0 (i.e., the intersection between the J2000 equatorial
plane and the ecliptic plane).
• zCRS axis: This axis is defined by the direction of the earth
mean rotation pole at J2000.0.
• yCRS axis: Is the orthogonal to the formers ones, so the
system is right handed.
Coordinate Systems

• This reference system is also known as Earth-Centred,
Earth-Fixed (ECEF), it is an earth-fixed, i.e. rotating (not
space-fixed as CRS reference system).
• Its origin is the Earth's centre of mass,
• the fundamental plane contains this origin and it is
perpendicular to the Earth's Conventional Terrestrial
Pole (CTP) (defined as an average of the poles from 1900
to 1905).
• Its principal axis is pointing to the intersection of the mean
Greenwich meridian and the equator.
• Since this coordinate system follows the diurnal rotation of
earth, this is not an inertial reference system.
Coordinate Systems
Conventional Terrestrial Reference System

Coordinate Systems

• The three axis that define this system are showed in
the figure above.
• zTRS: This axis is defined by the Conventional Terrestrial
Pole (CTP).
• xTRS: This axis is defined as the intersection between the
equatorial plane and the mean Greenwich meridian plane.
The equatorial plane is orthogonal to the CTP and in the
Mean Greenwich meridian direction. This meridian was
established by the Bureau International de l'Heure (BIH)
observatory.
• yTRS: It is orthogonal to the other axes so that the system is
right-handed.
Coordinate Systems

• The Conventional Terrestrial Pole is commonly referred to as the
Earth's North Pole. However it should be remembered that the Earth's
polar axis precesses and nutates,
• Thus the position of the "instantaneous" pole is given in seconds of arc
from the CTP,
• the International Earth Rotation Service (IERS) tracks the position of
the pole in relation to the CTP as a function of time,
Coordinate Systems

• An example of a CT system is the International
Terrestrial Reference Frame (ITRF) where stations are
located with reference to the GRS 80 ellipsoid using
VLBI and SLR techniques.
• This world-wide datum takes into account the temporal
effects such as plate tectonics and tidal effects. Thus it is
regularly updated and the date of the update is appended
to its name. For example, ITRF 00 is the datum as
defined in J2000.0. Previous versions were ITRF 97,
ITRF 96, and ITRF 94.
Coordinate Systems

• The datum known as WGS 84 (not to be confused
with the WGS 84 ellipsoid) is another example of a
TRF system of coordinates. Both of these systems of
points with coordinates are known as worldwide
datums.
• Since NAD 83 uses points only on the North American
continent, it is known as a local datum. NAD 83 is
also called a regional datum.
Coordinate Systems

• Used to define coordinates of celestial bodies – stars,
• Established by first defining celestial sphere on which
stars are located,
• The celestial sphere is very large compared to the
earth such that it is considered as a point at the centre
of the sphere – dimensionless,
Coordinate Systems
Celestial Coordinate System

Coordinate Systems

• In the celestial coordinate system the North and South
Celestial Poles are determined by projecting the rotation
axis of the Earth to intersect the celestial sphere, which in
turn defines a Celestial Equator.
• The celestial equivalent of latitude is
called declination and is measured in degrees North
(positive numbers) or South (negative numbers) of the
Celestial Equator.
• The celestial equivalent of longitude is called right
ascension. Right ascension can be measured in degrees,
but for historical reasons it is more common to measure it
in time (hours, minutes, seconds): the sky turns 360
degrees in 24 hours and therefore it must turn 15 degrees
every hour; thus, 1 hour of right ascension is equivalent to
15 degrees of (apparent) sky rotation.
• The position of a star is given as (r,θ,λ)
Coordinate Systems

• In general there are the following celestial coordinate
systems:
• Ecliptic coordinate system
• commonly used for representing the positions
and orbits of Solar System objects.
• Because most planets (except Mercury), and many small solar
system bodies have orbits with small inclinations to
the ecliptic, it is convenient to use it as the fundamental plane.
• The system's origin can be either the center of the Sun or the
center of the Earth,
• its primary direction is towards the vernal equinox, and it has
a right-handed convention.
• It may be implemented in spherical or rectangular coordinates
Coordinate Systems

• The Ecliptic is the path that the Sun appears to follow across the sky
over the course of a year.
• It is also the projection of the Earth's orbital plane onto the Celestial
Sphere.
• The latitudinal angle is called the Ecliptic Latitude, and the
longitudinal angle is called the Ecliptic Longitude.
• Like Right Ascension in the Equatorial system, the zero point of the
Ecliptic Longitude is the Vernal Equinox.
Coordinate Systems

• Right Ascension Coordinate System
• In Figure 1, S is a celestial body on the celestial hemisphere whose
position is to be fixed by spherical coordinates. The earth is located
at the centre, O, of the sphere with its axis in the direction of OP,
• Hour circles on the celestial sphere compare with the meridian
circles or meridians of longitude of the earth. In the figure, PSU is
an hour circle arc.
• Parallels of declination of the celestial sphere compare with the
parallels of latitude of the earth.
• The equinoctial colure of the celestial sphere passes through the
vernal equinox, V, an imaginary point among the stars where the sun
apparently crosses the equator from south to north on March 21 of
each year. The E.C. compares with the prime meridian through
Greenwich.
• Right ascension of the sun or any star (comparable to the longitude
of a station on earth) is the angular distance, alpha, measured along
the celestial equator between the vernal equinox and the hour circle
through the body. Right ascensions are measured eastward from the
vernal equinox and may be expressed in degrees of arc (0� to
360�) or in hours of time (0h to 24h).
Coordinate Systems

• Right Ascension Coordinate System
• Declination of any celestial body is the angular distance, delta, of
the body above or below the celestial equator. It is comparable with
the latitude of the station on earth. If the body is above the equator
its declination is said to be north and is considered as positive; if it
is below the equator its declination is said to be south and is
considered negative. Declinations are expressed in degrees and
cannot exceed 90� in magnitude.
• Polar distance of any celestial body is = 90� - delta with due
regard to the sign of the declination.
• For the present purpose the vernal equinox is assumed to be a fixed
point on the celestial equator. However, the coordinates of celestial
bodies with respect to the celestial equator and the equinoctial
colure change slightly with the passage of time, due to:
• Precession and nutation,
• Proper motion
• Aberration
• parallax
Coordinate Systems

• The Hour Angle Coordinate System
• In Figure 1, let the plane of the hour circle MNPN'M' coincide at
the time of observation with the plane of the observer's meridian
circle, and let S be some heavenly body whose position with
respect to the observer's meridian and the equator MM'UV it is
desired to establish,
• The spherical coordinates of the star are given by (1) the angular
distance of the star above or below the equator, which in the
figure is given by the arc US, defined previously as the
declination, and (2) the angular distance measured along the
equator between the meridian and the hour circle through the star.
When this measurement is from east to west it is called an hour
angle. The hour angle of any celestial body may then be defined
as the angular distance measured westward along the equator
from the meridian of reference to the hour circle through the
body.
• Hour angles are expressed either in hours of time or in degrees of
arc.
Coordinate Systems

• The Horizontal Coordinate System
• uses the observer's local horizon as the Fundamental Plane. This conveniently
divides the sky into the upper hemisphere that you can see, and the lower
hemisphere that you can't (because the Earth is in the way).
• The pole of the upper hemisphere is called the Zenith. The pole of the lower
hemisphere is called the nadir.
• The angle of an object above or below the horizon is called the Altitude (Alt
for short). The angle of an object around the horizon (measured from the North
point, toward the East) is called the Azimuth.
• The Horizontal Coordinate System is sometimes also called the Alt/Az
Coordinate System.
• The Horizontal Coordinate System is fixed to the Earth, not the Stars.
Therefore, the Altitude and Azimuth of an object changes with time, as the
object appears to drift across the sky.
• because the Horizontal system is defined by your local horizon, the same
object viewed from different locations on Earth at the same time will have
different values of Altitude and Azimuth.
• Horizontal coordinates are very useful for determining the Rise and Set times
of an object in the sky. When an object has Altitude=0 degrees, it is either
Rising (if its Azimuth is < 180 degrees) or Setting (if its Azimuth is > 180
degrees).
Coordinate Systems

• zenith:the direction straight up, i.e., directly overhead.
• nadir:the direction diametrically opposite to the zenith.
• horizon:1. the great circle midway between zenith and nadir 2. the
great circle formed by the intersection of the celestial sphere with a
plane perpendicular to the line from an observer to the zenith.
• meridian:the great circle passing through the observer's zenith, and
north and south points on the horizon. It is both a vertical circle and
an hour circle. The observer's meridian is the most important of all
circles of reference.
• vertical circle:any great circle passing through both the observer's
zenith and nadir. Vertical circles receive their name from the fact that
they are perpendicular to the horizon.
• altitude:the angle from the horizon along the vertical circle to the
object.
• azimuth:the angle from the north point of the horizon clockwise to the
foot of the vertical circle through the object.
• transit:when a star crosses the observer's meridian; a.k.a.culminate
Coordinate Systems

• Surveyors generally use a three-dimensional Cartesian system called the
Local Astronomical (LA) coordinates to describe positions in reference to
their own location.
• The origin (0,0,0) corresponds with location of the instrument used to
make surveying measurements on the surface of the Earth: from now on
called the observer's station.
• The x axis (N) points from the origin towards the CTP (north) and is a
tangent with the curvature of the Earth.
• The z axis (U) points away from the surface of the Earth opposite the
direction of gravity towards the observer's zenith. Its negative axis points
in the direction of gravity and the observer's nadir.
• The y axis (E) creates a left-handed Cartesian coordinate system by being
perpendicular to both the x and z axes and pointing east from the
observer's station. This axis is tangent to the curvature of the Earth at the
observer's station.
• Note that unless the observer is at the North Pole, the direction of the U
axis (local astronomical z axis) will not align with the Z axis in the CT
coordinate system.
Coordinate Systems
Celestial Coordinate System: Local Astronomical System

Ellipsoidal and Cartesian Coordinates
Conversion
• The (x,y,z) ECEF cartesian coordinates can be expressed in the
ellipsoidal coordinates λ,φ,h, where λ and φ are, respectively, the
longitude and latitude from the ellipsoid, and h the height above it.
• Figure 1 illustrates the relation between Cartesian and ellipsoidal
coordinates.

Ellipsoidal and Cartesian Coordinates
Conversion

From Ellipsoidal to Cartesian coordinates

From Cartesian to Ellipsoidal coordinates

Reference Frames in GNSS
GPS reference frame WGS-84
• From 1987, GPS uses the World Geodetic System WGS-84,
developed by the US Department of Defense (DoD), which is a
unified terrestrial reference system for position and vector
referencing.
• The GPS broadcast ephemeris are linked to the position of the
satellite antenna phase centre in the WGS-84 reference frame,
thus, the user receiver coordinates will be expressed in the same
ECEF frame.
• The initial implementation of WGS-84 was realized from a set of
more than a thousand terrestrial sites, which coordinates were
derived from Transit observations.
• Successive refinements (which also lead to some adjustments of
the fundamental constants), using more accurate coordinates of
the monitor stations, approximate to some ITRS realizations.
• For instance, realizations WGS84(G730) and WGS84(G873)
correspond to ITRF92 and ITRF94, respectively. The refined
frame WGS84(G1150) was introduced in 2002, which agrees
with ITRF2000 at the centimetre level.

The parameters of the WGS-84 ellipsoid are given in the following table 1:
Table 1: Ellipsoidal parameters WGS-84 (revised in 1997).
GPS reference frame WGS-84

• The GLONASS broadcast ephemeris are given in the
Parametry Zemli 1990 (Parameters of the Earth 1990) (PZ-
90) reference frame.
• As the WGS-84, this is an ECEF frame with a set of
fundamental parameters associated (see table 2 from
[GLONASS ICD, 2008]).
• The determination of a set of parameters to transform the
PZ-90 coordinates to the ITRF97 was the target of the
International GLONASS Experiment (IGEX-98).
• [Boucher and Altamimi, 2001] presents a review of the
IGEX-98 experiment and, as a conclusion, they suggest
the following transformation from (x,y,z) in PZ-90
to (x',y',z') in WGS-84, with a meter level of accuracy.
GLONASS reference frame PZ-90

Following the notation of equation (3) in Transformation between Terrestrial Frames:
the previous transformation (1) is defined by the parameters table:

• According to the GLONASS modernisation plan, the
ephemeris information implementing the PZ-90.02
reference system was updated on all operational
GLONASS satellites from 12:00 to 17:00 UTC,
September 20th., 2007.
• From this time on, the satellites are broadcasting in the
PZ-90.02. This ECEF reference frame is an updated
version of PZ-90, closest to the ITRF2000.
• The transformation from PZ-90.02 to ITRF2000
contains only an origin shift vector, but no rotations
nor scale factor, as it is shown in equation (2)
[Revnivykh, 2007]

• The parameters associated to the PZ-90 and PZ-90.02 are
given in the next table 2 ([GLONASS ICD, 1998] and
[GLONASS ICD, 2008]):

TIME SYSTEMS
• to appreciate the role of time in GPS data analysis it is necessary to
review briefly the various time systems involved, and their
associated time scales.
• Some of th
• ese definitions are standard and inherent to all space positioning
technologies, while others are particular to the GPS system.
• In general there are three different time systems that are used in
space geodesy (KING et al, 1987; LANGLEY, 1991d; SEEBER, 1993)
based on various periodic processes as follows:

TIME SYSTEMS
• Dynamical time
• Atomic time
• Sidereal time
The major types of these systems are shown in Table 1
below.

Time
Time scales - are based on the observation of uniform and repetitive
astronomical or physical phenomena
Time scale - time interval between two consecutive phenomena forms the scale
measure of a particular time scale
Time unit - a certain multiple or fraction of the scale measure
Second – basic time unit
The starting point or origin has to be fixed (eg astronomical event)
Datation – event of reading of the particular time scale
Epoch – datation in astronomy
Absolute time measurement – epoch determination
Relative time measurement – determination of time intervals between two epochs

Dynamical Time
• required to describe the motion of bodies in a particular
reference frame and according to a particular gravitational
theory.
• The most nearly inertial (non-accelerating) reference
frame to which we have access through gravitational
theory has its origin located at the centre-of-mass of the
solar system (the barycentre).
• Dynamical time measured in this system is
called Barycentric Dynamical Time (TDB -- the
abbreviation for this and most other time scales reflects
the French order of the words).
• A clock fixed on the earth will exhibit periodic variations as
large as 1.6 milliseconds with respect to TDB due to the
motion of the earth in the sun's gravitational field.

Dynamical Time
• However, in describing the orbital motion of near-earth
satellites we need not use TDB, nor account for these
relativistic variations, since both the satellite and the
earth itself are subject to essentially the same
perturbations.
• For satellite orbit computations it is common to
use Terrestrial Dynamical Time (TDT), which represents a
uniform time scale for motion within the earth's gravity
field and which has the same rate as that of an atomic
clock on the earth, and is in fact defined by that rate.
• In the terminology of General Relativity, TDB corresponds
to Coordinate Time, and TDT to Proper Time. The
predecessor of TDB was known as Ephemeris Time (ET).

Atomic Time
• The fundamental time scale for all the earth's time-
keeping is International Atomic Time (TAI). It results from
analyses by the Bureau International des Poids et Mesures
(BIPM) in Sèvres, France, of data from atomic frequency
standards (atomic "clocks") in many countries. (Prior to 1
January, 1988, this function was carried out by the Bureau
International de l'Heure (BIH).)
• TAI is a continuous time scale and serves as the practical
definition of TDT, being related to it by: TDT = TAI + 32.184
seconds
• The fundamental unit of TAI (and therefore TDT) is the SI
second, defined as "the duration of 9192631770 periods
of the radiation corresponding to the transition between
two hyperfine levels of the ground state of the cesium 133
atom". The SI day is defined as 86400 seconds and the
Julian Century as 36525 days.

• Because TAI is a continuous time scale, it has one
fundamental problem in practical use:
• the earth's rotation with respect to the sun is slowing down
by a variable amount which averages, at present, about 1
second per year. Thus TAI would eventually become
inconveniently out of synchronisation with the solar day.
• This problem has been overcome by
introducing Coordinated Universal Time (UTC), which
runs at the same rate as TAI, but is incremented by 1
second jumps ( so-called "leap seconds") when
necessary, normally at the end of June or December of
each year.
• During the period mid-1994 to the end of 1995, one
needed to add 29 seconds to UTC clock readings to
obtain time expressed in the TAI scale.
Atomic Time

• The time signals broadcast by the GPS satellites are
synchronised with atomic clocks at the GPS Master
Control Station, in Colorado Springs, Colorado.
• These clocks define GPS Time (GPST), and are in turn
periodically compared with UTC, as realised by the U.S.
Naval Observatory (USNO) in Washington D.C.
• GPST is a continuous measurement of time from an epoch
set to UTC at 0hr on 6 January, 1980 and is often stated in
a number of weeks and seconds from the GPS-Time
epoch. As a result there will be integer-second differences
between the two time scales.
• GPS-Time does not introduce leap seconds and so is
ahead of UTC by an integer number of seconds (10
seconds as of 1 July 1994, 11 seconds at 1 January 1996 ).
GPS Time is steered by the Master Control site to be
within one microsecond (less leap seconds) of UTC.
Atomic Time

• For example, in December 1994 clocks running on GPST
were offset from UTC by 10 seconds. There is therefore
a constant offset of 19 seconds between the GPST and TAI
time scales:
GPST + 19 seconds = TAI
• The GPS Navigation Message contains parameters that
allow the GPS user to compute an estimate of the current
GPS-UTC sub-microsecond difference as well as the number
of leap seconds introduced into UTC since the GPS epoch.
• GPS-Time is derived from the GPS Composite Clock (CC),
consisting of the atomic clocks at each Monitor Station and
all of the GPS SV frequency standards. Each of the current
(Block II) SVs contains two cesium and two rubidium clocks
(Langley 1991).
Atomic Time

• The U. S. Naval Observatory (USNO) monitors the GPS SV
signals. The USNO tracks the GPS SVs daily, gathering
timing data in 130 six-second blocks. These 780-second
data sets include a complete 12.5-minute Navigation
Message, containing a GPS-UTC correction and an
ionospheric model.
• Compared to the USNO Master Clock, a set of some sixty
cesium and from seven to ten hydrogen maser clocks,
these GPS SV data sets are used to provide time steering
data for introduction into the CC at a rate of 10-18
seconds per second squared.
• Each GPS SV signal is transmitted under control of the
atomic clocks in that SV. This space vehicle time (SV-
Time) is monitored and the difference between GPS-
Time and the SV-Time is uploaded into each satellite for
transmission to the user receiver as the SV Clock
Correction data.
Atomic Time

Universal Time and Sidereal Time
• A measure of earth rotation is the angle between a
particular reference meridian of longitude (preferably
the Greenwich meridian) and the meridian of a
celestial body.
• The most common form of solar time is Universal
Time (UT) (not to be confused with UTC, which is an
atomic time scale).
• UT is defined by the Greenwich hour angle (augmented
by 12 hours) of a fictitious sun uniformly orbiting in the
equatorial plane. However, the scale is not uniform
because of oscillations of the earth's rotational axis.
• UT corrected for polar motion is denoted by UT1, and
is otherwise known as Greenwich Mean Time (GMT).
The precise definition of UT1 is complicated because
of the motion both of the celestial equator and the
earth's orbital plane with respect to inertial space,
and the irregularity of the earth's polar motion.

• UT1 is corrected for:
• non-uniformities in the earth’s orbital speed,
• inclination of the earth’s equator with respect to its orbital plane,
• Polar motion
• Defines the actual orientation of the ECEF coordinate system
with respect to space and celestial objects,
• Is the basic time scale for navigation,
• Even with the corrections above, it remains a non-uniform
time scale due to variations in the Earth’s rotation,
• Drifts with respect to atomic time @ ̃several milliseconds
per day and can accumulate to 1 second per year,
• Civil and military time keeping applications require a time
scale with UT1 characteristics but with uniformity of an
atomic timescale – UTC has these characteristics.

• IERS determines when to add or subtract leap seconds to UTC so that the
difference between UTC and UT1 does not exceed 0.9 sec.
• UT1 is derived from the analysis of observations carried out by the IERS, and can
be reconstructed from published corrections (UT1) to UTC:
UT1 = UTC + UT1
• A measure of sidereal time is Greenwich Apparent Sidereal Time (GAST),
defined by the Greenwich hour angle of the intersection of the earth's equator
and the plane of its orbit on the Celestial Sphere (the vernal equinox). Taking
the mean equinox as the reference leads to Greenwich Mean Sidereal Time
(GMST).
• The conversion between mean solar time corrected for polar motion (UT1) and
GAST is through the following relation:
θg =1.0027379093.UT1 + θo + ∆Ψ.cos ε

• Where ∆Ψ is the nutation in longitude, ε is the obliquity of the ecliptic
and θo represents the sidereal time at Greenwich midnight (0hr UT). The
omission of the last term in the above equation permits the GMST to be
determined. θo is represented by a time series:
θo =24110.54841s + 8640184.812866s.To +0.093104s.To
2 6.2s.10-6.To
3
• where To represents the time span expressed in Julian centuries (of 36525
days of 86400 SI seconds) between the reference epoch J2000.0 and the
day of interest (at 0hr UT)

Relationship Between Time Scales

• The Figure above illustrates the relationship between
the various time scales discussed.
• The vertical axis indicates the relative offsets of the
origins of the time scales, and the slope of the lines
indicate their drift.
• Note that with the exception of UT1 (or GAST) all time
scales (nominally) have zero drift as defined by TAI.
Relationship Between Time Scales

TIME SYSTEMS - Summary
• TIME SYSTEMS
• The last concept essential in astronomical positioning is the concept of time. The
hour angle h of the star is the angle between the astronomical meridian of the
star and that of the observer. The local apparent sidereal time (LAST) is the hour
angle of the true vernal equinox. GAST (W) is the hour angle of the true vernal
equinox as seen at Greenwich.
• LAST and GAST can be linked together by the equation: LAST = GAST + LIT
• In practice, GAST is measured through universal time (UT) which differs from
every day standard time by an integral number of hours dependent on the hour
angle. Below are the different version of UT that are used.
• UT reflects the actual non-uniform rotation of the earth. It is affected by polar motion since
local astronomical meridians are slightly displaced.

• UT1, also depicts the non-uniform rotation of the earth, but does not
account for polar motion. UT1 corresponds to GAST and is needed for
transforming the true right ascension (TRA) system to the instantaneous
(IT) system.
• UTC (universal coordinated time) is the broadcast time that represents a
smooth rotation of the earth. (It does not account for propagation delays.)
UTC is kept to within ±0.7s of UT1 by the introduction of leap seconds.
• UT2 is the smoothest time, and has all corrections applied to it.
• International Atomic Time (IAT) is based on an atomic second. To keep IAT
and UT1 close, leap seconds are introduced.

• GPS time is also based on an atomic second. It coincided with UTC
time on January 6, 1980 at 0.0 hours. With the introduction of leap
seconds to IAT, there is now a constant offset of 19 seconds between
GPS time and IAT.
• Relationships in Time Standards
• IAT = GPS + 19.000
• ITS = UTC + 1.000 n where n was 32 in June of 2000.
• UTC = GPS + 13.000

references
• Time Scales in Satellite Geodesy,
http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap2/214time.ht
m#dynamical_time, accessed 31/10/2012, 1815 hrs
• Peter H. Dana, 1997, Global Positioning System (GPS) Time
Dissemination for Real-Time Applications,
http://pdana.com/PHDWWW_files/Rtgps.pdf

Signal propagation
• Signals, on their path between satellites and ground stations, propagate
through atmospheric regions of different nature and variable state
• Signals experience different kinds of influences.
• Perturbations may occur to the direction of propagation, to the velocity
of propagation and to the signal strength.
• The atmosphere introduces unwanted perturbations.
• The impacts on the observational results are, in many cases, much
larger than the accuracy required in satellite geodesy.
• Consequently, atmospheric influences have to be determined directly
by measurements and/or by modeling,

Some Fundamentals of Wave Propagation
Basic Relations and Definitions
• The relation between the wavelength, λ, the frequency, f , and the propagation velocity,v, is:
v = λ · f.
• The relation between frequency and period is:
f = 1/P
• The phase, Φ , of a periodic wave is the fractional part t/ T of the period, P , through which the
time t has advanced with respect to an arbitrary time origin t0
• Furthermore:
ω = 2πf the angular frequency
and
k = 2π/χ the phase constant or wave number

Cont’d
• It follows for the propagation velocity v, that
v = λ · f. = λ/P = ω/k
• A periodic wave which can be modeled by a sinusoidal function in space and time is a
sinusoidal wave. In what follows only waves that are periodic functions in time are
considered:
y = Asin 2π(t/P + Φ0)
where y is the magnitude of the disturbance at time t ; Φ0 is the phase of the wave at t = 0,
and A is the maximum magnitude or the amplitude of the wave. The phase at time t is then
Φ = t/P + Φ0
2πΦ is called the phase angle φ
It follows that
y = Asin(ωt + φ0)

Wave propagation
• the geometrical interpretation of equation

Cont’d
• The wavelengths of electromagnetic waves, and hence their
propagation velocity, depend on certain properties of the medium in
which the waves are propagating. In a vacuum the velocity is:
c = χ/p = fχ
• The value currently in use in satellite geodesy is (McCarthy, 2000)
c = 2.997 924 58 · 108
ms−1 .

Frequency domains
• The frequency spectrum of electromagnetic waves spans nearly 20
orders of magnitude
• In satellite geodesy only two rather small domains are used, namely
the visible light (0.4–0.8 ·1015 Hz) and microwave domains (107 –
1010 Hz).

Spectrum of electromagnetic waves

• Some prefixes and symbols which are commonly used for the
description of frequencies
prefix symbol value prefix symbol value
femto f 10-15 Peta P 1015
pico p 10-12 Tera T 1012
nano n 10-9 Giga G 109
micro μ 10-6 Mega M 106
milli m 10-3 Kilo K 103
centi c 10-2 Hecto H 102

Radar bands
• Different kinds of subdivisions and terminology are in use for
electromagnetic waves.
• In satellite geodesy the subdivision into radar bands is used
• The particular assignments to capital letters were generated in a
random way during World War II.

Radar bands
Denomination Frequency Mean wavelength
P-band 220–300 MHz 115 cm
L-band 1–2 GHz 20 cm
S-band 2–4 GHz 10 cm
C-band 4–8 GHz 5 cm
X-band 8–12.5 GHz 3 cm
Ku-band 12.5–18 GHz 2 cm
K-band 18–26.5 GHz 1.35 cm
Ka-band 26.5–40 GHz 1 cm

Structure and Subdivision of the Atmosphere
• The structure of the atmosphere can be described, as a set of concentric spherical
shells with different physical and chemical properties.
• Various subdivisions are possible,
• With respect to signal propagation a subdivision into troposphere and ionosphere
is advisable, because the particular propagation conditions are quite different.
The troposphere - is the lower part of Earth’s atmosphere which extends from the
surface to about 40 km.
• Signal propagation depends mainly on the water vapor content and on
temperature.
The ionosphere - is the upper part of Earth’s atmosphere between approximately 70
and 1000 km.
• Signal propagation is mainly affected by free charged particles.

Possible subdivision schemes of the earth’s atmosphere

TROPOSPHERE
• The gaseous atmosphere where the daily weather takes place.
• The temperature decreases with height by 6.50 C/km.
• Horizontal temperature gradients are only a few degrees/100 km.
• Charged particles are virtually absent.
• The uncharged atoms and molecules are well mixed, and thus the troposphere is
practically a neutral gas.
• The index of refraction is slightly greater than 1. It decreases with increasing
height and becomes nearly 1 at the upper limit of the troposphere
• Nearly 90% of the atmospheric mass is below 16 km altitude, and nearly 99% is
below 30 km (Lutgens, Tarbuck, 1998).
• The troposphere is not a dispersive medium.
• The index of refraction depends on air pressure, temperature, and water vapor
pressure.
• it is difficult to model the index of refraction.

THE IONOSPHERE
• That part of the high atmosphere where sufficient electrons and ions are
present to affect the propagation of radio waves (Davies, 1990; Langley,
1998b).
• The generation of ions and electrons is proportional to the radiation
intensity of the sun, and to the gas density.
• A diagram indicating the number of ions produced as a function of height
shows a maximum in ion production rate. Such a diagram is called the
Chapman-profile;
• the general behavior of this profile is illustrated below.
• The spatial distribution of electrons and ions is mainly determined by two
processes:

Cont’d
• photo-chemical processes that depend on the insolation of the sun, and govern
the production and de- composition rate of ionized particles, and
• transportation processes that cause a motion of the ionized layers.
• Both processes create different layers of ionized gas at different heights.
• The main layers are known as the D-, E-, F1 -, and F2 -layers. In particular, the F1
-layer, located directly below the F2 -layer, shows large variations that correlate
with the relative sun spot number.
• Geomagnetic influences also play an important role.
• Hence, signal propagation in the ionosphere is severely affected by solar activity,
near the geomagnetic equator, and at high latitudes
• The state of the ionosphere is described by the electron density ne with the unit
[number of electrons/m3 ] or [number of electrons/cm3 ].

Signal Propagation through the Ionosphere and the Troposphere
• Refractivity, N for the troposphere is positive, and independent of the
frequency used.
• For the ionosphere, N is negative, and depends on the frequency.
• The refractivity decreases with increasing frequency.
• One consequence is that higher accuracy can be obtained in
propagation modeling when higher frequencies are used
• Two considerations, however, limit the increase of the selected
frequencies:

Cont’d
− Higher frequencies are technically demanding. The frequency domain
above 10 GHz cannot easily be utilized with existing technology.
− With higher frequencies the atmospheric absorption in the troposphere
increases.
• Without rainfall, the absorption can be neglected for frequencies between 30
• MHz and 30 GHz.
• With precipitation, however, signals in the frequency domain > 1 GHz
experience considerable attenuation.

Effect of the ionospheric propagation delay on range measurements for single-
frequency observations, and residual errors for dual-frequency observations (Hieber,
1983
single-frequency 400 MHz 1600 MHz 2000 MHz 8000 MHz
average effect 50 m 3 m 2 m 0.12 m
for 90% <
maximum effect
250 m
500 m
15 m
30 m
10 m
20 m
0.6 m
1.2 m
dual-frequency 150/400 400/2000 1227/1572 2000/8000
MHz MHz MHz MHz
average effect 0.6 m 0.9 cm 0.3 cm 0.04 cm
for 90% <
maximum effect
10 m
36 m
6.6 cm
22 cm
1.7 cm
4.5 cm
0.21 cm
0.43 cm

Implications
• The selection of frequencies for a particular satellite system is always a
compro- mise.
• This was the case with the TRANSIT system [6] when 150/400 MHz were
selected reflecting the technological progress of the 1960’s.
• And this is true for the GPS system [7] with the selection of 1.2/1.6 GHz.
• Table above gives an impression of how the ionosphere affects the
propagation delay at different frequencies, and it indicates the residual
errors when measurements on two frequencies are available.
• It becomes clear that for the GPS system, operating with two frequencies,
the residual errors are mostly below 1cm.

CHAPTER 3
Satellite Orbital Motion

INTRODUCTION
• Precise time-dependent satellite positions in a suitable reference frame are required for
nearly all tasks in satellite geodesy.
• The computation and prediction of precise satellite orbits, together with appropriate
observations and adjustment techniques is, for example, essential for the determination of
− geocentric coordinates of observation stations,
− field parameters for the description of the terrestrial gravity field as well as for the
determination of a precise and high resolution geoid
− trajectories of land-, sea-, air-, and space-vehicles in real-time navigation
− Earth’s orientation parameters in space.
• Essentially, the accuracy of the final results depends on the accuracy of the available
satellite orbits. The requirement for 1 cm relative accuracy in coordinates implies the
requirement for the knowledge of satellite orbits on the few meter accuracy level or even
better.

Fundamentals of Celestial Mechanics, Two-Body Problem
• In celestial mechanics we are concerned with motions of celestial bodies under the
influence of mutual mass attraction.
• The simplest form is the motion of two bodies (two-body problem).
• For artificial satellites the mass of the smaller body (the satellite) usually can be
neglected compared with the mass of the central body (Earth).
• The two-body problem can be formulated in the following way:
Given at any time the positions and velocities of two particles of known mass
moving under their mutual gravitational force calculate their posi-tions and
velocities at any other time.
• Under the assumption that the bodies are homogeneous and thus generate the
gravitational field of a point mass the orbital motion in the two-body problem can
be described empirically by Kepler’s laws. It can also be derived analytically from
Newtonian mechanics.

Con’td
• To determine positions we need accurate information about
the position of satellites
• It is thus important to understand how GPS orbits are
characterised,
• All positioning of satellites today is based on the laws of
Johannes Kepler who lived in Germany from 1571 to 1630.
• Keplers work was based on observations carried out by the
Danish astronomer Tycho Brahe (1546-1601).
• Kepler developed a number of theorems and laws describing
the motion of the planets in their orbits around the sun.
• These laws do, in general, also describe the motion of a
satellite orbiting around the earth and the laws are therefore
repeated below.

KEPLERS 1st LAW
• The orbit of each planet is an ellipse with the sun in
one of the foci.
Effect on satellites:
• The orbit of a satellite is an ellipse with the gravitational
centre of the earth in one of the foci.
• Referring to Figure 1:
• F are the two foci of the ellipse
• P is perigee, the point on the orbit closest to the earth
• A is apogee, the point on the orbit farthest away from the earth
• a is the semi major axis of the ellipse
• b is the semi minor axis of the ellipse

KEPLERS 2nd LAW: LAW OF AREAS
• The planets revolve with constant area velocity, e.g. the radius vector
of the planet sweeps out equal areas in equal lengths of time,
independent of the location of the planet in the orbit.
Effect on satellites:
• Satellites revolve with a constant area velocity within the orbit. The speed of
the satellite is not constant, but varies with the location of the satellite in the
orbit, so the speed is higher when the satellite is close to the earth (see Figure
2).

KEPLERS 2. LAW
Figure 2. The satellite sweeps out equal areas in the ellipse in equal time intervals while
orbiting

KEPLERS 3rd LAW
• The relation between the square of the period, T, and the cube of the
semi major axis, a, is constant for all planets:
• Effect on satellites:
• Two satellite orbits with the same size of their semi major axes, will have the
same T even if the eccentricities of the orbital ellipses are different (see Figure
3).

KEPLERS 3rd LAW
Figure 3. Two orbits with same size of semi major axis and period, but with different
eccentricity.

KEPLERS 3rd LAW
• The value of the constant given in Equation (1) was determined
several years later by Isac Newton (1624 - 1727) based on his work on
gravity.
• Where GM is the earths gravitational constant of 3986004.418 x 108
m3/s2 (Misra and Enge, 2001)

KEPLERS 3rd LAW
• Keplers three laws would be true for satellites today if
the satellite and the earth were point masses (or
homogeneous bodies with a spherical mass
distribution), and if no other forces than earths gravity
were affecting the satellites.
• This is of course not the case, and the expressions of
satellite motions are therefore more complicated since
we have to account for the variations in the earths
gravity field, and several external forces e.g. lunar gravity
and solar radiation affecting the satellites.

ORBITAL COORDINATES SYSTEM
• In order to describe the motion of a satellite within its orbit, we
define an orbital coordinate system, called q.
• The axis of the coordinate system are defined so that:
• the origin is located in the mass center of the earth,
• the first axis, q1, is directed towards perigee,
• the second axis, q2, is located in the orbital plane, perpendicular to the first
axis in the direction of the satellite motion, and
• the third axis, q3, is perpendicular to both first and second axis to form a right
hand system.
• In Figure 4 the q3 axis is thus pointing out of the plot towards the
reader.

Figure 4. Elements of the orbital coordinate system, q.

• Further, in order to described the location of the satellite
within the orbital coordinate system we need to define a
number of parameters for the orbital ellipse (Figures 4
and 5):

Figure 5. Parameters for describing the location of a satellite in the orbital coordinate
system, q. Figure inspired by Kaula (1969).

CONTD
• The position of the satellite for a given epoch in time is given as:
• The q3 coordinate is zero, since the coordinate system is defined so
the q3-axis is perpendicular to the orbital plane. The satellite motion
is, according to the laws of Kepler, a 2D motion within the q
coordinate system.

CONTD
• Equation (3) can also be given as:
• where the satellite motion is described using the eccentric
anomaly as the angular variable.
• The eccentric anomaly, E and the true anomaly, are two
different angles, both indicating the satellite position in the
orbit as a function of time.
• Depending on the use of the expressions, and the variables
given, one expression is usually preferable to the other

The expressions given in equation (3) and (4) are solutions to the
basic equation of motion in a force field, Equation (10), which is a
second order non-linear differential equation.

CONVENTIONAL INERTIAL REFERENCE
SYSTEM (CIS)
• Having defined a coordinate system for describing the
motion of a satellite within its orbit, we now need a
relation between the orbital coordinate system and the
coordinate systems we use for referencing of the
positions on the surface of the earth (e.g., WGS84) in
order to use the satellites for positioning on the surface
of the earth.
• The Conventional Inertial System (CIS) is necessary as an
intermediate step in this conversion. The CIS is used for
positioning and orientation of the earth in space and is
defined by orienting the axes towards distant quasars.

CONVENTIONAL INERTIAL REFERENCE
SYSTEM (CIS)
• The Conventional Inertial System (CIS) is defined with:
• the origin coinciding with the center of mass of the earth.
• The third axis, Z, is defined to be coinciding with the
rotational axis of earth rotation,
• the first axis, X, is located in the equatorial plane towards the
vernal equinox, and finally
• the second axis, Y, is located in the equatorial plane to
complete a right handed cartesian coordinate system.

Figure 6. Coordinate axes of the inertial reference system.

• The vernal equinox is the point in space where the equatorial plane of
the earth intersects with the ecliptic (the plane of the earth and the
sun) in the spring time. I.e. the direction to the sun as seen from the
earth when the sun is moving from the southern to the northern
hemisphere. The point is also called the spring equinox.
• the CIS does not rotate with the earth, this property makes it
convenient for positioning of satellites.

• Since the mass distribution of the earth is not
homogenous, the rotational axis of the earth is time
variant, and the motion of the axis is composed of two
periodic movements called precession and nutation.
• Precession is caused by gravitational attraction of the
sun, the moon and other celestrial objects, and it
causes the spin axis to move in a slow circular motion
like a top.
• Nutation is a smaller movement with a shorter period
superimposed on the precession.
• The axis of the CIS are thus not constant in time, and
when converting positions from the inertial reference
system to an earth fixed system as for instance the
WGS84, this motion must be taken into consideration.

CONVERSION OF SATELLITES POSITIONS BETWEEN
ORBITAL SYSTEM AND CIS
• The CIS and the orbital coordinate system both have the center of
mass of the earth as origin. This means that conversion of coordinates
from one system to the other does not include translations, but only
rotations of the coordinate axes with respect to each other.
• The three rotation angles are given in the inertial reference system,
they are shown in Figure 7 and are denoted as:

• Ω - right ascension of the ascending node. The angle between the first axis
of the CIS, and the vector in the CIS pointing from origo to the point in the
Equatorial plane where the orbital plane intersects with the Equatorial
plane. This point is denoted the ascending node, and the right ascension of
the ascending node identifies the point where the satellite moves from the
southern hemisphere of the earth to the northern hemisphere.
• i - is called the inclination, and is the inclination angle of the orbital plane
with respect to the Equatorial plane.
• ω- is the argument of perigee. The angle between the position vector of
the ascending node and the position vector of the satellite at the current
epoch in time.

• Coordinates of the satellite position as given in the orbit coordinate
system can now be converted to coordinates in the inertial reference
system by rotating about the first and the third axis of the CIS, using
the three rotation angles; Ω, i, and ω , and corresponding rotation
matrices.

Figure 7. Rotation angles between orbital and inertial coordinate systems.

KEPLER ELEMENTS
• the parameters we need for describing the satellite
orbit and its relation to the inertial reference system
are the following six variables, which are normally
referred to as the Kepler Elements
• Satellite orbit size and shape:
• a – semi major axis
• e - eccentricity
• Location of orbit in the inertial reference system:
• i - inclination
• Ω– right ascension of the ascending node
• ω – argument of perigee
• Further, to describe the location of a satellite in its orbit, we
need:
• ν– true anomaly
• or
• E - eccentric anomaly

Perturbed Satellite Motion
• The satellite motion is affected by external forces dragging and pushing the
satellite from the theoretically smooth orbit
• The most important perturbing effect is, however, caused by variations in
earths gravity field.
• The earth is not a point mass and the mass is not homogeneously distributed
inside the earth.
• The deviation of the gravity field from a central sphere, and the variations in
the earth gravity field as a function of the distribution of masses inside the
earth are well modeled today, mainly because of many years of studies of
satellite orbit perturbations, but also because of a very dense network of
gravity reference stations on the surface of the earth, where gravity is
measured precisely at regular intervals.
• The models of the earths gravity field are therefore also used to model the
effect of the satellite orbits.

Perturbed Satellite Motion
• The non-spherical and non-central gravity field causes a rotation of the
orbital plane within the inertial coordinate system.
• The gravity field basically tries to drag the satellite orbit into the
equatorial plane.
• The effect on the Kepler elements, describing the size, shape and
location of the satellite orbit, is rather large, and must be considered
when dealing with real satellite positions.
• The effect is larger for satellites located in orbits close to the surface of
the earth, the so-called LEO satellites (low earth orbiters).

• Other forces affecting the satellite motion are:
• gravitational effects of the sun and the moon,
• solar radiation pressure,
• albedo (reflection of solar light from the surface of the earth back into space),
• effects of earth and ocean tides,
• radiation from space,
• atmospheric drag etc.

Perturbing forces
• Perturbing forces are in particular responsible for:
1. Accelerations due to the non-spherically and inhomogeneous mass distribution within
Earth (central body), r¨ E .
2. Accelerations due to other celestial bodies (Sun, Moon and planets), mainly r¨ S , r¨ M .
3. Accelerations due to Earth and oceanic tides, r¨ e , r¨ o .
4. Accelerations due to atmospheric drag, r¨ D .
5. Accelerations due to direct and Earth-reflected solar radiation pressure, r¨ SP , r¨ A .
• The perturbing forces causing 1 to 3 are gravitational in nature; the remaining forces are
non-gravitational. The total is:
ks = rË + r¨S + r¨M + rë + rö + r¨D + r¨SP + r A .

Perturbing forces acting on a satellite
sun
moon
O
orbit rA
Earth
satellite
rE, rO
rM
rSP
rD
rS

Implications of perturbations on GPS satellite orbit. From Seeber (2003)
Perturbation Effect on satellite
acceleration m /
S2
Deviation of earth gravity field
from a sphere
Variations in earth gravity field
Solar and lunar gravitation
Earth and ocean tides
Solar radiation pressure
Albedo
5 · 10-5
3 · 10-7
5 · 10-6
1 · 10-9 each
1 · 10-7
1 · 10-9

CHAPTER 4
Basic Observation Concepts and Satellites
Used in Geodesy

Satellite Geodesy as a Parameter Estimation Problem
• The fundamental equation of satellite geodesy can be formulated as:
r S (t ) = r B (t ) + ρ(t )
or
rj (t ) = r i (t ) + ,r ij (t ).

Basic relations for satellite observations
ri
rij
Bi
Sj
Y
X
Z
rj

Observation Concepts
• For a solution to equation above we have to establish a relation
between the observations, characterized by:
• the vector, r ij (t ),
• the parameters which describe the satellite position rj (t ),
• the location of the observation station r i (t ).
• In the estimation process either all parameters can be treated as
unknowns, or some of the parameters are considered to be known, in
order to stabilize and to simplify the solution.

Classification of parameters
• The parameters in the equation can be subdivided into different groups, for
instance into:
(1) Parameters describing the geocentric motion of the observation station rB(t ).
• The first of these are the geocentric station coordinates.
• Then there are geo-dynamic parameters, describing the relation between the Earth-fixed
terrestrial reference system and the space-fixed inertial reference system, namely the polar
motion and Earth rotation parameters.
• Also belonging to this group are the parameters used for the modeling of solid Earth tides
and tectonic crustal deformations.
• Finally, the transformation parameters between geocentric and particular geodetic or
topocentric reference frames may be considered.

Classification of parameters
(2) Parameters describing the satellite motion r s (t ).
• The satellite coordinates,
• the harmonic coefficients of Earth’s gravity field,
• parameters describing other gravitational or non-gravitational perturbations,
like the solar radiation pressure.
(3) Parameters influencing directly the observations ρ(t ).
• atmospheric parameters,
• clock parameters,
• signal propagation delays.

Observables and Basic Concepts
• The observation techniques used in satellite geodesy can be
subdivided in different ways. One possibility has been already
introduced, namely a classification determined by the location of the
observation platform
− Earth based techniques (ground station → satellite),
− satellite based techniques (satellite → ground station),
− inter-satellite techniques (satellite → satellite).
• Another classification follows from the observables in question.
• A graphical overview is given below.

Overview of observation techniques in Satellite Geodesy

Determination of Directions
• Photographical methods are almost exclusively used for the determination of
directions.
• An artificial satellite which is illuminated by sunlight, by laser pulses, or by some
internal flashing device, is photographed from the ground, together with the
background stars.
• The observation station must be located in sufficient darkness on the night side of
Earth.
• The stars and the satellite trajectory form images on a photographic plate or film
in a suitable tracking camera, or on a CCD sensor.
• The photogram provides rectangular coordinates of stars and satellite positions in
the image plane, which can be transformed into topocentric directions between the
observation station and the satellite, expressed in the reference system of the star
catalog (equatorial system, CIS).

Determination of Directions
• Two directions, measured at the same epoch from the endpoints of a
given baseline between observing stations, define a plane in space
whose orientation can be determined from the direction cosines of the
rays.
• This plane contains the two ground- stations and the simultaneously
observed satellite position.
• The intersection of two or more such planes, defined by different
satellite positions, yields the inter-station vector between the two
participating ground stations.

The use of directions with satellite cameras

Determination of Ranges
• For the determination of distances in satellite geodesy the propagation
time of an electromagnetic signal between a ground station and a
satellite is measured.
• According to the specific portion of the electromagnetic spectrum we
distinguish between optical systems and radar systems
• Optical systems are weather-dependent. Laser light is used
exclusively, in order to achieve the required signal strength and
quality.
• Radar systems are weather- independent; wavelengths of the
centimeter and decimeter domain are used. The propagation behavior,
however, is significantly affected by atmospheric refraction.

Determination of ranges
• We distinguish the one-way mode and the two-way mode.
• In the two-way mode the signal propagation time is measured by the
observer’s clock.
• The transmitter at the observation station emits an impulse at epoch tj . The
impulse is reflected by the satellite at epoch tj +Δ tj, and returns to the
observation station where it is received at epoch tj + Δtj
• The basic observable is the total signal propagation time ,tj .
• In the one-way mode we assume that either the clocks in the satellite and in
the ground receiver are synchronized with each other, or that a remaining
synchronization error can be determined through the observation technique.
This is, for instance, the case with the Global Positioning System (GPS).
j

• Further we distinguish between either impulse or phase comparison methods.
• When a clear impulse can be identified, as is the case in satellite laser ranging,
the distance is calculated from the signal propagation time
• phase comparison method, the phase of the carrier wave is used as the
observable.
• In the two-way mode the phase of the outgoing wave is compared with the phase
of the incoming wave.
• In the one-way mode the phase of the incoming wave is compared with the
phase of a reference signal generated within the receiver.
• In both cases the observed phase difference, corresponds to the residual portion,
,λ, of a complete wavelength.
• The total number, N , of complete waves between the observer and the satellite
is at first unknown. This is the ambiguity problem.

• Different methods are used for the solution of the ambiguity term N ,
for example:
− measurements with different frequencies (e.g. SECOR),
− determination of approximate ranges with an accuracy better
than λ/2 (e.g. GPS with code and carrier phases),
− use of the changing satellite geometry with time (e.g. GPS
carrier phase observations),
− ambiguity search functions (e.g. GPS).

Determination of Range Differences (Doppler method)
• The range differences are derived from the measurement of the
frequency shift caused by the change of range between the observer
and the satellite during a given satellite pass.
• The satellite transmits a signal of known frequency fs which is
tracked by a ground receiver. The relative motion d s/d t between the
receiver and the transmitter causes the received frequency fr (t ) to
vary with time
• This is the well-known Doppler effect.
• The frequency shift in a given time interval tj , tk is observed, and is
scaled into a range difference ,rij k

Doppler effect
• The observation of the Doppler effect is frequently used in satellite geodesy.
• The technique is always applicable when a satellite, or a ground-beacon,
transmits on a stable frequency.
• The orbital elements of the very first satellites were determined by observing the
Doppler-shift of the satellite signals.
• The most important application of the Doppler method in geodesy has been with
the Navy Navigation Satellite System (TRANSIT).
• A current space system based on the Doppler technique is DORIS
• The Doppler effect can also be used for the high precision determination of range
rates |,r˙jk | between satellites.
• This method is named Satellite-to-Satellite Tracking (SST), and it can be applied to
the mapping of a high resolution Earth gravity field.

Satellite Altimetry
• Altimetry is a technique for measuring height,
• Satellite altimetry was the first operational satellite-borne observation
technique in satellite geodesy.
• Satellite radar altimetry measures the time taken by a radar pulse to
travel from the satellite antenna to the surface and back to the
satellite receiver,
• The altimeter emits a radar wave and analyses the return signal that
bounces off the surface
• Surface height is the difference between the satellite’s position on
orbit w.r.t an arbitrary reference surface (the Earth’s center or the
Earth’s ellipsoid)
• We can also measure wave height and wind speed over the oceans,
backscatter coefficient and surface roughness for most surfaces off
which the signal is reflected, by looking at the return signal’s amplitude
and waveform

Satellite Altimetry
• Altimetry satellites are able to measure the distance between
the satellite and the surface of the Earth.
• This distance is called range.
• Altimetry satellites transmit a radar signal to the Earth.
• This signal is reflected by the Earth's surface and the satellite
receives the reflected signal.
• The time elapsed between transmission and reception of the
radar signal is the key parameter in calculating the distance
between the satellite and the ground surface.

Satellite Altimetry
• Precise orbit altitude is needed to calculate the range.
• The SENTINEL-3 instruments, GNSS and DORIS, retrieve the orbit
altitude.
• The orbit altitude is the distance between the satellite and an
arbitrary reference surface (the reference ellipsoid or the geoid).
• The scientific community is usually interested in the surface
height in relation to this reference surface (the reference ellipsoid
or the geoid) instead of being referenced to the position of the
satellite.

Satellite Altimetry
• The surface height can be approximately derived from range and
altitude using the following equation:
Surface Height = Altitude - Range
• The complete calculation of surface height should also include all
corrections due to environmental conditions.
• Examples of these corrections are atmospheric propagation
corrections (ionosphere and troposphere) and geophysical
corrections (tides and atmospheric pressure loading).
• satellite altimetry can be used to determine the geoid over the
oceans.

Satellite altimetry
MSL (geoid)
M
A
MSL (geoid)
H

Interferometric Measurements
• The basic principle of interferometric observations is shown in Fig.
below.
• A1 and A2 are antennas for the signal reception.
• When the distance to the satellite S is very large compared with the
baseline length b, the directions to S from A1 and A2 can be
considered to be parallel.
• From geometric relations we obtain
d = b.cosθ

Interferometric measurements
P
A2
A1
d
b
χ
S
S
θ

• If λ is the wavelength of a continuous signal from the satellite, then the
phase difference Φ, caused by the range difference d , can be observed
at both antennas.
• The observed phase difference is uniquely determined only as a frac-
tion of one wavelength; a certain multiple, N , of whole wavelengths
has to be added in order to transform the observed phase difference
into the range difference d .
• The basic interferometric observation equation is hence
d = b · cos θ = 1/2π λ + Nλ.

• The interferometric principle can be realized through observation techniques in
very different ways.
− the baseline length b between the two antennas,
− the residual distance d between the antenna and the satellite, and
− the angle θ between the antenna baseline and the satellite.
• In each case it is necessary to know, or to determine, the integer ambiguity term
N .
• The determination is possible through a particular configuration of the ground
antennas, through observations at different frequencies, or through well defined
observation strategies.
• With increasing baseline lengths the antennas cannot be connected directly with
cables.
• The phase comparison between the antennas must then be supported by the use
of very precise oscillators (atomic frequency standards).
• This is, for instance, the case with the Very Long Baseline Interferometry (VLBI)
concept.

• When artificial Earth satellites are used in the VLBI technique, it cannot be
assumed that the directions from the antennas to the satellites are parallel.
• Instead, the real geometry has to be introduced by geometric corrections;
• The interferometric principle has been widely used in the geodetic application of
the GPS signals.
(a) The signals from the GPS satellites can be recorded at both antenna sites
without any a priori knowledge of the signal structure, and later correlated for
the determination of the time delay τ .It is used to some extent in modern GPS
receiver technology, in order to access the full wavelength of L2 under “Anti-
Spoofing” (A-S) conditions.
(b) The phase of the carrier signal at both antenna sites can be compared, and the
difference formed.
• These so-called single phase differences can be treated as the primary
observables.
• The method is now widely used for processing GPS observations

Very Long Baseline Interferometry
• the most accurate of all the extraterrestrial positioning
techniques.
• initially developed by astronomers as a tool to improve the
resolution of radio telescopes, but even before the first
successful tests of the concept in 1967, it was realized that it
would be an ideal geodetic instrument.
• uses the principle of wave interference.
• Signals from a radio source, usually the random noise signals
of a quasar or other compact extragalactic object, are
received at the antennas of two or more radio telescopes.

Very Long Baseline Interferometry
• These signals are amplified and translated to a lower
frequency band under control of a hydrogen maser frequency
standard.
• The translated signals are digitized, time-tagged, and recorded
on wide bandwidth magnetic tape. Subsequently the tape
recordings are played back at a central processing site.
• The processor is a computer-controlled cross-correlator which
delays and multiplies the signals from the tapes recorded at a
pair of radio telescopes.
• The output of the processor is a sampled cross-correlation
function equivalent to the fringes of Young's experiment.

Very long baseline interferometry
• The primary observable of geodetic VLBI is the group delay,
the difference in arrival times of the quasar signal wave
fronts at the radio telescopes.
• In principle, the delay can be measured in the correlation
process by noting the time offset between a pair of tape
recordings required to achieve maximum correlation.
• The phase (delay) of the correlation function and its time
rate of change, the delay rate, are also measured.
• In practice, the group delay is obtained from measurements
of the phase delay at different frequencies.

• The primary component of the measured group delays is the
geometric delay,
• where B is the baseline vector connecting two radio telescopes, S
is the unit vector in the direction of the radio source, and c is the
speed of light.
• From observations of a dozen or more radio sources during a
nominal 24-hour session, the three components of the baseline
vector can be retrieved.
• A number of biases in the data must be carefully measured or
modelled.

Basic principle of VLBI Geometrical relationship
for VLBI

Applications of VLBI
• The accuracy of the celestial reference system, for modern needs
was achieved with the astrometric satellite mission HIPPARCOS
(Kovalevsky et al., 1997), and Very Long Baseline Interferometry
(VLBI).
• On January 1, 1988 the International Earth Rotation Service
(IERS) took over the task of determining Earth rotation
parameters. The principle observation techniques used are laser
ranging to satellites and to the Moon and Very Long Baseline
Interferometry.

Applications of VLBI
• the main contributions of VLBI to space geodesy are:
• to establish and maintain the International Celestial Reference Frame (ICRF),
• to establish and maintain the International Terrestrial Reference Frame (ITRF),
• to establish and maintain the time dependent Earth Orientation Parameters (EOP)
that relate the ITRF to the ICRF.
• VLBI is unique in that it is the only technique for establishing and
maintaining the ICRF, and the relationship between the ITRF and the
ICRF, by directly monitoring the nutation parameters and UT1.
• As well as this, it is the only geodetic space technique that contributes
to all three of the above mentioned items. Other advantages, when
compared with satellite techniques, come from the fact that VLBI is
independent of the gravity field. As a consequence (Drewes, 2000):
• VLBI is not affected by satellite orbit errors caused by gravity field mismodeling,
• VLBI is not influenced by variations of the geocenter, and
• VLBI is independent of the uncertainty of the GM value and hence of the related
scale problems.
• Compared with satellite laser ranging, VLBI has the advantage of being
weather independent.

Disadvantages of VLBI
• VLBI is a rather expensive technology, hence only a limited number
of telescopes is available,
• instrumental errors, like telescope deformation, are difficult to
handle,
• results are not yet available in real-time.
• VLBI also does not provide absolute coordinates with respect to
the geocenter, but baselines between stations or relative
coordinates with respect to some arbitrarily selected origin.
• Due to the high efficiency of modern satellite techniques like GPS,
the VLBI technology is not used for operational positioning in
geodesy and geodynamics.
• VLBI, due to its unique capacities, will however remain the primary
geodetic technique for maintaining the fundamental reference
frames and their inter-relationship.

Images of associated telescopes
Transportable 6-mVLBI telescope
20-m VLBI telescope

Satellites Used in Geodesy
• Most of the satellites which have been used, and still are used, in
satellite geodesy were not dedicated to the solution of geodetic
problems; their primary goals are various.
• Typical examples of this group are the navigation satellites of the
TRANSIT and of the GPS systems, and remote sensing (Earth
observation) satellites carrying a radar altimeter.
• Examples of satellites which were exclusively, or primarily, launched
for geodetic and/or geodynamic purposes are:

• PAGEOS (PAssive GEOdetic Satellite) USA 1966,
• STARLETTE, STELLA France 1975, 1993,
• GEOS-1 to 3 (GEOdetic Satellite 1 to 3) USA 1965, 1968, 1975,
• LAGEOS-1, 2(LAser GEOdynamic Satellite) USA 1976, 1992,
• AJISAI (EGS, Experimental Geodetic Satellite) Japan 1986,
• GFZ-1 (GeoForschungs Zentrum) Germany 1986,
• CHAMP (CHAllenging Mini Satellite Payload) Germany 2000.

• A frequently used distinction for the purposes of subdivision is passive
and active satellites.
• Passive satellites are exclusively used as targets. They have no
“active” electronic elements, and are independent of any power supply.
Their lifetime is usually extremely long.
• Active satellites in most cases carry various subsystems like sensors,
transmitters, receivers, computers and have a rather limited lifetime.
Table below gives an overview of the most important satellites that are
in use, or have been used, in satellite geodesy.

PASSIVE SATELLITES ACTIVE SATELLITES
ECHO-1 ETALON-1 ANNA-1B ERS-2
ECHO-2 ETALON-2 GEOS-3 TOPEX/POSEIDON
PAGEOS GFZ-1 SEASAT-1 GFO (Geosat Follow On)
STARLETTE NNSS satellites CHAMP
STELLA NAVSTAR satellites JASON
LAGEOS-1 GLONASS satellites ENVISAT
LAGEOS-2 GEOSAT GRACE
EGS (AJISAI) ERS-1

• Another possible subdivision is into:
− Geodetic Satellites,
− Earth Sensing Satellites,
− Positioning Satellites, and
− Experimental Satellites.
Geodetic satellites are mainly high targets like LAGEOS, STARLETTE, STELLA,
ETALON, ASIJAI, and GFZ which carry laser retro-reflectors.
They are massive spheres designed solely to reflect laser light back to the
ranging system. The orbits can be computed very accurately, because the
non-gravitational forces are minimized.

• Earth sensing satellites like ERS, GFO, TOPEX, JASON, ENVISAT carry
instruments designed to sense Earth, in particular to monitor
environmental changes. Many of these satellites carry altimeters. The
satellites are rather large with irregular shape, hence drag and solar
radiation forces are also large and difficult to model
• Positioning satellites are equipped with navigation payload. To this class
belong the former TRANSIT, GPS, GLONASS, and future GALILEO satellites.
Some of the spacecraft carry laser reflectors (e.g. GPS-35, -36, and all
GLONASS satellites).
• Experimental satellites support missions with experimental character. They
are used in the development of various other kinds of satellites, to test
their performance in real space operations.

The Doppler effect
• discovered by Christian Doppler a nineteenth century
Austrian physicist,
• is familiar to anyone who has waited patiently at a railway level
crossing for a train to pass. The pitch of the train's horm or whistle
changes as the train passes. It starts out high, changing
imperceptibly as the train approaches, then drops noticeably as the
train goes through the crossing, and maintains a lower pitch as the
train recedes in the distance.
• This same phenomenon which is so readily apparent at audio
frequencies also affects electromagnetic waves.
• The frequencies of both radio and light waves are shifted if
the source (transmitter) and the observer (receiver) are in
relative motion.

The Doppler effect
• The classical explanation of the effect is that the observer receives
more wave crests per second, i.e., the frequency is increased if the
source and the observer are moving closer together, whereas
fewer wave crests per second are received, i.e., the frequency is
decreased, if the source and the observer are moving farther
apart.
• If the relative speed of the source and observer is much less than
the speed of light, then the received frequency is given
approximately as
•
• where fs is the frequency at the source, c is the speed of light, and
S the distance or range between the source and the observer;
dS/dt is the range rate.

The Doppler effect
• Returning to the train at the level crossing, the closer you are to
the track, the faster the change in pitch of the horn. And even if
you could not see or feel the train, you can tell when it passes the
crossing (the point of closest approach) by noting the instant when
the pitch of the horn is mid-way between the high and low
extremes (fs).
• Therefore by monitoring the frequency of the received sound as
the train passes and knowing its assumed constant speed, you can
establish your position in a two-dimensional coordinate system
where the x-axis, say, runs along the track and they-axis runs
perpendicular to it.
• The origin may be assigned arbitrarily. This is the principle of
Doppler positioning.

The Doppler effect
• In the case of a Transit satellite (or any other satellite for that
matter), the position of a receiver can be established by
continuously recording the Doppler shift of the received signals (or
the number of cycles of the Doppler frequency which is a more
precisely obtained observable).
• Subsequently these data are combined with accurate coordinates of
the satellite to determine the position of the receiver.
• As with the passage of a train, a single satellite pass can provide at
most only two coordinates of the receiver's position.
• Whereas this may be satisfactory for navigation at sea where the
height above the reference ellipsoid is approximately known, three-
dimensional positioning requires observing multiple satellite
passes.

The Doppler effect
• The approximate frequency of a received satellite radio signal (ignoring
relativistic effects) is given by
• fr ≈ fs (1 - 1/c dS/dt) ,
• where fs is the frequency of the signal measured at the satellite, cis the
speed of light, and dS/dt is the range rate.
• The Doppler shift frequency, fr - fs, is approximately proportional to the
range rate, the component of the satellite‘s velocity vector along the line of
sight from the receiver.
• The maximum range rate of a Transit satellite is about 7.4 km/s implying a
maximum Doppler shift when the satellite rises or sets of 25 ppm of the
transmitted frequency.
• This corresponds to 8.4 kHz at a frequency of 400 MHz.

The Doppler effect
• The Doppler shifts may be measured by differencing the received
frequencies from constant reference frequencies in the receiver.
• For most Transit receivers, these frequencies are 400 MHz and 150 MHz
precisely. The satellite transmitter frequencies are approximately 80 ppm
lower than the receiver reference frequencies in order that the Doppler
shift does not go through zero.
• If the transmitter frequencies were not offset, the receiver would have
difficulty distinguishing between positive and negative Doppler shifts.
• A record of the Doppler shift of a Transit signal during a typical pass is
shown in the upper part of this figure.
• The point of closest approach of the satellite, when the Doppler shift is
zero, occurred 6 minutes after the receiver locked onto the signal.

The Doppler effect
• Most Transit Doppler receivers count the number of accumulated
cycles of the Doppler frequency (actually, f0 - fr) rather than measure
the instantaneous Doppler frequency itself, since counting cycles can
be carried out more precisely than measuring the instantaneous
frequency. The counter is read out at intervals and the data stored.
The counter is reset either after each two minute paragraph or at the
end of the pass. Sequential differences in counter readings actually
constitute a series of biased range differences.
• The curves in this figure are based on actual data collected from
Oscar 19 by a Canadian Marconi CMA-722B receiver near Ottawa,
Canada, on 30 July 1983. ·

CHAPTER 6
THE GLOBAL POSITIONING SYSTEM
(GPS)

What is GPS?
• Official name of GPS is NAVigational Satellite Timing And Ranging Global
Positioning System (NAVSTAR GPS)
• Global Positioning Systems (GPS) is a form of Global Navigation Satellite
System (GNSS):
• GPS - USA
• GLONASS – Russian
• GALELIO – European Union
• BeiDou/CAMPSS – Chinese
• QZSS - Japanese
• Developed by the United States of
America Department of Defense (USA DoD)

What is GPS?
• The Global Positioning System (GPS) was designed for military applications.
• Its primary purpose was to allow soldiers to keep track of their position and
to assist in guiding weapons to their targets.
• The satellites were built by Rockwell International and were launched by
the U.S. Air Force.
• The entire system is funded by the U.S. government and controlled by the
U.S. Department of Defense.
• The total cost for implementing the system was over $12 billion
• It costs about $750 million to manage and maintain the system per year

History of GPS
• Initiated by U.S. Department of Defense
• Military planners wanted a technology where a position could be
obtained without the use of radio transmissions
• Feasibility studies begun in 1960’s.
• Pentagon appropriates funding in 1973.
• First satellite launched in 1978.
• System declared fully operational in April, 1995.
• Open to the public, 2000.

How does GPS work?
 Stations on earth, and a GPS
receiver, the distances between
each of these points can be
calculated.
 The distance is calculated based
on the amount of time it takes for
a radio signal to travel between
these points.
 Using satellites in the sky,
ground allows the GPS receiver
to know where you are, in terms
of latitude and longitude, on the
earth.
 The more satellites the GPSr can “see”, the more accurate your
reading.
 The GPSr must “see” the satellites, so it does not work well in dense
forests, inside caves, underwater, or inside buildings.

GPS SEGMENTS
GPS is made up of 3 segments
• Space Segment (SS)
• Control Segment (CS)
• User Segment (US)

Control Segment
Space Segment
User Segment
Three Segments of the GPS
Monitor Stations
Ground
Antennas
Master Station

Space Segment
• Satellite constellation consist of 24 satellites
• 21 satellite vehicles
• 3 spare satellite
• GPS satellites fly in circular orbits at an altitude of 20,200 km
• Orbital period of 11 hrs. 55 mins.
• Powered by solar cells, the satellites continuously orient
themselves to point their solar panels toward the sun and their
antenna toward the earth.
• Orbital planes are centered on the Earth
• Each planes has about 55° tilt relative to Earth's equator in order
to cover the polar regions.

Space Segment (Continued)
• Each satellite makes two complete orbits each
sidereal day.
• Sidereal - Time it takes for the Earth to turn 360 degrees in
its rotation
• It passes over the same location on Earth once each
day.
• Orbits are designed so that at the very least, six
satellites are always within line of sight from any
location on the planet.

Space Segment (Continued)
• Redundancy is used by the additional satellites to
improve the precision of GPS receiver calculations.
• A non-uniform arrangement improves the reliability
and availability of the system over that of a uniform
system, when multiple satellites fail
• This is possible due to the number of satellites in the
air today

GPS Satellite Vehicle
• Four atomic clocks
• Three nickel-cadmium batteries
• Two solar panels
• Battery charging
• Power generation
• 1136 watts
• S band antenna—satellite control
• 12 element L band antenna—user
communication
Block IIF satellite vehicle (fourth
generation)

GPS Satellite Vehicle
• Weight
• 2370 pounds
• Height
• 16.25 feet
• Width
• 38.025 feet including
wing span
• Design life—10 years
Block IIR satellite vehicle
assembly at Lockheed
Martin, Valley Forge, PA

Control Segment
• The CS consists of 3 entities:
• Master Control System
• Monitor Stations
• Ground Antennas

Kwajalein Atoll
US Space Command
Control Segment
Hawaii
Ascension
Is.
Diego Garcia
Cape Canaveral
Ground Antenna
Master Control Station Monitor Station

Master Control Station
• The master control station, located at Falcon Air Force
Base in Colorado Springs, Colorado, is responsible for
overall management of the remote monitoring and
transmission sites.
• GPS ephemeris is the tabulation of computed
positions, velocities and derived right ascension and
declination of GPS satellites at specific times for
eventual upload to GPS satellites.

Monitor Stations
• Six monitor stations are located at Falcon Air Force
Base in Colorado, Cape Canaveral, Florida, Hawaii,
Ascension Island in the Atlantic Ocean, Diego Garcia
Atoll in the Indian Ocean, and Kwajalein Island in the
South Pacific Ocean.
• Each of the monitor stations checks the exact altitude,
position, speed, and overall health of the orbiting
satellites.

Monitor Stations (continued)
• The control segment uses measurements collected by
the monitor stations to predict the behavior of each
satellite's orbit and clock.
• The prediction data is up-linked, or transmitted, to
the satellites for transmission back to the users.
• The control segment also ensures that the GPS
satellite orbits and clocks remain within acceptable
limits. A station can track up to 11 satellites at a time.

Monitor Stations (continued)
• This "check-up" is performed twice a day, by each
station, as the satellites complete their journeys
around the earth.
• Variations such as those caused by the gravity of the
moon, sun and the pressure of solar radiation, are
passed along to the master control station.

Ground Antennas
• Ground antennas monitor and track the satellites
from horizon to horizon.
• They also transmit correction information to
individual satellites.

User Segment
• The user's GPS receiver is the US of the GPS system.
• GPS receivers are generally composed of an antenna,
tuned to the frequencies transmitted by the satellites,
receiver-processors, and a highly-stable clock,
commonly a crystal oscillator).
• They can also include a display for showing location
and speed information to the user.
• A receiver is often described by its number of
channels this signifies how many satellites it can
monitor simultaneously. As of recent, receivers
usually have between twelve and twenty channels.

User Segment (continued)
• Using the RTCM SC-104 format, GPS receivers may
include an input for differential corrections.
• This is typically in the form of a RS-232 port at 4,800 bps
speed. Data is actually sent at a much lower rate, which
limits the accuracy of the signal sent using RTCM.
• Receivers with internal DGPS receivers are able to
outclass those using external RTCM data.

Trilateration
• GPS can be compared to trilateration.
• Both techniques rely exclusively on the measurement of distances to fix positions.
• One of the differences between them, however, is that the distances, called ranges in GPS, are not measured
to control points on the surface of the earth.
• Instead they are measured to satellites orbiting in nearly circular orbits at a nominal altitude of about 20,183
km above the earth.
• Trilateration is based upon distances rather than the intersection of lines based on angles.
• Now, in a terrestrial survey as indicated in this image here, there would probably be a minimum of three
control stations and from them would emanate three intersecting distances, i.e. L1, L2, and L3.
• This is very similar to what's done with GPS except instead of the control points being on the surface of the
Earth, they are orbiting the Earth. The GPS satellites are the control points orbiting about 20,000 kilometers
above the Earth.
• There's another difference, instead of there being three lines intersecting at the unknown point, there are
four.
• Four are needed because there are four unknown - X, Y, Z, and time - that need to be resolved.

Unknowns
• Time
• Time measurement is essential to GPS surveying in several ways.
• The determination of ranges, like distance measurement in a modern trilateration survey, is done electronically. In both cases,
distance is a function of the speed of light, an electromagnetic signal of stable frequency and elapsed time.
• Control
• In GPS the control points are the satellites themselves; therefore, knowledge of the satellite's position is critical.
• In the image here the satellites themselves are the control points.
• A Passive System
• The ranges are measured with signals that are broadcast from the GPS satellites to the GPS receivers in the microwave part of the
electromagnetic spectrum; this is sometimes called a passive system.
• GPS is passive in the sense that only the satellites transmit signals; the users simply receive them.
• Time is one of the unknowns that needs to be resolved to provide a position on the Earth using GPS.
• The elapsed time it take the electromagnetic signal to travel from the satellite to the receiver is important.
• Therefore, it's important to know where the satellite is in the sky at the moment that a measurement is taken. This is the purpose
of the ephemeris of the satellite.

One way ranging
• A GPS signal must somehow communicate to its receiver:
• what time is it on the satellite,
• the instantaneous position of a moving satellite,
• some information about necessary atmospheric corrections, and
• some sort of satellite identification system to tell the receiver where it came from and where the
receiver may find the other satellites.
• If we are to measure distances from the satellite to the receiver, and that is the
foundation of GPS survey, some information needs to be communicated from the
satellite to the receiver and that information needs to come along with the signal from
the satellite to the receiver.
• One aspect is the time on the satellite because, of course, the elapsed time that the
signal spends going from one place to the other is the basis of the distance measurement
- ranging.
• Therefore, it is important to know, the time on the satellite, the instant that the signal
left.

One-way ranging
• Secondly, the position of the moving satellite at an instant is critical.
• The coordinate of the satellite at that moment of measurement is important so that it can be used to derive the position of the
receiver
• Satellites are moving at a pretty tremendous rate of speed relative to the GPS receiver so the ephemeris needs to provide the
coordinates of the satellites at an instant of time. This is another way that time is important.
• Some information about the atmosphere needs to be communicated to the receiver too. If you're familiar with electronic distance
measurement (EDM) surveying you know that when an electromagnetic signal goes through atmosphere, it is attenuated by the
humidity, the temperature and the barometric pressure. Therefore these data are introduced into the processing of the distances
that are measured with EDM instruments.
• The GPS signal is going through a good deal more of the atmosphere than even the longest EDM shot. The first component of the
atmosphere that the GPS signal encounters is the ionosphere. The ionosphere has some characteristics that differ from the next
atmospheric layer the signal encounters, the troposphere. In any case the signal can be attenuated rather dramatically during its
trip. It follows that it is important to have some representation of the atmosphere through which the signal is passing
communicated to the GPS receiver from the satellite. This is so that the resultant delays can be introduced into the calculation of
the GPS derived position of the receiver.
• Some sort of satellite identification system is required too. Each distance that the receiver measures from each satellite must be
correlated to that satellite. Since the receiver will need to have at least four distances from at least four different satellites it needs
to be able to assign the appropriate range, the appropriate distance or length, to the correct satellite. It needs to identify the
origin of each signal.
• This is just some of the information that needs to come down on that signal from the satellite to the receiver

The Navigation Message
• This is the primary vehicle for communicating the NAV message to GPS receivers.
• The NAV message is also known as the GPS message.
• It includes some of the information the receivers need to determine positions.
• The NAV code is broadcast at a low frequency of 50 Hz on both the L1 and the L2 GPS carriers.
• It carries information about the location of the GPS satellites called the ephemeris and data used
in both time conversions and offsets called clock corrections.
• Both GPS satellites and receivers have clocks on board.
• It also communicates the health of the satellites on orbit and information about the ionosphere.
• It includes data called almanacs that provide a GPS receiver with enough little snippets of
ephemeris information to calculate the coordinates of all the satellites in the constellation with
an approximate accuracy of a couple of kilometres.
• The Navigation code, or message, is the vehicle for telling the GPS receivers some of the most
important things they need to know.

The Navigation Code
• The Navigation code has a low frequency, 50 Hz.
• It is modulated onto the GPS carriers.
• It communicates a stream of data called the GPS message, or Navigation
message.
• The entire Navigation message, the Master Frame, contains 25 frames.
• Each frame is 1500 bits long and is divided into five subframes.
• Each subframe contains 10 words and each word is comprised of 30 bits.
• Therefore, the entire Navigation message contains 37, 500 bits and at a
rate of 50 bits-per-second takes 12½ minutes to broadcast and to receive.
• There are five sub-frames of the legacy Navigation Message.
• TLM stands for telemetry. HOW stands for handover word.

The Navigation Code
• The entire navigation message contains 37,500 bits, and so on. Perhaps it is important to take a look that 12.5 minutes to
broadcast and receive at 50 bits per second is the amount of time that it takes to acquire the entire navigation message from a
cold boot with a GPS receiver. It does take a bit of time for the receiver to update its Navigation Message.
• The essential point here is that this message is the fundamental vehilce for the satellite to communicate important information to
the receiver.
• The Navigation Message it is capable of telling the receiver where the satellite is after the receiver has acquired the signal from
that satellite. The Navigation Message comes in at a pretty low frequency, 50 Hertz, and it does take some time for the satellite to
acquire the whole thing.
• The clock correction is one of the ways that the satellite can tell the receiver what time it is on-board the satellite.
• Then the PRN is an abbreviation of pseudo random noise. This term is used because the GPS signals that the receiver uses for
positioning appear to be random noise.
• The signals are very carefully designed and consistent. . They just seem to be irregular. The PRN numbers 25 to 32 in sub-frame
number four mean that satellite's almanac's from number 25 to number 32 be found there.
• Now the PRNs from 1 to 24, those satellites have their almanac's, in other words, a little bit of their ephemerides in sub frame
number five.
• When a receiver acquires the Navigation Message from one satellite - embedded in that message - there's a bit of information,
just a bit, that will tell the receiver where it can find the rest of the constellation the entire in the sky. This helps it acquire the
additional satellites after it's got the first one. That's what the satellite Almanac does.

The Broadcast Ephemeris
• Contain information about the position of the satellite, with respect to time.
• The ephemeris that each satellite broadcasts to the receivers provides information about its position relative
to the earth.
• Most particularly it provides information about the position of the satellite antenna's phase center.
• The ephemeris is given in a right ascension (RA) system of coordinates.
• There are six orbital elements;
• the size of the orbit, that is its semimajor axis, a
• its shape, that is the eccentricity, e.
• the right ascension of its ascending node, Ω,
• the inclination of its plane, i.
• the argument of the perigee, ω,
• The description of the position of the satellite on the orbit, known as the true anomaly,
• provides all the information the user’s computer needs to calculate earth-centered, earth-fixed, World
Geodetic System 1984, GPS Week 1762 (WGS84 [G1762]) coordinates of the satellite at any moment.
• The Control Segment uploads the ephemerides to the Navigation Message for each individual satellite.

The Almanac, Time to First Fix and Satellite Health

The Almanac
• Contained in subframes 4 and 5
• Almanac tell the receiver where to find all the GPS satellites.
• Subframe 4 contains the almanac data for satellites with pseudorandom noise (PRN)
numbers from 25 through 32
• subframe 5 contains almanac data for satellites with PRN numbers from 1 through 24.
• The Control Segment generates and uploads a new almanac every day to each satellite.
• it is convenient for a receiver to be able to have some information about where all the
satellites in the constellation are by reading the almanac from just one of them.
• The almanacs are much smaller than the ephemerides because they contain coarse
orbital parameters and incomplete ephemerides but they are still accurate enough for a
receiver to generate a list of visible satellites at power-up.
• They, along with a stored position and time, allow a receiver to find its first satellite.

Satellite Health
• Subframe 1 contains information about the health of the satellite the receiver is tracking when it
receives the NAV message and allows it to determine if the satellite is operating within normal
parameters.
• Subframes 4 and 5 include health data all of the satellites, data that is periodically uploaded by
the Control Segment.
• These subframes inform users of any satellite malfunctions before they try to use a particular
signal.
• The codes in these bits may convey a variety of conditions.
• They may tell the receiver that all signals from the satellite are good and reliable or that the
receiver should not currently use the satellite because there may be tracking problems or other
difficulties.
• They may even tell the receiver that the satellite will be out of commission in the future, perhaps
it will be undergoing a scheduled orbit correction.
• GPS satellites health is affected by a wide variety of breakdowns, particularly clock trouble. That is
one reason they carry multiple clocks.

TLM and HOW
• Each of these five subframes begins with the same two words: the telemetry word (TLM)
and the handover word (HOW).
• These two words are generated by the satellite itself.
• GPS time restarts each Sunday at midnight (0:00 o’clock). These data contain the time
since last restart of GPS time on the previous Sunday 0:00 o’clock.
• TLM contains information about the age of the ephemeris data. It also has a constant
unchanging 8-bit preamble of 10001011, and a string helps the receiver reliably find the
beginning of each subframe.
• The HOW provides the receiver information on the time of the GPS week (TOW) and the
number of the subframe, among other things.
• The HOW tells the receiver exactly where the satellite stands in the generation of
positioning codes.
• helps the receiver go from tracking the C/A code to tracking the P(Y) code, the primary
GPS positioning codes. It is used by military receivers.

The P and C/A Codes
• The Precise and Coarse Acquisition codes
• The P and C/A codes are complicated; so complicated that they
appear to be noise at first.
• they are known as pseudorandom noise, or PRN, codes.
• They must be capable of repetition and replication.
• However, unlike the Navigation Message, the P and C/A codes are not
vehicles for broadcasting information that has been uploaded by the
Control Segment.
• They carry the raw data from which GPS receivers derive their time
and distance measurements.

The P code
• The P code is called the Precise code.
• It is a particular series of ones and zeroes generated at a rate of 10.23 million bits per second. It is carried on both L1 and L2 and it
is very long, 37 weeks (2x1014 bits in code)
• Each GPS satellite is assigned a part of the P code all its own and then repeats its portion every 7 days.
• This assignment of one particular week of the 37-week-long P code to each satellite helps a GPS receiver distinguish one satellite’s
transmission from another.
• For example, if a satellite is broadcasting the fourteenth week of the P code it must be Space Vehicle 14 (SV 14). The encrypted P
code is called the P(Y) code.
• There is a flag in subframe 4 of the NAV message that tells a receiver when the P code is encrypted into the P(Y) code.
• This security system has been activated by the Control Segment since January of 1994.
• It is done to prevent spoofing from working.
• Spoofing is generation of false transmissions masquerading as the Precise Code.
• This countermeasure called Antispoofing (AS) is accomplished by the modulation of a W-Code to generate the more secure Y-Code
that replaces the P code.
• Commercial GPS receiver manufacturers are not authorized to use the P(Y) code directly. Therefore, most have developed
proprietary techniques both for carrier wave and pseudorange measurements on L2 indirectly. Dual-frequency GPS receivers must
also overcome AS.

The C/A code
• The C/A code is also a particular series of ones and zeroes but the rate
at which it is generated is 10 times slower than the P(Y) code.
• The C/A code rate is 1.023 million bits per second.
• Not only does each GPS satellite broadcast its own completely unique
1023 bit C/A code, it repeats its C/A code every millisecond.
• The C/A code is broadcast on L1 only.
• It used to be the only civilian GPS code, but no longer, it has been
joined by a new civilian signal known as L2C that is carried on L2.

SPS and PPS
• The C/A code is the vehicle for the Standard Positioning Service, SPS, which is used for most civilian surveying applications.
• The P(Y) code on the other hand provides the same service for the precise positioning servicer, PPS.
• The idea of SPS and PPS was developed by the Department of Defense many years ago.
• SPS was designed to provide a minimum level of positioning capability considered consistent with national security, ±100m, 95% of
the time, when intentionally degraded through Selective Availability (SA).
• Selective Availability, the intentional dithering of the satellite clocks by the Department of Defense was instituted in 1989 because
the accuracy of the C/A point positioning as originally rolled out was too good!
• As mentioned above, the accuracy was supposed to be ±100 meters horizontally, 95% of the time with a vertical accuracy of about
±175 meters.
• But, in fact, it turned out that the C/A-code point positioning gave civilians access to accuracy of about ±20 meters to ±40 meters.
• That was not according to plan, so the satellite clocks’ accuracy was degraded on the C/A code.
• The good news is that the intentional error source called SA is gone .
• It was switched off on May 2, 2000 by presidential order.
• The intentional degradation of the satellite clocks is a thing of the past. Actually, Selective Availability never did hinder the
surveying applications of GPS.
• However, satellite clock errors, the unintentional kind, still contribute error to GPS positioning.

EDM ranging
• All the codes mentioned come to a GPS receiver on a modulated carrier,
• The signal created by an electronic distance meter (EDM) in a total station is a good example of a modulated carrier.
• Distance measurement in modern surveying is done electronically.
• Distance is measured as a function of the speed of light, an electromagnetic signal of stable frequency and elapsed time.
• Frequencies generated within an electronic distance measuring device (EDM) can be used to determine the elapsed travel time of its signal because
the signal bounces off a reflector and returns to where it started.
• An EDM only needs one oscillator at the point of origin because its electromagnetic wave travels to a retroprism and is reflected back to its
origination.
• The EDM is both the transmitter and the receiver of the signal.
• Therefore, in general terms, the instrument can take half the time elapsed between the moment of transmission and the moment of reception,
multiply by the speed of light, and find the distance between itself and the retroprism (Distance = Elapsed Time x Rate).
• The fundamental elements of the calculation of the distance measured by an EDM, ρ, are the time elapsed between transmission and reception of the
signal, Δt, and the speed of light, c.
• Distance = ρ
• Elapsed Time = Δt
• Rate = c
•

GPS Ranging
• The one-way ranging used in GPS is more complicated.
• It requires the use of two clocks.
• The broadcast signals from the satellites are collected by the receiver, not reflected.
• Nevertheless, in general terms, the full time elapsed between the instant a GPS signal leaves a satellite and
arrives at a receiver, multiplied by the speed of light, is the distance between them.
• Unlike the wave generated by an EDM, a GPS signal cannot be analyzed at its point of origin.
• The measurement of the elapsed time between the signal’s transmission by the satellite and its arrival at the
receiver requires two clocks, one in the satellite and one in the receiver.
• This complication is compounded because to correctly represent the distance between them, these two
clocks would need to be perfectly synchronized with one another.
• the problem is addressed mathematically.
• In the image the basis of the calculation of a range measured from a GPS receiver to the satellite, ρ, is the
multiplication of the time elapsed between a signal’s transmission and reception, Δt, by the speed of light, c.
• A discrepancy of 1 microsecond, 1 millionth of a second, from perfect synchronization, between the clock
aboard the GPS satellite and the clock in the receiver can create a range error of 300 meters, far beyond the
acceptable limits for nearly all surveying work.

Phase Angle
• The time measurement devices used in both EDM and GPS measurements are clocks only in the most
general sense.
• They are more correctly called oscillators, or frequency standards.
• they keep time by chopping a continuous beam of electromagnetic energy at extremely regular intervals.
• The result is a steady series of wavelengths and the foundation of the modulated carrier. 1 hertz is a full
wavelength that takes 1 second to cycle through 360 degrees.
• As long as the rate of an oscillator’s operation is very stable, both the length and elapsed time between the
beginning and end of every wavelength of the modulation will be the same.
• Phase angles are important to the modulation of the carrier by phase that is the method of attaching the
codes to the GPS carriers.
• Here's a sine wave 0, 90, 180, 270, and 360 are known as phase angles in a single wavelength.
• The oscillators in the EDM or in the GPS satellite create very constant wavelengths, because like clocks or
oscillators, they're known as frequency standards.
• They create electromagnetic energy that has a very constant wavelength.
• Therefore the phase angles occur at definite distances.

Phase Shift
• With the original Gunter’s chain, the surveyor simply looked at the chain and estimated the fractional part of the last link that
should be included in the measurement.
• the EDM must find the fractional part of its measurement electronically.
• It compares the phase angle of the returning signal to that of a replica of the transmitted signal to determine the phase shift.
• That phase shift represents the fractional part of the measurement.
• This principle is used in distance measurement by both EDM and GPS systems.
• When two modulated carrier waves reach exactly the same phase angle at exactly the same time, they are said to be in phase,
coherent, or phase locked.
• However, when two waves reach the same phase angle at different times, they are out of phase or phase shifted.
• For example, in the image the sine wave shown by the dashed line has returned to an EDM from a reflector. Compared with the
sine wave shown by the solid line, it is out of phase by one-quarter of a wavelength. The distance between the EDM and the
reflector, ρ, is then:
• ρ= ( Nλ+d )/ 2
• where:
• N = the number of full wavelengths the modulated carrier has completed
• d = the fractional part of a wavelength at the end that completes the doubled distance.

Carrier phase ranging
• the same time an external carrier wave is sent to the reflector, the EDM
keeps an identical internal reference wave at home in its receiver circuits.
• In Figure 1.8, the external beam returned from the reflector is compared to
the reference wave and the difference in phase between the two can be
measured.
• Both EDM and GPS ranging use the method represented in this illustration.
• In GPS, the measurement of the difference in the phase of the incoming
signal and the phase of the internal oscillator in the receiver reveals the
small distance at the end of a range.
• In GPS, the process is called carrier phase ranging. And as the name implies
the observable is the carrier wave itself.
• The image shows again the EDM sending out the transmitted wave in blue
with the phase angles indicated as before.

Observation Principle and Signal Structure
• NAVSTAR GPS is a one-way ranging system
• Passive system
• signals are only transmitted by the satellite, need to know
where satellite is at any given instant of time
• Each GPS Satellite transmits on 2 (carrier) frequencies L1
and L2
• Their frequencies are derived from the fundamental clock
frequency (f0 = 10.23 MHz)
• L1 = 154* f0 (f = 1575.42 MHz, wavelength =19 cm)
• L2 = 120* f0 (f = 1227.64 MHz, wavelength =24 cm)

• Signal travel time between the satellite and the receiver is
observed and the range distance is calculated through the
knowledge of signal propagation velocity.
• a clock reading at the transmitted antenna is compared with
a clock reading at the receiver antenna
• since the two clocks are not strictly synchronized, the
observed signal travel time is biased with systematic
synchronization error.
• Biased ranges are known as pseudoranges. Simultaneous
observations of four pseudoranges are necessary to
determine X, Y, Z coordinates of user antenna and clock bias.

GPS Signal Structure
GPS Codes
• Real time positioning through GPS signals is possible by
modulating carrier frequency with 2 Pseudo-Random
noise codes (PRN codes),
• PRN are:
• sequences of binary values (+/-1's, 0's) having random
character but identifiable distinctly,
• are derived from travel time of an identified PRN signal code
• codes replicated in the GPS Receiver are aligned with
the received code from the satellite,
• knowing the instant of time the signal was transmitted,
the travel time is computed,

GPS Codes

GPS Codes
• There are two different codes in use:
• P-code - precision or protected code, and
• C/A code - C/A means clear/acquisition or coarse acquisition
code.
• precision of range dependent on chip length
• The C/A code is only transmitted on the L1 carrier:
• 1023 binary digits (chips), repeated every millisecond, and
one chip has a duration of 1 microsecond (chip length is
293.1 m)
• a chipping rate of 1.023 MHz,
• a wavelength of 300 meters.
• Each SV has its own C/A code

GPS Satellite Signal Components

GPS Codes
• P- code (Precise - Military) code
• 10230 chips,
• has a frequency of 10.23 MHz. This refers to a sequence of
10.23 million binary digits or chips per second (i.e. the
chipping rate of P-code),
• Wavelength corresponding to one chip is 29.30m,
• The P-code sequence is extremely long and repeats only
after 266/7 days,
• Portions of 7 days each are assigned to the various
satellites,

GPS Codes
• thus all satellites can transmit on the same
frequency and be identified by their unique
one-week segment (Each SV has a one week
segment of the same P-code),
• This technique is also called as Code Division
Multiple Access (CDMA).
• P-code is the primary code for navigation and
is available on carrier frequencies L1 and L2.

GPS Codes
• A GPS receiver normally has a copy of the code
sequence for determining the signal propagation time,
• this is phase-shifted in time step by step and correlated with
the received code signal until maximum correlation is
achieved.
• necessary phase-shift in the two sequences of codes is a
measure of the signal travel time between the satellite and
the receiver antennas.
• This technique can be explained as code phase observation.
• For precise geodetic applications, the pseudoranges
should be derived from phase measurements on the
carrier signals because of much higher resolution.
• Problems of ambiguity determination are vital for such
observations.

GPS Broadcast Data
• The third type of signal transmitted from a GPS
satellite is the broadcast message (a satellite
broadcasts its own Navigation Message) consisting
of:
• orbital information, offset from true GPS time, health,
expected range accuracy, signal information, almanac and
health for all other GPS satellites, and at a
• slow rate of 50 bits per second (50 bps) on L1 and L2 carrier,
repeated every 30 seconds and a total of 37500 bits
• Fresh navigation data is transmitted every hour
• Chip sequence of P-code and C/A code are separately
combined with the stream of message bit by binary
addition (same value for code and message chip gives
0 and different values result in 1).

• The signal structure permits both the phase and the phase
shift (Doppler effect) to be measured along with the direct
signal propagation.
• The necessary bandwidth is achieved by phase modulation of
the PRN code as shown below,

Structure of the GPS Navigation Data
• to get access to the navigation data, the user has to decode the
data signal.
• This is done by the internal processor within the receiver for
on line navigation purposes,
• Most manufacturers provide decoding software for post
processing purposes.

• With a bit rate of 50 bps and a cycle time of 30 seconds, the total
information content of a navigation data set is 1500 bits.
• The complete data frame is subdivided into five subframes of six-
second duration comprising 300 bits of information.
• Each subframe contains the data words of 30 bits each.
• Six of these are control bits. The first two words of each subframe are
the Telemetry Word (TLM) and the C/A-P-Code Hand over Word
(HOW).
• The TLM work contains a synchronization pattern, which facilitates
the access to the navigation data.

• The navigation data record is divided into three data
blocks:
• Data Block I
• appears in the first subframe and contains the clock
coefficient/bias.
• Data Block II
• appears in the second and third subframe and contains all
necessary parameters for the computation of the satellite
coordinates.
• Data Block III
• appears in the fourth and fifth subframes and contains the almanac
data with clock and ephemeris parameter for all available satellite
of the GPS system. This data block includes also ionospheric
correction parameters and particular alphanumeric information for
authorized users.
• Unlike the first two blocks, the subframe four and five are
not repeated every 30 seconds.

Biases and Solutions
• The understanding and management of errors is indispensable for
finding the true geometric range ρ between a satellite and a receiver
from either a pseudorange, or carrier phase observation.

The Satellite Clock Bias, dt
• One of the largest errors can be attributed to the satellite clock bias.
• It can be quite large especially if the broadcast clock correction is not used
by the receiver to bring the time signal acquired from a satellite’s on-board
clock in line with GPS time.
• The onboard satellite clocks are independent of one another.
• The rates of these rubidium and cesium oscillators are more stable if they
are not disturbed by frequent tweaking and adjustment is kept to a
minimum.
• While GPS time itself is designed to be kept within one microsecond, 1
μsec or one-millionth of a second, of UTC, excepting leap seconds, the
satellite clocks can be allowed to drift up to a millisecond, 1 msec or one-
thousandth of a second, from GPS time.

Satellite clock errors
• The broadcast clock correction is the correction that the control
segment provides to the receiver to bring the satellite clock in line
with GPS time.
• The control segment doesn't want to constantly tweak the clocks as
this would cause the clocks to deteriorate more rapidly.
• the clocks are one of the weakest aspects of the satellites, although
the GPS satellites have done very well.
• Since constant tweaking would diminish their longevity they are
allowed to drift up to a thousandth of a second from GPS time.

Relativistic Effects on the Satellite Clock
• Albert Einstein’s special and general theories of relativity apply to the clocks involved here.
• At 3.874 kilometers per second the clocks in the GPS satellites are traveling at great speed, and that makes the clocks on the
satellites appear to run slower than the clocks on earth by about 7 microseconds a day.
• However, this apparent slowing of the clocks in orbit is counteracted by the weaker gravity around them.
• The weakness of the gravity makes the clocks in the satellites appear to run faster than the clocks on earth by about 45
microseconds a day.
• Therefore, on balance the clocks in the GPS satellites in space appear to run faster by about 38 microseconds a day than the clocks
in GPS receivers on earth.
• So, to ensure the clocks in the satellites will actually produce the correct fundamental frequency of 10.23 MHz in space, their
frequencies are set to 10.22999999543 MHz before they are launched into space.
• There is yet another consideration, the eccentricity of the orbit of GPS satellites.
• With an eccentricity of 0.02 this effect on the clocks can be as much as 45.8 nanoseconds.
• Fortunately, the offset is eliminated by a calculation in the GPS receiver itself; thereby avoiding what could be ranging errors of
about 14 meters.
• The receiver is moving too; of course so an account must be made for the motion of the receiver due to the rotation of the earth
during the time it takes the satellites signal to reach it.
• This is known as the Sagnac effect and it is 133 nanoseconds at its maximum.
• Luckily these relativistic effects can be accurately computed and removed from the system.

The Ionospheric Effect, dion
• One of the largest errors in GPS positioning is attributable to the atmosphere.
• The long relatively unhindered travel of the GPS signal through the virtual vacuum of space changes as it
passes through the earth’s atmosphere.
• Through both refraction and diffraction, the atmosphere alters the apparent speed and, to a lesser extent,
the direction of the signal.
• This causes an apparent delay in the signals transit from the satellite to the receiver.
Ionized Plasma
• The ionosphere is ionized plasma comprised of negatively charged electrons which remain free for long
periods before being captured by positive ions.
• It extends from about 50 km to 1000 km above the earth’s surface and is the first part of the atmosphere
that the signal encounters as it leaves the satellite.
• The magnitude of these delays is determined by the state of the ionosphere at the moment the signal passes
through so it's important to note that its density and stratification varies.
• The sun plays a key role in the creation and variation of these aspects.
• Also, the daytime ionosphere is rather different from the ionosphere at night.

Ionosphere and the Sun
• When gas molecules are ionized by the sun’s ultraviolet radiation free electrons are released.
• As their number and dispersion varies so does the electron density in the ionosphere.
• This density is often described as total electron content or TEC, a measure of the number of free electrons in
a column through
• h the ionosphere with a cross-sectional area of 1 square meter: 1016 is one TEC unit.
• The higher the electron density the larger the delay of the signal, but the delay is by no means constant.
• The ionospheric delay changes slowly through a daily cycle.
• It is usually least between midnight and early morning and most around local noon or a little after.
• During the daylight hours in the midlatitudes the ionospheric delay may grow to be as much as five times
greater than it was at night, but the rate of that growth is seldom more than 8 cm per minute.
• It is also nearly four times greater in November, when the earth is nearing its perihelion, its closest approach
to the sun, than it is in July near the earth’s aphelion, its farthest point from the sun.
• The effect of the ionosphere on the GPS signal usually reaches its peak in March, about the time of the
vernal equinox.

Ionospheric Stratification
• The ionosphere has layers sometimes known as the mesosphere and thermosphere that are themselves composed of D, E, and F
regions.
• Neither the boundaries between these regions, nor the upper layer of the ionosphere, can be defined strictly.
• The lowest detectable layer, the D region, extends from about 50 km to 90 km has almost no effect on GPS signals and virtually
disappears at night.
• The E region, also a daytime phenomenon, is between 90 km and 120 km its effect on the signal is slight but it can cause the signal
to scintillate.
• The layer that affects the propagation of electromagnetic signals the most is the F region.
• It extends from about 120km to 1000km
• The F region contains the most concentrated ionization in the atmosphere.
• In the daytime, the F layer can be further divided into F1 and F2.
• F2 is the most variable.
• F1, the lower of the two, is most apparent in the summer.
• These two layers combine at night.
• Above the F layer is fully ionized. It is sometimes known as the photosphere or the H region.
• The ionosphere is also not homogeneous.
• Its behavior in one region of the earth is liable to be unlike its behavior in another.

Satellite Elevation and Ionospheric Effect
• The severity of the ionosphere’s effect on a GPS signal depends on
the amount of time that signal spends traveling through it.
• A signal originating from a satellite near the observer’s horizon must
pass through a larger amount of the ionosphere to reach the receiver
than does a signal from a satellite near the observer’s zenith.
• In other words, the longer the signal is in the ionosphere, the greater
the ionosphere’s effect on it.

Group and Phase Delay
• The ionosphere is dispersive, which means that the apparent time delay contributed by the ionosphere depends on the frequency
of the signal.
• This dispersive property causes the codes, the modulations on the carrier wave, to be affected differently than the carrier wave
itself during the signal’s trip through the ionosphere.
• The P code, the C/A code, the Navigation message and all the other codes appear to be delayed, or slowed, affected by what is
known as the group delay.
• But the carrier wave itself appears to speed up in the ionosphere.
• It is affected by what is known as the phase delay.
• It is sometimes called phase advancement.
• It is governed by the same properties of electron content as the group delay, phase delay just increases negatively.
• Please note that the algebraic sign of dion is negative in the carrier phase equation and positive in the pseudorange equation.
• In other words, a range from a satellite to a receiver determined by a code observation will be a bit too long and a range
determined by a carrier observation will be a bit too short.
• But really, the most important thing about the ionosphere to the GPS signal is that it attenuates, or slows, the signal, depending on
the density of the layer of atmosphere.
• The ionosphere is not homogeneous and unchanging. It is in constant flux. Therefore, it's impossible to have a correction that's
static.

Different Frequencies Are Affected Differently
• Another consequence of the dispersive nature of the ionosphere is that the
apparent time delay for a higher frequency carrier wave is less than it is for a
lower frequency wave.
• That means that L1, 1575.42 MHz, is not affected as much as L2, 1227.60 MHz,
and L2 is not affected as much as L5, 1176.45MHz
• This fact provides one of the greatest advantages of a dual-frequency receiver
over the single-frequency receivers.
• The separations between the L1 and L2 frequencies (347.82 MHz), the L1 and L5
frequencies (398.97 MHz) and even the L2 and L5 frequencies (51.15 MHz) are
large enough to facilitate estimation of the ionospheric group delay.
• Therefore, by tracking all the carriers, a multiple-frequency receiver can model
and remove, not all, but a significant portion of the ionospheric bias.
• There are now several possible combinations, L1/L2, L1/L5 and L2/L5. It is even
possible to have a triple frequency combination to help ameliorate this bias.

Broadcast Correction
• A predicted total UERE is provided in each satellite's Navigation message as the user range accuracy (URA), but it is minus ionospheric error.
• To help remove some of the effect of the ionospheric delay on the range derived from a single frequency receiver there is an ionospheric correction
available in another part of the Navigation message, subframe 4.
• However, this broadcast correction should not be expected to remove more than about three-quarters of the error, which is most pronounced on long
baselines.
• Where the baselines between the receivers are short the effect of the ionosphere can be small, but as the baseline grows so does the significance of
the ionospheric bias.
• The ionosphere is dispersive. That means that it affects different frequencies differently. And it's fortunate, therefore, that GPS has three carrier
frequencies, L1, L2 and L5.
• The higher frequency carrier is less affected by the ionosphere than is the lower frequency wave.
• This fact is one of the greatest advantages of a multiple frequency receiver over a single frequency.
• This separation between the frequencies allows for fairly good modeling by the GPS receiver of the effect of the atmosphere, the ionosphere, on the
trip that the signal had through that layer.
• The formula allows you to have some idea of how that total electron count affects the signal.
• It's inversely proportional to the score of the frequency.
• A multiple frequency receiver can factilitate the removal of a substantial portion of the ionospheric effect.
• Even through there is an atmospheric correction in the Navigation Message, the atmosphere that was used to derive that correction may have been
over the middle of the Pacific, at Kwajalein. The atmosphere there would be different than the atmosphere over your GPS observation. So while the
atmospheric correction and the navigation message is a good start, a multiple frequency receiver derived model is better.

The Receiver Clock Bias, dT
An Oven-Controlled Quartz Crystal Oscillator (OCXO) on a Board

THE RECEIVER CLOCK BIAS, dT
• The third largest error which can be caused by the receiver clock, is its oscillator.
• Both a receiver’s measurement of phase differences and its generation of replica codes depend
on the reliability of this internal frequency standard.
Typical Receiver Clocks
• GPS receivers are usually equipped with quartz crystal clocks, which are relatively inexpensive and
compact.
• They have low power requirements and long life spans.
• For these types of clocks, the frequency is generated by the piezoelectric effect in an oven-
controlled quartz crystal disk, a device sometimes symbolized by OCXO.
• Their reliability ranges from a minimum of about 1 part in 108 to a maximum of about 1 part in
1010, a drift of about 0.1 nanoseconds in 1 second.
• Even at that, quartz clocks are not as stable as the atomic standards in the GPS satellites and are
more sensitive to temperature changes, shock, and vibration.
• Some receiver designs augment their frequency standards by also having the capability to accept
external timing from cesium or rubidium oscillators.

Receiver bias
• It really isn't necessary for a GPS receiver clock to be wonderful
because we are solving for time.
• There are four unknowns (x, y, z and time) and, therefore, four
observations to make the solution.
• Still we can't get along without an oscillator in the receiver.
• It is necessary for producing the replica code, for example.
• The replica code needs to match the incoming signals from the
satellites.
• So obviously, a receiver clock is necessary, but it doesn't need to be
anything like an atomic standard.

The Orbital Bias
The Sources of Some Forces Disturbing the Satellite's Orbit

Orbital bias
• Orbital bias has the potential to be the fourth largest error.
• It is addressed in the broadcast ephemeris.
• The orbital motion of GPS satellites is not only a result of the earth's
gravitational attraction, there are several other forces that act on the
satellite.
• The primary disturbing forces are:
• the non-spherical nature of the earth's gravity,
• the attractions of the sun and the moon, and
• solar radiation pressure.
• The best model of these forces is the actual motion of the satellites
themselves and the government facilities distributed around the
world, known collectively as the Control Segment or the Operational
Control System (OCS), track them for that reason, among others.

Orbital bias
• Even the motion of the satellite from darkness to light affects it's orbit
and make it a rather bumpy road for the satellite.
• The modeling of the orbit by the Control Segment is good, but they
can upload the ephemerides only so frequently.
• There is always a certain amount of age in the ephemerides and that
means that the position of the satellite expressed in it's ephermeris at
the moment of observation cannot be perfect.

Control stations
• The data that feeds the MCS comes from monitoring stations.
• These stations track the entire GPS constellation.
• In the past there were limitations.
• There were only six tracking stations.
• It was possible for a satellite to go unmonitored for up to two hours each day.
• It was clear that the calculation of the ephemerides and the precise orbits of the constellation could be
improved with more monitoring stations in a wider geographical distribution.
• It was also clear that if one of the six stations went down the effectiveness of the Control Segment could be
considerably hampered.
• These ideas, and others, led to a program of improvements known as the Legacy Accuracy Improvement
Initiative, L-AII.
• During this initiative from August 18 to September 7 of 2005, six National Geospatial Intelligence Agency,
NGA, stations were added to the Control Segment.
• This augmented the information forwarded to the MCS with data from Washington
• The modernization of the Control Segment has been underway for some time and it continues

The Tropospheric Effect, dtrop

Troposphere
• The troposphere is that part of the atmosphere closest to the earth.
• It extends from the surface to about 9 km over the poles and about 16 km over the equator,
• The troposphere and the ionosphere are by no means alike in their effect on the satellite’s signal.
• While the troposphere is refractive its refraction of a GPS satellite’s signal is not related to its frequency.
• The refraction is tantamount to a delay in the arrival of a GPS satellite's signal.
• It can also be conceptualized as a distance added to the range the receiver measures between itself and the satellite. T
• he troposphere is part of the electrically neutral layer of the earth’s atmosphere meaning it is not ionized.
• The troposphere is also nondispersive for frequencies below 30 GHz or so.
• Therefore L1, L2 and L5 are equally refracted.
• This means that the range between a receiver and a satellite will be shown to be a bit longer than it actually is.
• However, as it is in the ionosphere, density affects the severity of the delay of the GPS signal as it travels through the
troposphere.
• For example, when a satellite is close to the horizon, the delay of the signal caused by the troposphere is maximized.
• The tropospheric delay of the signal from a satellite at zenith, directly above the receiver, is minimized.

Satellite elevation and tropospheric effect
• The situation is analogous to atmospheric refraction in astronomic
observations; the effect increases as the energy passes through more of
the atmosphere.
• The difference in GPS is that it is the delay, not the angular deviation,
caused by the changing density of the atmosphere that is of primary
interest.
• The GPS signal that travels the shortest path through the troposphere will
be the least delayed by it.
• So, even though the delay at an elevation angle of 90° at sea level will only
be about 2.4 meters, it can increase to about 9.3 meters at 75° and up to
20 meters at 10°.
• There is less tropospheric delay at higher altitudes.

Modeling.
• Modeling the troposphere is one technique used to reduce the bias in GPS data processing, and it
can be up to 95% effective.
• However, the residual 5% can be quite difficult to remove. Several a priori models have been
developed, for example, the Saastamoinen model and the Hopfield models, which perform well
when the satellites are at reasonably high elevation angles.
• However, it is advisable to limit GPS observations to those signals above 15% or so to ameliorate
the effects of atmospheric delay.
The dry and wet components of refraction.
• Refraction in the troposphere has a dry component and a wet component.
• The dry component which contributes most of the delay, perhaps 80% to 90%, is closely
correlated to the atmospheric pressure.
• The dry component can be more easily estimated than the wet component.
• It is fortunate that the dry component contributes the larger portion of range error in the
troposphere because the size of the delay attributable to the wet component depends on the
highly variable water vapor distribution in the atmosphere.
• Even though the wet component of the troposphere is nearer to the Earth’s surface,
measurements of temperature and humidity are not strong indicators of conditions on the path
between the receiver and the satellite.

Atmosphere and Baseline Length

Receiver spacing and the atmospheric biases
• The character of the atmosphere is never homogeneous; therefore, the importance of atmospheric
modeling increases as the distance between GPS receivers grows.
• Consider a signal traveling from one satellite to two receivers that are close together.
• That signal would be subjected to very similar atmospheric effects, and, therefore, atmospheric bias
modeling would be less important to the accuracy of the measurement of the relative distance between
them.
• But a signal traveling from the same satellite to two receivers that are far apart may pass through levels of
atmosphere quite different from one another.
• In that case, atmospheric bias modeling would be more important.
• In other words, the importance of atmospheric correction increases as the differences in the atmosphere
through which the GPS satellite signal must pass to reach the receivers increase.
• Such differences can generally be related to length.
• The atmospheric bias grows larger as the baselines grow longer on the earth's surface.
• If two receivers are very close together the atmospheric is less of a concern.
• However, if they are far apart then the atmosphere above them can be substantially different.

multipath
• Multipath is an uncorrelated error.
• It is a range delay symbolized by εmp in the pseudorange equation and εmφ in the carrier phase
equation.
• it is the reception of the GPS signal via multiple paths rather than from a direct line of sight.
• Multipath differs from both the apparent slowing of the signal through the ionosphere and
troposphere and the discrepancies caused by clock offsets.
• The range delay in multipath is the result of the reflection of the GPS signal.
• The affect of multipath on pseudorange solutions is orders of magnitude larger than it is in carrier
phase solutions.
• However, multipath in carrier phase is much harder to mitigate than multipath in pseudoranges.
• Multipath occurs when part of the signal from the satellite reaches the receiver after one or more
reflections from the ground, a building, or another object.
• These reflected signals can interfere with the signal that reaches the receiver directly from the
satellite and cause the correlation peak become skewed.

multipath
• The effect of multipath on a carrier phase measurement can reach a quarter of a wavelength which is about 5 cm.
• The effect of multipath on a pseudorange measurement can reach 1.5 times the length of a chip, though it is more often a few
meters.
• multipath delays of less than one chip, those that are the result of a single reflection, are the most troublesome.
• Fortunately, there are factors that distinguish reflected multipath signals from direct, line-of-sight, signals.
• For example, reflected signals at the frequencies used for L1, L2 and L5 tend to be weaker and more diffuse than the directly
received signals.
• Another difference involves the circular polarization of the GPS signal.
• The polarization is actually reversed when the signal is reflected.
• Reflected, multipath signals become Left Hand Circular Polarized, LHCP, whereas the signals received directly from the GPS
satellites are Right Hand Circular Polarized, RHCP.
• RHCP means that it rotates clockwise when observed in the direction of propagation.
• But while the majority of multipath signals may be LHCP, it is possible for them to arrive at the received in-phase usually through
an even number of multiple reflections.
• These characteristics allow some multipath signals to be identified and rejected at the receiver’s antenna.

Antenna Design and Multipath
• GPS antenna design can play a role in minimizing the effect of multipath.
• Ground planes, usually a metal sheet, are used with many antennas to reduce multipath interference by eliminating signals from
low elevation angles.
• However, such ground planes do not provide much protection from the propagation of waves along the ground plane itself.
• When a GPS signal’s wave front arrives at the edge of an antenna’s ground plane from below, it can induce a surface wave on the
top of the plane that travels horizontally
• Another way to mitigate this problem is the use of a choke ring antenna.
• Choke ring antennas, based on a design first introduced by the Jet Propulsion Laboratory (JPL), can reduce antenna gain at low
elevations.
• This design contains a series of concentric circular troughs that are a bit more than a quarter of a wavelength deep. A choke ring
antenna can prevent the formation of these surface waves.
• But neither ground planes nor choke rings remove the effect of reflected signals from above the antenna very effectively. There
are signal processing techniques that can reduce multipath.
• A widely used strategy is the 15° cutoff or mask angle.
• This technique calls for tracking satellites only after they are more than 15° above the receiver’s horizon.
• Careful attention in placing the antenna away from reflective surfaces, such as nearby buildings, water or vehicles, is another way
to minimize the occurrence of multipath.

Receiver Noise, εp and εφ
• Receiver noise is directly related to thermal noise, dynamic stress, and so on in the GPS receiver
itself.
• Receiver noise is also an uncorrelated error source.
• The effects of receiver noise on carrier phase measurements symbolized by εφ, like multipath, are
small when compared to their effects on pseudorange measurements, εp.
• Generally speaking the receiver noise error is about 1% of the wavelength of the signal involved.
• In other words in code solutions the size of the error is related to chip width.
• For example, the receiver noise error in a C/A code solution can be around 3m which is about an
order of magnitude more than it is in a P code solution, about 3cm.
• And in carrier phase solutions the receiver noise error contributes millimeters to the overall error.
• Receiver noise is inevitable and it must be considered.
• It is a relatively small contributor to the GPS error budget, in most cases.
• It is an uncorrelated error, meaning that both multipath and the receiver noise are not related to
the length of the baseline between GPS receivers. They are uncorrelated in that regard.

Differencing
• In GPS the word differencing has come to represent several types of simultaneous
baseline solutions of combined measurements.
• One of the foundations of differencing is the idea of the baseline as it is used in
GPS.
• There are three types of differencing, the single difference, double difference, and
triple difference.
• Within the single difference category, there are the between-receivers single
difference and the between-satellites single difference.
• Both require that all the receivers observed the same satellites at the same time.
• a single difference, also known as a between-receivers difference, refers to the
difference in the simultaneous carrier phase measurements from one GPS
satellite as measured by two different receivers. In the illustration there are two
receivers-- q and r-- observing the same satellite.

Between Receiver Single Differencing
Between Receivers Single Difference

Between-Receivers Single Difference
• A between-receivers single difference reduces the effect of biases even though it doesn’t eliminate them.
• Since the two receivers are both observing the same satellite at the same time, the difference between the satellite clock bias, dt,
at the first receiver and dt at the second receiver, Δdt, is obviously zero.
• Also, since the baseline is typically short compared with the 20,000-km altitude of the GPS satellites, the atmospheric biases and
the orbital errors, i.e. ephemeris errors, recorded by the two receivers at each end are similar.
• This correlation obviously decreases as the length of the baseline increases.
• Generally speaking this correlation allows centimeter level carrier phase positioning with baselines up to 10km or so and meter
level positioning with baselines of a few hundreds of kilometers using pseudorange observations.
• The between-receivers single difference provides better position estimates for the receivers by subtracting, differencing, each
receiver’s observation equation from the other.
• For example, if one of the receivers is a base standing at a control station whose position is known it follows that the size of the
positional error of the receiver there is knowable.
• Therefore the positional error at the other end of the baseline can be estimated by finding the difference between the biases at
the base and the biases at the rover.
• Corrections can then be generated which can reduce the three-dimensional positional error at the unknown point by reducing the
level of the biases there.
• It is primarily this correlation and the subsequent ability to reduce the level of error that distinguishes differenced relative
positioning from single point positioning.

Between-Satellites Single Difference

Between-Satellites Single Difference
• The between-satellites single difference involves a single receiver observing
two GPS satellites simultaneously and the code and/or phase
measurement of one satellite are differenced, subtracted, from the other.
• The data available from the between-satellites difference allows the
elimination of the receiver clock error because there is only one involved.
• And the atmospheric effects on the two satellite signals are again nearly
identical as they come into the lone receiver, so the effects of the
ionospheric and tropospheric delays are reduced.
• However, unlike the between-receivers single difference the between-
satellites single difference does not provide a better position estimate for
the receiver involved.
• In fact, the resulting position of the receiver is not better than would be
derived from single point positioning.

Double Difference
• When the two types of single differences are combined the result is known as a double difference.
• A double difference can be said to be a between-satellite single difference of a between-receiver single
difference.
• The improved positions from the between-receiver single difference step are not further enhanced by the
combination with the between-satellite single difference.
• Still including the between-satellite single difference is useful because the combination virtually eliminates
clock errors; both the satellite and receiver clock errors.
• The removal of the receiver clock bias in the double difference makes it possible to segregate the errors
attributable to the receiver clock biases from those from other sources.
• This segregation improves the efficiency of the estimation of the integer cycle ambiguity in a carrier phase
observation, N.
• In other words, the reduction of all the non-integer biases makes the computation of the final accurate
positions more efficient.
• The double difference, for all practical purposes, has eliminated the receiver clock errors and the satellite
clock errors.
• This is used in most GPS post-processing and software.
• The integer ambiguity, N, still remains with the carrier phase observation.

Triple Difference
• A triple difference is the difference of two double differences over
two different epochs.
• The triple difference has other names.
• It is also known as the receiver satellite-time triple difference and
the between-epochs difference.
• Triple differencing serves as a good pre-processing step because it can
be used to detect and repair of cycle slips.

A cycle slip
• A cycle slip is a discontinuity in a receiver’s continuous phase lock on a satellite’s signal.
• A power loss, a very low signal-to-noise ratio, a failure of the receiver software, a malfunctioning
satellite oscillator can cause a cycle slip. I
• t can also be caused by severe ionospheric conditions.
• Most common, however, are obstructions such as buildings, trees and etc. that are so solid they
prevent the satellite signal from being tracked by the receiver.
• Under such circumstances, when the satellite reappears, the tracking resumes.
• Coded pseudorange measurements are virtually immune from cycle slips, but carrier phase
positioning accuracy suffers if cycle slips are not detected and repaired.
• A cycle slip causes the critical component for successful carrier phase positioning, a resolved
integer cycle ambiguity, N, to become instantly unknown again.
• In other words, lock is lost. When that happens correct positioning requires that N be
reestablished.
• There are several methods of handling cycle slips. They are often controlled in post-processing
rather than real-time.

Repairing Cycle Slips
• In post-processing the location and their size of cycle slips must be determined;
then the data set can be repaired with the application of a fixed quantity to all
the subsequent phase observations.
• One approach is to hold the initial positions of the stations occupied by the
receivers as fixed and edit the data manually.
• Another approach is to model the data on a satellite-dependent basis with
continuous polynomials to find the breaks and then manually edit the data set a
few cycles at a time
• One of the most convenient of these methods is based on the triple difference.
• It can provide an automated cycle slip detection system that is not confused by
clock drift and, once least-squares convergence has been achieved, it can provide
initial station positions even using the unrepaired phase combinations.
• They may still contain cycle slips but the data can nevertheless be used to process
approximate baseline vectors.

Receivers and Methods
• The receivers are the most important hardware in a GPS surveying operation.
• Their characteristics and capabilities influence the techniques available to the user
throughout the work.
• There are many different GPS receivers on the market. Some of them are appropriate for
surveying and they share some fundamental elements.
• Most are also capable of performing differential GPS, real-time GPS, static GPS, etc. and
are usually accompanied by processing and network adjustment software and so on.
• GPS receivers come in a variety of shapes and sizes.
• Some have external batteries, data collectors.
• Some are tripod mounted.
• Some are hand-held and have all components built in and some can be used in both
ways, with externals and without.
• Nevertheless most have similar characteristics.

GPS Receiver
• A GPS receiver must collect and then convert signals from GPS satellites into measurements of position, velocity and time.
• There is a challenge in that the GPS signal has low power.
• An orbiting GPS satellite broadcasts its signal across a cone of approximately 28º of arc.
• From the satellite’s point of view, about 11,000 miles up, that cone covers a substantial portion of the whole planet.
• the typical GPS receiver has a small, relatively non-directional antenna.
• GPS satellite spreads a low power signal over a large area rather than directing a high power signal at a very specific area.
• Fortunately, antennas used for GPS receivers do not have to be pointed directly at the signal source.
• The GPS signal also intentionally occupies a broader bandwidth than it must to carry its information.
• This characteristic is used to prevent jamming and mitigate multipath but most importantly the GPS signal itself would be
completely obscured by the variety of electromagnetic noise that surrounds us if it were not a spread spectrum coded signal.
• When a GPS signal reaches a receiver its power is actually less than the receivers natural noise level, fortunately the receiver can
still extract the signal and achieve unambiguous satellite tracking using the correlation techniques
• To do this job the elements of a GPS receiver function cooperatively and iteratively.
• From the point of view of a GPS satellite, the earth presents a disk that really, from 11,000 miles up, has a spread of approximately
28 degrees.

The Antenna
• Most receivers have an antenna built in, but many can accommodate a separate tripod-
mounted or range pole-mounted antenna as well.
• These separate antennas with their connecting coaxial cables in standard lengths are
usually available from the receiver manufacturer.
• The longer the cable, the more of the GPS signal is lost traveling through it.
• These connecting coaxial cables are usually at standard lengths in an effort to make sure
that the impedance of the trip through the cable can be calibrated to the receiver.
• As mentioned earlier the wavelengths of the GPS carriers are 19 cm (L1), 24 cm (L2) and
25 cm (L5) and antennas that are a quarter or half wavelength tend to be the most
practical and efficient so GPS antenna elements can be as small as 4 or 5 cm.
• Most of the receiver manufacturers use a microstrip antenna. These are also known as
patch antennas.
• The microstrip may have a patch for each frequency. Microstrip antennas are durable,
compact, have a simple construction and a low profile.

Antenna
• The next most commonly used antenna is known as a dipole.
• A dipole antenna has a stable phase center and simple construction, but needs a
good ground plane
• A quadrifilar antenna is a single frequency antenna that has two orthogonal
bifilar helical loops on a common axis.
• Quadrifilar antennas perform better than a microstrip on crafts that pitch and roll
like boats and airplanes.
• They are also used in many recreational handheld GPS receivers.
• Such antennas have a good gain pattern, do not require a ground plane, but are
not azimuthally symmetric.
• The least common design is the helix antenna.
• A helix is a dual frequency antenna. It has a good gain pattern, but a high profile.

Antenna height
• The antenna's configuration also affects another measurement critical to
successful GPS surveying - the height of instrument.
• The measurement of the height of the instrument in a GPS survey is
normally made to some reference mark on the antenna.
• However, it sometimes must include an added correction to bring the total
vertical distance to the antenna’s phase center.
• Here in this diagram, you see very many ways of measuring that height.
• It can be measured at slant height or measured with a tape, usually to the
antenna reference point. the ARP, or the antenna reference point, is
frequently the bottom of the mount of the antenna.
• Of course, then there's usually a correction that is needed to be added to
actually bring that measurement up to the phase center of the antenna.

Pre-amplifier
• The pre-amplifier is necessary because the signal coming in from the GPS satellite is weak.
• It needs to be amplified to some degree to be accessible to the rest of the circuits in the receiver.
• It's important that the gain in the signal coming out of the preamp is higher than the noise.
• Noise is always part of the signal. The signal to noise ratio (SNR) is a statistic in any GPS signal.
• Since the signal processing is easier if the signals arriving from the antenna are in a common
frequency, the incoming frequency is combined with the signal at a harmonic frequency.
• The sinusoidal signal is the previously mentioned reference signal generated by the receiver's
oscillator.
• The two frequencies are multiplied together in a device known as a mixer.
• Two frequencies emerge.
• One of them is the sum of the two that went in and the other is the difference between them.
The sum and the difference of the frequencies then go through a band-pass filter.

The RF Section
• The sum and difference frequencies then go through a bandpass filter
• an electronic filter that removes the unwanted high frequencies and
selects the lower of the two.
• It also eliminates some of the noise from the signal.
• For tracking the P-code this filter will have a bandwidth of about 20 MHz,
but it will be around 2 MHz if the C/A code is required.
• The signal that results is known as the intermediate frequency (IF), or beat
frequency signal.
• This beat frequency is the difference between the Doppler-shifted carrier
frequency that came from the satellite and the frequency generated by the
receiver’s own oscillator.

Tracking Loops, Channels and the Microprocessor

Tracking Loops, Channels and the Microprocessor
• The antenna itself does not sort the information it gathers.
• The signals from several satellites enter the receiver simultaneously.
• But in the channels of the RF section the undifferentiated signals are
identified and segregated from one another.
• A receiver may have 6 channels, 12 channels or hundreds of channels.
• At any given moment, one frequency from one satellite can have its
own dedicated channel and the channels operate in parallel.

The Microprocessor
• The microprocessor controls the entire receiver, managing its collection of data.
• It controls the digital circuits that in turn manage the tracking and measurements,
extract the ephemerides and other information from the Navigation message or
CNAV, and mitigate multipath and noise among other things.
• The GPS receivers used in surveying often send these data to the storage unit.
• But more and more they are expected to process the ranging data, do datum
conversion, and produce their final positions instantaneously, that is, in real-time.
• And then serve up the position through the control and display unit (CDU). There
is a two-way street between the microprocessor and the CDU each can receive
information from or send information to the other.

The CONTROL DISPLAY UNIT (CDU)

CDU
• A GPS receiver will often have a control and display unit.
• From handheld keyboards to soft keys around a screen to digital map displays and interfaces to
other instrumentation there are a variety of configurations.
• Nevertheless they all have the same fundamental purpose, facilitation of the interaction between
the operator and the receiver’s microprocessor.
• A CDU typically displays status, position data, velocity and time.
• It may also be used to select different surveying methods waypoint navigation and/or set
parameters such as epoch interval, mask angle, and antenna height.
• The CDU can offer a combination of help menus, prompts, datum conversions, readouts of survey
results, estimated positional error, and so forth.
• But when four or more satellites are available they can generally be expected to display the PRN
numbers of the satellites being tracked,
• the receiver’s position in three dimensions, and velocity information.
• Most of them also display the dilution of precision and GPS time.

The Storage
• Most GPS receivers today have internal data logging.
• The amount of storage required for a particular session depends on several
things: the length of the session, the number of satellites above the
horizon, the epoch interval, and so forth.
• For example, presuming the amount of data received from a single GPS
satellite is ~100 bytes per epoch, a typical twelve channel dual-frequency
receiver observing 6 satellites and using a 1-second epoch interval over the
course of a 1-hour session would require ~2MB of storage capacity for that
session.
• The miniaturization of storage continues. The cassettes, floppy disks and
drives used with the Macrometer are past and extraordinary amounts of
data can be stored in small convenient devices.

The Power
• Since most receivers in the field operate on battery power, batteries and their characteristics are
fundamental to GPS surveying. A variety of batteries are used and there are various
configurations.
• in surveying applications rechargeable batteries are the norm. Lithium, Nickel Cadmium, and
Nickel Metal-Hydride may be the most common categories, but lead-acid car batteries still have
an application as well.
• The obvious drawbacks to lead-acid batteries are size and weight. And there are a few others—
the corrosive acid, the need to store them charged, and their low cycle life. Nevertheless lead-
acid batteries are especially hard to beat when high power is required. They are economical and
long lasting.
• Nickel Cadmium batteries (NiCd) cost more than lead-acid batteries but are small and operate
well at low temperatures. Their capacity does decline as the temperature drops. Like lead-acid
batteries, NiCd batteries are quite toxic. They self-discharge at the rate of about 10% per month
and even though they do require periodic full discharge these batteries have an excellent cycle
life. Nickel Metal-Hydride (NiMH) batteries self-discharge A bit more rapidly than NiCd batteries
and have a less robust cycle life, but are not as toxic.

POWER
• Lithium–ion batteries overcome several of the limitations of the others. They have a
relatively low self-discharge rate. They do not require periodic discharging and do not
have a memory issues as do NiCd batteries. They are light, have a good cycle life and low
toxicity. On the other hand, the others tolerate overcharging and the lithium-ion battery
does not. It is best to not charge lithium-ion batteries at temperatures at or below
freezing. These batteries require a protection circuit to limit current and voltage but are
widely used in powering electronic devices, including GPS receivers.
• The use of lithium ion is becoming more and more common. They don't require
discharging and don't have the memory problems. They're light and have low toxicity.
• About half of the available GPS carrier phase receivers have an internal power supply and
most will operate 5½ hours or longer on fully charged 6-amp-hour battery. Most code-
tracking receivers, those that do not also use the carrier phase observable, could operate
for about 15 hours on the same size battery.
• It is fortunate that GPS receivers operate at low power, from 9 to 36 volts DC, is generally
required. This allows longer observations with fewer, and lighter, batteries than might be
otherwise required. It also increases the longevity of the GPS receivers themselves.

CHOOSING A RECEIVER
Factors to consider when choosing a receiver
• What observable is to tracked?
• C/A code on the L1 frequency
• C/A and P codes on L1 and L2 frequency
• L1 carrier phase tracking receivers
• Dual-frequency carrier phase tracking receiver
• Memory size
• Cost
• Accuracy

GPS Survey Methods
• GPS positioning techniques may be categorized as being
predominantly based on code or carrier measurements.
• Code techniques are generally simple and produce low accuracies, while
• carrier techniques are more complex and produce higher accuracies (Table
2.2).
• For both code and carrier measurements, a variety of positioning
methods exist. The suitability of each for a specific application is
dependent on the desired accuracies, logistical constraints and costs.

Absolute GPS Positioning Techniques
• The accuracy obtained by GPS
point positioning is dependent on
the user’s authorization.
• The SPS user can provide an
accuracy of 80-100 m.
• SPS data are most often expressed
in real time.

Absolute (Point Positioning) Techniques
• There are two techniques used for point positioning
in the absolute mode. They are long-term averaging
of positions and differencing between signals.
• In long-term averaging, a receiver is set up to store
positions over a period of observation time. The length of
observation time varies based upon the accuracy required.
The longer the period of data collection, the better average
position. These observation times can range between 1 and
24 hr. This technique can also be used in real-time (i.e., the
receiver averages the positions as they are calculated).
• The process of differencing between signals can only be
performed in a post-processed mode. Currently, the
Defense Mapping Agency has produced software that can
perform this operation.

Differential Code Phase GPS Positioning
Techniques
• Differential (or relative) GPS surveying is the determination of one
location with respect to another location.
• When using this technique with the C/A- or P-code it is called relative
code phase positioning or surveying.
• Relative code phase positioning has limited application to detailed
engineering surveying and topographic site plan mapping
applications.

Relative Code Phase Positioning
• Although greater positional
accuracies can be obtained
with use of the P-code, DoD’s
implementation of A/S will
limit its use.
• A real-time dynamic DGPS
positioning system includes a
reference station,
communication link, and user
(remote) equipment.
• If results are not required in
real-time, the communication
link can be eliminated and the
positional information is
postprocessed.

Differential Carrier Phase GPS Horizontal
Positioning Techniques
• There are basically six different GPS differential
surveying techniques in use today:
1. Static.
2. Pseudo-kinematic.
3. Stop and go kinematic.
4. Kinematic.
5. Rapid static.
6. On-the-fly (OTF)/Real-time kinematic (RTK).

GPS survey techniques
• Procedurally, all six methods are similar in that each
measures a 3D baseline vector between a receiver at
one point (usually of known local project coordinates)
and a second receiver at another point, resulting in a
vector difference between the two points occupied.
• The major distinction between static and kinematic
baseline measurements involves the method by
which the carrier wave integer cycle ambiguities are
resolved; otherwise they are functionally the same
process.

Ambiguity resolution
• Cycle ambiguity is the unknown number of whole carrier
wavelengths between the satellite and receiver. It is also
referred to as “Integer Ambiguity.”
• Successful ambiguity resolution is required for successful
baseline formulations. Generally, in static surveying,
instrumental error and ambiguity resolution can be
achieved through long-term averaging and simple
geometrical principles, resulting in solutions to a linear
equation that produces a resultant position.
• But ambiguity resolution can also be achieved through a
combination of the pseudo-range and carrier beat
measurements, made possible by a knowledge of the PRN
modulation code.

Post-observation data reduction
• Currently, all carrier phase relative surveying
techniques, except OTF and RTK, require post-
processing of the observed data to determine the
relative baseline vector differences.
• OTF and RTK can be performed in real-time or in the
post processed mode. Post-processing of observed
satellite data involves the differencing of signal phase
measurements recorded by the receiver.
• The differencing process reduces biases in the receiver
and satellite oscillators and is performed in a computer.
• It is recommended that all baseline reductions be
performed in the field, if possible, in order to allow an
onsite assessment of the survey adequacy.

Static GPS Survey Techniques
• the most common method of densifying project network
control.
• Two GPS receivers are used to measure a GPS baseline
distance.
• The line between a pair of GPS receivers from which
simultaneous GPS data have been collected and processed is
a vector referred to as a baseline.
• The station coordinate differences are calculated in terms of a
3D, earth centred coordinate system that utilizes X-, Y-, and Z-
values based on the WGS 84 geocentric ellipsoid model.
• These coordinate differences are then subsequently shifted to
fit the local project coordinate system.

Survey procedure
• GPS receiver pairs are set up over stations of either
known or unknown location.
• Typically one of the receivers is positioned over a
point whose coordinates are known (or have been
carried forward as on a traverse), and the second is
positioned over another point whose coordinates are
unknown, but are desired.
• Both GPS receivers must receive signals from the
same four (or more) satellites for a period of time that
can range from a few minutes to several hours,
depending on the conditions of observation and
precision required.

Static baseline occupation time
• Station occupation time is dependent on baseline
length, number of satellites observed, and the GPS
equipment used.
• In general, 30 min to 2 hr is a good approximation for
baseline occupation time for shorter baselines of 1-30
km.
• For baselines greater than 50 km in length, the
ionosphere may have an adverse effect on the solution.
• Adverse ionosphere effects for baselines of this length
can be reduced by using a dual-frequency GPS receiver,
as opposed to a single frequency as is normally used.

Accuracy of static surveys
• One of the main reasons for occupying sites for over an hour (sometimes
several hours) is to exploit the change in geometry as satellites track paths
across the sky.
• It is this change in geometry which assists in ambiguity resolution and
helps to improve the strength of solution.
• The range of accuracy using conventional static GPS varies depending on
the observing and processing procedures followed, the baseline lengths
measured and the receivers used, among other variables.
• In very precise applications (e.g. for crustal motion studies, geodetic
surveys etc.) sophisticated processing techniques which handle errors in
special ways are employed. Using such techniques, accuracies of less than 1
cm rms have been achieved for baselines of up to 600 km in length.

Stop-and-Go Kinematic GPS Survey Techniques
• Stop-and-go surveying is similar to static surveying in that each
method requires at least two receivers simultaneously recording
observations.
• A major difference between static and stop-and-go surveying is the
amount of time required for a receiver to stay fixed over a point of
unknown position.
• In stop – and – go surveying, the first receiver—the home or reference
receiver – remains fixed on a known control point. The second
receiver— the “rover” receiver – collects observations statically on a
point of unknown position for a period of time (usually a few
minutes), and then moves to subsequent unknown points to collect
signals for a short period of time.
• During the survey, at least four common satellites (preferably five)
need to be continuously tracked by both receivers.

Stop-and-Go Kinematic GPS Survey Techniques
• Once all required points have been occupied by the rover
receiver, the observations are then post-processed by a
computer to calculate baseline vector/coordinate differences
between the known control point and points occupied by the
rover receiver during the survey session.
• The main advantage of this form of GPS surveying over static
surveying is the reduced occupation time required over the
unknown points.
• Because stop-and-go surveying requires less occupation time
over unknown points, time and cost for the conduct of a
survey are significantly reduced. Achievable accuracies
typically equal or exceed Third-Order, which is adequate for
most USACE projects.

Survey procedure
• Stop-and-go GPS surveying is performed similarly to a conventional EDM
traverse or electronic total station radial survey. The system is initially
calibrated by performing either an antenna swap with one known point
and one unknown point or by performing a static measurement over a
known baseline.
• This calibration process is performed to resolve initial cycle ambiguities.
This known baseline may be part of the existing network or can be
established using static GPS survey procedures described above.
• The remote roving receiver then traverses between unknown points as if
performing a radial topographic survey. Typically, the points are double-
connected, or double-run, as in a level line.
• Optionally, two fixed receivers may be used to provide redundancy on the
remote points. With only 1-1/2 min at a point, X-Y-Z coordinate production
is high and limited only by satellite observing windows, travel time
between points, and overhead obstructions.

Satellite lock
• During a stop-and-go kinematic survey, the rover station must
maintain lock on at least four satellites during the period of survey (the
reference station must be observing at least the same four satellites).
• Loss of lock occurs when the receiver is unable to continuously record
satellite signals or the transmitted satellite signal is disrupted and the
receiver is not able to record it.
• If satellite lock is lost, the roving receiver must re-observe the last
control station surveyed before loss of lock. The receiver operator
must monitor the GPS receiver when performing the stop-and-go
survey to ensure loss of lock does not occur.
• Some manufacturers have now incorporated an alarm into their
receiver that warns the user when loss of lock occurs, thus making the
operator’s job of monitoring the receiver easier.

Antenna swap calibration procedure
• Although the antenna swap procedure can be used to initialize a
survey prior to a stop-and-go survey, an antenna swap can also be
used to determine a precise baseline and azimuth between two
points.
• The procedure requires that both stations occupied and the path
between both stations maintain an unobstructed view of the horizon.
• A minimum of four satellites and maintainable lock are required to
perform an antenna swap; however, more than four satellites are
preferred.
• To perform an antenna swap, one receiver/ antenna is placed over a
point of known control and the second, a distance of 10 to 100 m
away from the other receiver.

• Referring to the Figure above, the receivers at each station collect
data for approximately 2 to 4 min. The receivers/antennae sets then
swap locations; the receiver/antenna at the known station is moved
to the unknown site while the other receiver/antenna at the
unknown site is moved to the known site.
• Satellite data are again collected for 2 to 4 min.
• The receivers are then swapped back to their original locations.
• This completes one antenna swap calibration.
• If satellite lock is lost during the procedure, the procedure must be
repeated.

Accuracy of stop-and-go surveys
• Accuracy of stop-and-go baseline measurements will usually well
exceed 1 part in 5,000; thus,
• Third-Order classification project/mapping horizontal control can be
effectively, efficiently, and accurately established using this technique
• Good satellite geometry and minimum multipath are also essential in
performing acceptable stop-and-go surveys

Kinematic GPS Survey Techniques
• Kinematic (dynamic) surveying using differential carrier phase
tracking is similar to the two previous types of differential carrier
phase GPS surveying because it also requires two receivers recording
observations simultaneously.
• As in stop-and-go surveying, the reference receiver remains fixed on a
known control point while the roving receiver collects data on a
constantly moving platform (vehicle, vessel, aircraft, manpack, etc.),
• Unlike stop-and-go surveying, kinematic surveying techniques do not
require the rover receiver to remain motionless over the unknown
point.
• The observation data are later post-processed with a computer to
calculate relative vector/coordinate differences to the roving receiver.

Survey procedure
• A kinematic survey requires two single frequency (L1) receivers. One
receiver is set over a known point (reference station) and the other is
used as a rover (i.e., moved from point to point or along a path).
• Before the rover receiver can rove, a period of static initialization or
antenna swap must be performed. This period of static initialization is
dependent on the number of satellites visible.
• Once this is done, the rover receiver can move from point to point as
long as satellite lock is maintained on at least four common (with the
reference station) satellites. If loss of satellite lock occurs, a new
period of static initialization must take place.
• It is important to follow manufacturers’ specifications when
performing a kinematic survey.

Kinematic data processing techniques
• In general, kinematic data processing techniques are similar to those
used in static surveying.
• When processing kinematic GPS data, the user must ensure that
satellite lock was maintained on four or more satellites and that cycle
slips are adequately resolved in the data recorded.

Accuracy of kinematic surveys
• Differential (carrier phase) kinematic survey errors are correlated
between observations received at the reference and rover receivers,
as in differential static surveys.
• Experimental test results indicate kinematic surveys can produce
results in centimeters and it has been verified (under ideal test
conditions) that kinematic GPS surveying could achieve centimeter-
level accuracy over distances up to 30 km.

Pseudo-Kinematic GPS Survey Techniques
• Pseudo-kinematic GPS surveying is similar to stop-and-go techniques
except that loss of satellite lock is tolerated when the receiver is
transported between occupation sites (in fact, the roving receiver can
be turned off during movement between occupation sites, although
this is not recommended).
• This feature provides the surveyor with a more favourable positioning
technique since obstructions such as bridge overpasses, tall buildings,
and overhanging vegetation are common.
• Loss of lock that may result due to these obstructions is more
tolerable when pseudo kinematic techniques are employed.

Survey procedure
• The pseudo-kinematic techniques require that one receiver be placed
over a known control station.
• A rover receiver occupies each unknown station for 5 min.
• Approximately 1 hr after the initial station occupation, the same rover
receiver must reoccupy each unknown station.

Common satellite requirements
• The pseudo-kinematic technique requires that at least four of the
same satellites are observed between initial station occupations and
the requisite reoccupation.
• For example, the rover receiver occupies Station A for the first 5 min
and tracks satellites 6, 9, 11, 12, 13; then 1 hr later, during the second
occupation of Station A, the rover receiver tracks satellites 2, 6, 8, 9,
19.
• In this example, only satellites 6 and 9 are common to the two sets,
so the data cannot be processed because four common satellites
were not tracked for the initial station occupation and the requisite
reoccupation

Planning
• Prior mission planning is essential in conducting a successful pseudo-
kinematic survey.
• Especially critical is the determination of whether or not common
satellite coverage will be present for the desired period of the survey.
• Also, during the period of observation, one receiver, the base
receiver, must continuously occupy a known control station.

Pseudo-kinematic data processing
• Pseudo-kinematic survey satellite data records and resultant baseline
processing methods are similar to those performed for static GPS
surveys.
• Since the pseudo-kinematic technique requires each station to be
occupied for 5 min and then reoccupied for 5 min approximately an
hour later, this technique is not suitable when control stations are
widely spaced and transportation between stations within the
allotted time is impractical.
Accuracy of pseudo-kinematic surveys.
• Pseudo kinematic survey accuracies are similar to kinematic survey
accuracies of a few centimetres.

Rapid Static Surveying Procedures
• Rapid static surveying is a combination of the stop-and-go kinematic,
pseudo-kinematic, and static surveying methods.
• The rover or remote receiver spends only a short time on each
station, loss of lock is allowed between stations, and accuracies are
similar to static.
• However, rapid static surveying does not require re-observation of
remote stations like pseudo-kinematic.
• The rapid static technique does require the use of dual-frequency
(L1/L2) GPS receivers with either cross correlation or squaring or any
other technique used to compensate for A-S.

Survey procedure
• Rapid static surveying requires that one receiver be placed over a
known control point.
• A rover or remote receiver occupies each unknown station for 5-20
min, depending on the number of satellites and their geometry.
• Because most receiver operations are manufacturer-specific,
following the manufacturers’ guidelines and procedures for this type
of survey is important.

Rapid Static Surveying Procedures
Rapid static data processing.
• Data collected in the rapid static mode should be processed in accordance
with the manufacturer’s specifications.
Accuracy of rapid static surveys.
• Accuracies of rapid static surveys are similar to static surveys of a centimetre
or less.
• This method can be used for medium-to high accuracy surveys up to
1/1,000,000.

OTF/RTK Surveying Techniques
• OTF/RTK surveying is similar to kinematic differential GPS surveying
because it requires two receivers recording observations
simultaneously and allows the rover receiver to be moving.
• Unlike kinematic surveying, OTF/RTK surveying techniques use dual-
frequency L1/L2 GPS observations and can handle loss of satellite
lock.
• Since OTF/RTK uses the L2 frequency, the GPS receiver must be
capable of tracking the L2 frequency during A-S.
• There are several techniques used to obtain L2 during A-S. These
include the squaring and cross-correlation methods.

Ambiguity resolution
• successful ambiguity resolution is required for successful baseline
formulations. The OTF/RTK technology allows the remote to initialize
and resolve these integers without a period of static initialization.
• With OTF/RTK, if loss of satellite lock occurs, initialization can occur
while in motion.
• The integers can be resolved at the rover within 10-30 sec, depending
on the distance from the reference station. OTF/RTK uses the L2
frequency transmitted by the GPS satellites in the ambiguity
resolution.
• After the integers are resolved, only the L1 C/A is used to compute
the positions.

Survey procedure
• OTF/RTK surveying requires dual frequency L1/L2 GPS receivers. One of the
GPS receivers is set over a known point, and the other is placed on a
moving or mobile platform. If the survey is performed in real time, a data
link and a processor (external or internal) are needed.
• The data link is used to transfer the raw data from the reference station to
the remote.
• (1) Internal processor. If the OTF/RTK system is done with an internal
processor (i.e., built into the receiver), follow manufacturer’s guidelines.
• (2) External processor. If OTF/RTK is performed with external processors
(i.e., notebook computer), then computer at the reference collects the raw
GPS data and formats it to be sent via a data link to the remote. The
computer at the rover processes the raw data from the reference and
remote receivers to resolve the integers and obtain a position.

Accuracy of OTF/RTK surveys
• OTF/RTK surveys are accurate to within 10 cm when the distance
from the reference to the rover does not exceed 20 km.
• Results of testing by TEC produced results of less then 10 cm.

The Receiver Independent Data Format RINEX
• Each receiver type has its own binary data format, and the observables are
defined following the manufacturers' individual concepts.
• Time tags may be defined in transmission time, or in receiver time; phase
measurement may be expressed in whole cycles, or in fractional parts of
cycles; code and phase may have different or identical time tags, and
satellites may be observed simultaneously or at different epochs.
• As a consequence, data of different receiver types cannot easily be
processed simultaneously with one particular GPS data processing
software package.
• To solve this problem, either all manufacturers have to use the same data
output format, or a common data format has to be defined that can be
used as a data interface between all geodetic receiver types, and the
different processing software systems.

RINEX
• The first has not been realized to date.
• However, a successful solution has been found to define and accept a
common data format for international data exchange.
• Receiver In- dependent Exchange Format RINEX was proposed by Gurtner
et al. (1989)
• RINEX has indeed been accepted by the international user community and
by the community of receiver manufacturers.
• For most geodetic receivers translator software is provided by the
manufacturers that converts the receiver dependent data into the RINEX
format.
• In addition, all major data processing software requires RINEX data as an
input. RINEX hence serves as a general interface between receivers and
multi- purpose data processing software.

RINEX
• With RINEX, one of the most serious obstacles to the routine mixing of data
from different receiver types is removed.
• RINEX defines three fundamental quantities in the GPS observables: Time,
Range, and Phase.
• The time of measurement is the receiver time of the received signals.
• It is identical for the phase and range measurements and is identical for all
satellites observed at that epoch. It is expressed in GPS time (not in UT).
• The pseudorange is the distance from the receiver antenna to the satellite
antenna, including receiver and satellite clock offsets and other biases
• so that the pseudorange reflects the actual behavior of the receiver and
satellite clocks.

RINEX
• The basic RINEX format consists of three ASCII file types:
1. Observation Data File
2. Meteorological Data File
3. Navigation Message File.
• Each file type consists of a header section and a data section.
• The observation file usually contains the data collected by one receiver at one station during one session.
• It is also possible to include observation data collected in sequence by a roving receiver during rapid static or
kinematic surveys.
• From the long list of revision details only some major items are indicated:
- inclusion of GLONASS data (since 1997),
- continuous numbering of the GPS week; no rollover (1998),
- inclusion of navigation data from GEO satellites (2000), and
- inclusion of navigation data from LEO satellites (2001).
• RINEX is the international exchange format for the postprocessing of GPS data.
• For the transmission of data corrections, in real-time, in relative (Differential) GPS applications, a particular
data format is available: the RTCM format.

Dilution of Precision (DOP)
• The distribution of the satellites above an observer’s horizon has a direct bearing on the quality of the
position derived from them.
• The accuracy of a GPS position is subject to a geometric phenomenon called dilution of precision (DOP).
• This number is somewhat similar to the strength of figure consideration in the design of a triangulation
network.
• DOP concerns the geometric strength of the figure described by the positions of the satellites with respect
to one another and the GPS receivers.
• A low DOP factor is good, a high DOP factor is bad.
• In other words, when the satellites are in the optimal configuration for a reliable GPS position the DOP is
low, when they are not, the DOP is high.
• Four or more satellites must be above the observer’s mask angle for the simultaneous solution of the clock
offset and three dimensions of the receiver’s position.
• But if all of those satellites are crowded together in one part of the sky, the position would be likely to have
an unacceptable uncertainty and the DOP, or dilution of precision, would be high.
• In other words, a high DOP is a like a warning that the actual errors in a GPS position are liable to be larger
than you might expect.
• But remember, it is not the errors themselves that are directly increased by the DOP factor; it is the
uncertainty of the GPS position that is increased by the DOP factor.

DOP
• Now since a GPS position is derived from a three dimensional solution there are several
DOP factors used to evaluate the uncertainties in the components of a GPS position.
• There is horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP)
where the uncertainty of a solution for positioning has been isolated into its horizontal
and vertical components, respectively.
• When both horizontal and vertical components are combined, the uncertainty of three-
dimensional positions is called position dilution of precision (PDOP).
• There is also time dilution of precision (TDOP), which indicates the uncertainty of the
clock.
• There is geometric dilution of precision (GDOP), which is the combination of all of the
above.
• And finally, there is relative dilution of precision (RDOP), which includes the number of
receivers, the number of satellites they can handle, the length of the observing session,
as well as the geometry of the satellites’ configuration.

DOP
• PDOP is perhaps the most common, which combines both horizontal and vertical.
• But the idea is very straightforward in the sense that the better the geometry, the
better the intersection of the ranges from the satellites, the lower that the
dilution of precision value will be and the better the position derived will be.
• This is a very practical consideration in GPS work.
• The size of the DOP factor is inversely proportional to the volume of the
tetrahedron described by the satellites positions and the position of the receiver.
• The larger the volume of the body defined by the lines from the receiver to the
satellites, the better the satellite geometry and the lower the DOP.
• An ideal arrangement of four satellites would be one directly above the receiver,
the others 120° from one another in azimuth near the horizon.
• With that distribution the DOP would be nearly 1, the lowest possible value.
• In practice, the lowest DOPs are generally around 2.

DOP
• The mask angle plays a part here.
• If you had four satellites and three of them were at the horizon and one was directly overhead
this would be a very low dilution of precision value.
• However, you wouldn't want to track satellites that were right against the horizon.
• You want them above this mask angle, 10 or 15 degree mask angle, to try to minimize the effect
of the ionosphere.
• The users of most GPS receivers can set a PDOP mask to guarantee that data will not be logged if
the PDOP goes above the set value.
• A typical PDOP mask is 6.
• As the PDOP increases the accuracy of the pseudorange positions probably deteriorate, and as it
decreases they probably improve.
• When a DOP factor exceeds a maximum limit in a particular location, indicating an unacceptable
level of uncertainty exists over a period of time, that period is known as an outage.
• This expression of uncertainty is useful both in interpreting measured baselines and planning a
GPS survey.

GPS PROCEDURES
• Although GPS positioning techniques vary significantly
their procedures may be grouped into four common
phases:
• planning and preparation;
• Field operations;
• data processing; and
• final reporting.
• Validation and reconnaissance form an integral part of the
planning and preparation phase.

PLANNING AND PREPARATION
• Planning and preparation for a GPS field project begins with the identification
of positioning requirements and ends with complete readiness for successful
field operations.
• The extent of all the intermediate steps varies greatly with the magnitude,
accuracy and locality of the project. As a preliminary step, the points to be
positioned and their accuracy requirements should be identified.
• Then, the sites to be positioned and the available survey control should be
plotted on a map. Topographical maps at 1:50,000 and 1:250,000 are well
suited for this purpose. Maps show the approximate distances between points,
site access information, and the potential for obstructions and interference.
They serve as a reference throughout the planning, project execution and final
reporting stages. Important steps within the planning and preparation phase
which follow, include:
• selection of positioning technique,
• selection of receiver type,
• validation,
• reconnaissance,
• survey design and preparations.
• As will be seen, many of these planning steps are quite interdependent.

Selection of Positioning Technique
• There are many aspects which influence the choice of positioning
technique. Accuracy requirements, the geographical environment,
the distance between points to be positioned and the costs are
major considerations. Suggested GPS positioning techniques to
achieve given horizontal accuracy requirements include:
•Note that the figure shows the technique which should be used to
achieve a given accuracy rather than the technique's accuracy range

Selection of Positioning Technique
• The cost of GPS positioning is closely tied to the technique used,
which in turn is chiefly a product of the accuracy requirements.
• Two major reasons for cost variations with technique are the time on
site requirements and the cost of the required receivers.
• Generally, the shorter the time required on site, the lower the survey
cost.
• The selection of a receiver type and its costs, to satisfy a required
positioning technique is worthy of discussion.

Selection of Receiver Type
• it is suggested that all receivers used together for relative positioning
be of the same make to avoid problems which often result from
mixing receiver types such as biases, complexities in data processing
and data rate incompatibilities.
• The receiver used must be capable of collecting the measurements
needed for the desired positioning technique.

Aspects to Consider in Receiver Selection

Validation
• In the planning phase of a GPS project the procedures and equipment
to be used, from data collection to the final product, should be tested
to ensure they reliably satisfy the desired accuracy requirements. This
testing is referred to as the validation process.
• If a user has previously successfully employed the same GPS
procedures and equipment for a similar application, revalidation may
not be necessary.
• Three main components are tested in the validation process:
• the positioning technique chosen,
• the equipment to be used and
• the processing method adopted.

Validation Concept
• The validation process also has the benefits of enabling users to
identify and solve problems before commencing costly production
surveys, to streamline operations, and to verify the accuracies which
can be expected using the tested procedures. The validation concept
is summarized in the Figure below.
• Validation testing should be carried out using points with coordinates
known to an accuracy superior to that desired for the project. The
distance between points should be representative of that planned for
the actual survey execution.

Validation Concept
• To provide a standard upon which GPS surveys may be
tested (and in particular high accuracy surveys), the
Geodetic Survey Division in cooperation with provincial
agencies, has established several GPS basenets across the
country. Each of these basenets consists of six to eight
stations marked with forced-centring pillars, with
interstation distances ranging from 2 to 50 kilometres in
most locations.
• In addition, each basenet includes an electronic distance
measurement (EDM) calibration baseline which provides a
selection of shorter baselines.
• Other alternatives exist for providing control for validation
surveys, particularly for lower accuracy surveys. For
example, existing high accuracy control monuments may be
used. Descriptions, coordinates and accuracy information
for control monuments in a given area may be acquired
from the Geodetic Survey Division.

Reconnaissance
• Reconnaissance consists of checking field project sites before
commencing GPS observations. Sites should be checked for
their suitability for GPS, availability of control, and logistical
requirements.
• A good GPS site should be free from obstructions and
interference. Through field reconnaissance, obstructions or
interference may be identified and avoided by alternate site
selection or through establishment of eccentric stations. . To
avoid satellite blockage, ideally a site should be obstruction-
free in all directions above 15° elevation.
• In less than ideal conditions where some obstructions do exist,
successful positioning may be possible if a sufficient number of
satellites with adequate geometry can still be tracked. For
surveys using carrier observations, or for base stations in
differential surveys using code observations, obstruction-free
sites should be sought. Code positioning techniques are
generally more forgiving than carrier techniques to
obstructions, since they are not subject to cycle slips.

Field Reconnaissance
• During field reconnaissance, control stations planned for
use should be checked to ensure they can be found, are in
stable condition and are suitable for GPS observations. If
control is unavailable in the area of interest to support,
one may desire to establish a new point through a
conventional static GPS survey using control in the
surrounding area.
• If vertical control is available in the area of interest but
unsuitable for GPS, one may desire to establish an
eccentric control point which would be suitable for GPS by
levelling between the existing and newly established
points. One must note that the accuracy of the eccentric
control point is only as good as the method used to tie the
eccentric station to the original station.

Field Reconnaissance
• Reconnaissance also provides much needed information
on logistical requirements. The method of transportation
and the time required to walk in to each point has
significant implications for both the cost and logistics of a
given survey. Similarly, any constraints which can be
identified will facilitate successful planning.
• For example, the suitability for semi-kinematic or rapid
static surveys may be assessed, the need for extra-tall
poles to mount the antenna on may be realized, or the
need for safety precautions for certain sites near
roadways may be identified.
• The final product of field reconnaissance will include a set
of points ready for GPS observations as well as a current
description for each site, access information and a
description of any special steps which need to be taken.

Survey Design
• Another important step in the planning and preparation process is
the survey design.
• Considerations in the survey design include control requirements,
network configuration and redundancy.
• Obviously, the survey design will vary greatly depending on the
accuracy sought and the GPS positioning technique employed. The
figure below summarizes the control requirements and network
configuration for various types of positioning.

control requirements and network
configuration

Conventional Static GPS Configuration
• Closed geometrical figures should be used for the
network configuration of conventional static GPS
surveys. Guidelines for designing such networks for
static surveys are given in "Guidelines and
Specifications for GPS Surveys" (Geodetic Survey
Division, 1992) and include the following:
1) Each station must be directly connected to at least two
others in the network.
2) Adjacent stations should be directly connected.
3) Each observation session should have at least one baseline
in common with another session.

• The example assumes four receivers (A,B,C and D) are
available for each observing session. The sites to be
observed together in the same session are connected by
the same line types in the network sketch, and are also
enumerated in the adjacent table.
• For clarity of illustration the connecting lines only show
four out of the six direct connections made with each
observation session. For example, for session 1, C1 to 2 and
1 to 7 are direct connections which are not shown.
• The last two sessions serve two purposes. First, by
including these last sessions, each station is observed at
least twice, providing redundancy and a means to detect
blunders. Second, all horizontal control points are directly
connected. This is useful for high accuracy surveys to
control errors which may result from using horizontal
control less accurate than the GPS survey.

Preparations
• Up to this point most of the main segments in the
planning and preparation phase have been presented:
• the selection of positioning method and receiver type,
• the validation and
• reconnaissance processes, and
• the survey design.
• Several aspects of preparation have yet to be
mentioned and so are listed below.

Preparations
• Determine the best window(s) available to collect GPS data based on
satellite availability and geometry.
• Decide the optimal number of GPS receivers and personnel for the
project and make the necessary arrangements.
• Plan the survey design, taking into account control requirements,
network configuration, travel time between sites, satellite window
and logistical constraints.
• Establish a unique numbering or naming system to clearly identify all
sites positioned on the ground with their related computer data
files, positional information and other associated attributes.
• Arrange for transportation between sites (e.g. car, helicopter, boat,
or foot).
• Train personnel on receiver operation, GPS observing procedures
and data processing.
• Organize accommodations for the field if required.
• Organize all required equipment and supplies to support GPS field
activities.

FIELD OPERATIONS
• With good planning and preparation, field operations
should be relatively smooth.
• Responsibilities in the field are typically divided
amongst a party chief, observers and a processor.
• Depending on the magnitude and methodology of the
project, these three groups of responsibility may all
be assigned to one person or shared amongst many.

Post-processing Differential GPS Observational Data

Post-processing Differential GPS
Observational Data
• a. Processing time is dependent on the accuracy required, software development,
computer hardware used, data quality, and amount of data. In general, high accuracy
solutions, crude computer software and hardware, low-quality data, and high volumes of
data will cause longer processing times.
• b. The ability to determine positions using GPS is dependent on the effectiveness of the
user to determine the range or distance of the satellite from the receiver located on the
earth. There are two general techniques currently operational to determine this range:
• Pseudoranging and
• carrier beat phase measurement.
• c. The user must take special care when attempting a baseline formulation with
observations from different GPS receiver manufacturers. It is important to ensure that
observables being used for the formulation of the baseline are of a common format (i.e.,
RINEX). The common data exchange formats required for a baseline formulation exist
only between receivers produced by the same manufacturer, but there are some
exceptions.

Pseudo-Ranging
• The pseudo-range observable is calculated from observations recorded
during a GPS survey. It is the difference between the time of signal
transmission from the satellite, measured in the satellite time scale,
and the time of signal arrival at the receiver antenna, measured in the
receiver time scale.
• When the differences between the satellite and the receiver clocks are
reconciled and applied to the pseudo-range observables, the resulting
values are corrected pseudo-range values.
• The value found by multiplying this time difference by the speed of
light is an approximation of the true range between the satellite and
the receiver, or a true pseudorange.
• A more exact approximation of true range between the satellite and
receiver can be determined if ionosphere and troposphere delays,
ephemeris errors, measurement noise, and unmodelled influences are
taken into account while pseudo-ranging calculations are performed.
• The pseudo-range can be obtained from either the C/A-code or the
more precise P-code (if access is available).

Carrier Beat Phase Observables
• The carrier beat phase observable is the phase of the signal remaining after the
internal oscillated frequency generated in the receiver is differenced from the
incoming carrier signal of the satellite. The carrier beat phase observable can be
calculated from the incoming signal or from observations recorded during a GPS
survey.
• By differencing the signal over a period or epoch of time, one can count the number
of wavelengths that cycle through the receiver during any given specific duration of
time. The unknown cycle count passing through the receiver over a specific
duration of time is known as the cycle ambiguity.
• There is one cycle ambiguity value per satellite/receiver pair as long as the receiver
maintains continuous phase lock during the observation period. The value found by
measuring the number of cycles going through a receiver during a specific time,
when given the definition of the transmitted signal in terms of cycles per second,
can be used to develop a time measurement for transmission of the signal.
• Once again, the time of transmission of the signal can be multiplied by the speed of
light to yield an approximation of the range between the satellite and receiver. The
biases for carrier beat phase measurement are the same as for pseudo-ranges
although a higher accuracy can be obtained using the carrier.
• A more exact range between the satellite and receiver can be formulated when the
biases are taken into account during derivation of the approximate range between
the satellite and receiver.

Baseline Solution by Linear Combination
• The accuracy achievable by pseudo-ranging and carrier beat phase
measurement in both absolute and relative positioning surveys can be
improved through processing that incorporates differencing of the
mathematical models of the observables.
• Processing by differencing takes advantage of correlation of error (e.g.,
GPS signal, satellite ephemeris, receiver clock, and atmospheric
propagation errors) between receivers, satellites, and epochs, or
combinations thereof, in order to improve GPS processing.
• Through differencing, the effects of the errors that are common to the
observations being processed are eliminated or at least greatly
reduced. Basically, there are three broad processing techniques that
incorporate differencing:
• single differencing,
• double differencing, and
• triple differencing.
• Differenced solutions generally proceed in the following order:
differencing between receivers takes place first, between satellites
second, and between epochs third.

Single differencing
• There are three general single differencing processing
techniques: between receivers, between satellites,
and between epochs.

Single differencing
(1) Between receivers. Single differencing the mathematical models for
a pseudo-range (P- or C/A-code) or carrier phase observable
measurements between receivers will eliminate or greatly reduce
satellite clock errors and a large amount of satellite orbit and
atmospheric delays.
(2) Between satellites. Single differencing the mathematical models for
pseudo-range or carrier phase observable measurements between
satellites eliminates receiver clock errors. Single differencing
between satellites can be done at each individual receiver during
observations as a precursor to double differencing and in order to
eliminate receiver clock errors.
(3) Between epochs. Single differencing the mathematical models
between epochs takes advantage of the Doppler shift or apparent
change in the frequency of the satellite signal by the relative motion
of the transmitter and receiver. Single differencing between epochs
is generally done in an effort to eliminate cycle ambiguities.

Single differencing
• There are three forms of single differencing techniques
between epochs currently in use today: Intermittently
Integrated Doppler (IID), Consecutive Doppler Counts
(CDC), and Continuously Integrated Doppler (CID).
• IID uses a technique whereby Doppler count is recorded
for a small portion of the observation period, the Doppler
count is reset to zero, and then at a later time the Doppler
count is restarted during the observation period.
• CDC uses a technique whereby Doppler count is recorded
for a small portion of the observation period, reset to
zero, and then restarted immediately and continued
throughout the observation period.

Double differencing
• Double differencing is actually a differencing of two
single differences.
• There are two general double differencing processing
techniques:
• receiver-time double and
• Receiver satellite
• Double difference processing techniques eliminate
clock errors.

Double differencing
(1)Receiver-time double differencing. This technique
uses a change from one epoch to the next, in the
between-receiver single differences for the same
satellite. Using this technique eliminates satellite-
dependent integer cycle ambiguities and simplifies
editing of cycle slips.
(2)Receiver-satellite double differencing. There are two
different techniques that can be used to compute a
receiver-satellite double difference. One technique
involves using two between-receiver single
differences.

Double differencing
• This technique also uses a pair of receivers, recording
different satellite observations during a survey session
and then differencing the observations between two
satellites.
• The second technique involves using two between-
satellite single differences. This technique also uses a
pair of satellites, but different receivers, and then
differences the satellite observations between the
two receivers.

Triple differencing
• There is only one triple differencing processing technique:
receiver-satellite-time. All errors eliminated during single-
and double-differencing processing are also eliminated
during triple differencing.
• When used in conjunction with carrier beat phase
measurements, triple differencing eliminates initial cycle
ambiguity. During triple differencing, the data are also
automatically edited by the software to delete any data that
cannot be solved, so that the unresolved data are ignored
during the triple difference solution.
• This feature is advantageous to the user because of the
reduction in the editing of data required; however,
degradation of the solution may occur if too much of the
data are eliminated during triple differencing.

OTHER GNSS TECHNOLOGIES
• GLONASS
• GALELIO
• BEIDOU/COMPASS
• ZENITH

The GLONASS system
• Is the Russian Federation's Global Navigation Satellite System (GNSS).
• Russian version of a global positioning system.
• GLONASS (Global'naya Navigatsionnaya Sputnikovaya Sistema ).
• Started in October 12, 1982 with the launch of the Kosmos-1413

The GLONASS system
• 24 Satellites orbiting the earth,
• where 21 satellites are considered active satellites,
• the remaining three are active on orbit spares.
• A minimum of four satellites in view allows:
• a GLONASS receiver to compute its position in three dimensions, as well as
• become synchronized to the system time

Satellite orbits
• GLONASS constellation consists of three orbital planes with eight
satellites evenly distributed in each plane.
• The planes have a nominal inclination of 64.8° and are spaced by 120°
in longitude.
• The satellite’s orbit are circular with a radius of about 25,508
kilometres.

Satellite orbits
• Shorter orbital radius yields a shorter orbital period of
8/17 of a sidereal* day i.e.,
• after eight sidereal days, the GLONASS satellites have
completed exactly 17 orbital revolutions.
• For an observer on the earth, a particular satellite will
reappear at the same place in the sky after eight
sidereal days.
• Because each orbital planes contains eight equally
spaced satellites, one of the satellites will be at the
same spot in the sky at the same sidereal time each
day.

Satellite signal
• All GLONASS satellites transmit carrier signals in
different L-band channels, i.e., at different
frequencies.
• A GLONASS receiver separates the total incoming
signal from all visible satellites by assigning different
frequencies to its tracking channels.
• This procedure is called frequency division multiple
access (FDMA).
• Because FDMA does not need to distinguish satellites by
their unique signal modulation, all GLONASS satellites
broadcast the same codes.

Satellite signal
• GLONASS, being a dual-use system, provides a high
accuracy signal for military use and a standard-
accuracy signal for civil use free of charge.
• Each GLONASS satellite continuously provides
navigation signals:
• standard-accuracy signal, i.e. the C/A-code (also denoted
as S-code), and
• the high accuracy signal, i.e., the P-code,

Satellite signal
• This is done in two carrier frequencies of the L-band,
denoted as G1 and G2. Where:
• G1: (1,602 + k x 9/16) MHz (C/A-code and P-code)
• G2: (1,246 + k x 7/16) MHz (P-code)
• k= Channel number
• N/B: this denotation enables a better distinction from the
GPS carriers L1 and L2.
• The C/A-code is modulated onto G1 only, whereas the
P-code is modulated onto G1 and G2.

Satellite signal
• For positioning and timing, GLONASS provides two
levels of services:
• Standard Precision Service (SP) with access for civilian users.
• High Precision Service (HP) with access for authorized users.
• The C/A-code is designated as the Standard Precision
Service.
• The C/A-code is presently modulated on G1 only.
• The P-code is designated as the High Precision Service .
• The P-code is modulated on both carriers G1 and G2.

GLONASS Time
• GLONASS system time is based on an atomic time scale
similar to GPS.
• This time scale is UTC as maintained by Russia (UTC (SU)).
• In contrast to GPS the broadcast GLONASS clock and
clock frequency offset yield the difference between the
individual GLONASS satellite’s time and the GLONASS
system time.
• Unlike GPS, the GLONASS time scale is not continuous
and must be adjusted for periodic leap seconds.

GLONASS Time
• Leap seconds are applied to all UTC time references as
specified by the International Earth Rotation and
Reference System Service (IERS).
• Leap seconds are used to keep UTC close to mean
solar time.
• Mean solar time, based on the spin of the Earth on its axis,
is not uniform and its rate is gradually changing due to tidal
friction and other factors such as motions of the Earth's
fluid core.
• Moscow offsets GLONASS system time from UTC (SU)
by plus three hours.

GLONASS Datum
• Datum is a set of parameters (translations, rotations,
and scale) used to establish the position of a reference
ellipsoid with respect to points on the Earth’s crust.
• GLONASS has a different way of transmitting satellite
orbit information. For every half hour epoch, each
satellite directly broadcasts it three-dimensional ECEF
position, velocity, and acceleration.

GLONASS Datum
• For a measurement time somewhere between these half-hour
epochs, the user interpolates the satellite’s coordinates using
position, velocity, and acceleration data from the half-hour marks
before and after the measurement time.
• The resulting ECEF coordinates are referenced to a different
geocentric datum Parametry Zemli 1990 (PZ-90) or in English
translation, Parameters of the Earth 1990, (PE-90) geodetic datum.

Segments of GLONASS
• The GLONASS system design consists of three parts:
• The Control segment
• The Space segment
• The User segment
• These operate together to provide accurate 3D
positioning, timing and velocity data to users
worldwide.

Segments of GLONASS
• The Control Segment
• consists of the system control center and a network of
command tracking stations across Russia.
• The GLONASS control segment, as with GPS, must:
• monitor the status of satellites,
• determine the ephemerides and satellite clock offsets with
respect to GLONASS time and UTC (Coordinated Universal Time),
and
• twice a day upload the navigation data to the satellites.

Segments of GLONASS
• The Space Segment
• The Space Segment is the portion of the GLONASS system that is located in
space, i.e., the GLONASS satellites that provide GLONASS ranging information.
• When complete, this segment will consist of 24 satellites in three orbital
planes, and eight satellites per plane.

Segments of GLONASS
• The User Segment
• Consists of equipment that tracks and receives the satellite signals.
• This equipment must be capable of simultaneously processing the signals
from a minimum of four satellites to obtain accurate position, velocity and
timing measurements.
• Like GPS, GLONASS is a dual military/civilian-use system.
• The system’s potential civil applications are many and mirror those of GPS.

Segments of GLONASS
• The GLONASS satellite signal identifies the satellite and provides:
• position, velocity and acceleration vectors at a reference epoch to compute
satellite locations
• synchronization bits, data age and satellite health
• offset of GLONASS time from UTC (SU) (formerly Soviet Union and now
Russia)
• almanacs of all other GLONASS satellites

Comparison between GPS and GLONASS
Compare Nominal Satellite Orbits

• In both systems, satellites broadcast two carrier signals, L1
and L2, in the L-band of the radio frequency spectrum.
These signals are modulated by two binary codes, the C/A
code and the P-Code, and by the data message.
• In both systems, the C/A-code is modulated onto the L1
carrier only, whereas the P-code appears on both L1 and L2.
• Accordingly, C/A-code receivers can use only the L1 signal for
ranging, and P-code receivers can measures ranges on both
frequencies to correct for ionospheric refraction.
• In both systems, the frequency of the C/A-codes is 10 times
lower than the P-code frequency. As a general rule, higher
signal frequencies yield a better range measuring accuracy
than low frequencies.
• Thus, both GPS and GLONASS have precise mode of
operation with the P-code and less accurate mode using the
C/A-code.

• Each satellite in both system transmits, at a rate of 50
bits per second, a data stream containing a wealth of
information regarding the status of the individual
broadcasting satellite and the whole satellite
configuration.
• Of primary importance from a user’s point of view are
two particular subsets of the message, the data
describing the satellite’s clock error and the data
representing the satellite’s position, called the satellite
ephemeris.
• Receiver need both data type to make computation
with the range.

• Compare Nominal satellite Signal Characteristics

Combined Services Performances
• By combining GLONASS with other GNSS systems, such as
GPS, Galileo, BeiDou, SBAS and GBAS, improved
performance in the following domains can be expected:
• Availability: Using as an example GLONASS in combination with
GPS, the number of operational satellites will increase from 8-9
satellites to 18-19. This is especially important in urban canyon
environments, where the presence of large buildings leads to
frequent shadowing of signal.
• Position Accuracy: Allied to an increased availability in restricted
environments (urban) is a better geometry of spacecraft or
enhanced positioning performance.
• Integrity: GNSS based integrity systems and techniques, such as
SBAS, RAIM and GBAS, would benefit from the addition of new
constellations, including GLONASS, in terms of lower achievable
protection levels and/or integrity risk.
• Redundancy: Safety of Life applications require a full backup
solution to be protected in the situation where the primary
system fails. The combination of independent systems will lead to
the required level of redundancy.

Combined Services Performances
The following table depicts a comparison example of the
navigation error (at 95% probability) provided by GLONASS
only solution and GLONASS in combination with GPS, as well
as the number of satellites in view in four different reference
stations:

References
• http://www.esa.int/Our_Activities/Navigation/The_future_-
_Galileo/What_is_Galileo
• Pedro Filipe Faria Nogueira Ferr˜ao, 2013, Positioning with
Combined GPS and GLONASS Observations, PHD Thesis,
Tecnico, Lisboa
• http://www.insidegnss.com/node/4267
• http://en.wikipedia.org/wiki/BeiDou_Navigation_Satellite_Syst
em
• http://en.wikipedia.org/wiki/Satellite_navigation#BeiDou
• http://en.wikipedia.org/wiki/Quasi-Zenith_Satellite_System
• http://en.wikipedia.org/wiki/Quasi-Zenith_Satellite_System

GALILEO
• Estimated cost of €5 billion project and named after the
Italian astronomer Galileo Galilei.
• Aims to provide an alternative high-precision positioning
system for European nations in case the
Russian GLONASS and US GPS systems, are disabled,
• Use of basic (low-precision) Galileo services will be free
and open to everyone, while high-precision capabilities will
be available for paying commercial users.
• Is intended to provide horizontal and vertical position
measurements within 1-metre precision, and better
positioning services at high latitudes than other positioning
systems.
• Headquarters of the Galileo project are in Prague -
the Czech Republic

GALILEO
• GALILEO is Europe’s own global navigation satellite
system,
• designed to provide a highly accurate and guaranteed
global positioning service under civilian control.
• The first two GALILEO satellites were launched in
2005 and 2008 respectively, reserving radio
frequencies and serving as test platforms for the
GALILEO technologies.

GALILEO
• GALILEO services will come with quality and integrity
guarantees to civilian users that in other systems are
restricted to military and authorized users only,
marking the key difference between GALILEO and
others GNSS’.
• The fully developed GALILEO constellation will consist
of 30 satellites (27 operational + 3 spares),
• orbiting in 3 circular Medium Earth Orbit planes,
• have 23 222 Km of altitude above the Earth, and
• a nominal inclination of 56 degrees relative to the equator.

GALILEO
• By offering dual frequencies as standard, Galileo is set to deliver real-
time positioning accuracy down to the metre range.
• will guarantee availability of the service under all but the most extreme
circumstances and will inform users within seconds of any satellite failure,
making it suitable for safety-critical applications such as guiding cars, running
trains and landing aircraft.

GALILEO
• the first two of four operational satellites designed to
validate the Galileo concept in both space and on Earth
were launched on 21 October 2011
• Two more followed on 12 October 2012.
• This In-Orbit Validation (IOV) phase was expected to be
followed by additional satellite launches to reach Initial
Operational Capability (IOC) around mid-decade.
• Once the IOC phase is reached, The Open Service, Search
and Rescue and Public Regulated Service will be available
with initial performances.
• As the constellation is built-up further, new services will
be tested and made available to reach Full Operational
Capability (FOC).

GALILEO
• On 22 August 2014, two more satellites were launched from French
Guiana but were injected into an incorrect orbit.
• Analysis indicated that the third stage of the Soyuz launch vehicle, the
Fregat space tug, failed to correctly circularize the satellites' orbit,
resulting in a semi-minor axis 3.7 Mm less than desired and a 5°
inclination error.

GALILEO
• Once FOC is achieved, the Galileo navigation signals will provide good
coverage even at latitudes up to 75 degrees north and beyond.
• The large number of satellites together with the carefully-optimised
constellation design, plus the availability of the three active spare
satellites, will ensure that the loss of one satellite should have no
discernible effect on the user.

GALILEO
• Two Galileo Control Centres (GCCs) have been
implemented on European ground to provide for the
control of the satellites and to perform the navigation
mission management.
• The data provided by a global network of Galileo Sensor
Stations (GSSs) are sent to the Galileo Control Centres
through a redundant communications network.
• The GCCs use the data from the Sensor Stations to
compute the integrity information and to synchronise the
time signal of all satellites with the ground station clocks.
• The exchange of the data between the Control Centres
and the satellites is performed through up-link stations.

GALILEO
• Other features,
• Provision of a global Search and Rescue (SAR) function,
based on the operational Cospas-Sarsat system.
• Satellites are equipped with a transponder, able to transfer
distress signals from user transmitters to regional rescue co-
ordination centres, which will then initiate rescue
operations.
• At the same time, the system will send a response signal to
the user, informing him that his situation has been detected
and that help is on the way.
• This is considered a major upgrade compared to the existing
system, which does not provide user feedback.

BEIDOU NAVIGATION SATELLITE
SYSTEM (Formally COMPASS)
• China’s second generation satellite navigation system
• aimed to provide positioning, navigation and timing services to users
on a continuous worldwide basis, similar to the GPS, GLONASS and
GALILEO .
• The Chinese Government approved its development and deployment
in 2004, and
• by December 2011 it became operational in China and surrounding
regions, with a constellation of 10 satellites.
• It’s expected to reach global coverage and its nominal constellation of
35 satellites by 2020.

BEIDOU
• consists of two separate satellite constellations:
• a limited test system that has been operating since 2000,
and
• a full-scale global navigation system that is currently under
construction.
• Will be a global satellite navigation system consisting of
35 satellites, and has been under construction as of
January 2013.
• became operational in China in December 2011, with
10 satellites in use,and began offering services to
customers in the Asia-Pacific region in December 2012.
• It is planned to begin serving global customers upon its
completion in 2020.

BEIDOU
• a constellation of 35 satellites, which include:
• 5 geostationary orbit satellites for backward compatibility with BeiDou-1, and
• 30 non-geostationary satellites (27 in medium earth orbit and 3 in inclined
geosynchronous orbit), that will offer complete coverage of the globe.

BEIDOU
• There are two levels of service provided;
• a free service to civilians
• has a 10-meter location-tracking accuracy, synchronizes clocks
with an accuracy of 10 nanoseconds, and measures speeds to
within 0.2 m/s.
• The restricted military service
• has a location accuracy of 10 centimetres, can be used for
communication, and will supply information about the system
status to the user.
• To date, the military service has been granted only to the People's
Liberation Army and to the Military of Pakistan.

BEIDOU
• The ranging signals are based on the CDMA principle
and have complex structure typical of Galileo or
modernized GPS.
• Similar to the other GNSS, there will be two levels of
positioning service: open and restricted (military).
• The public service shall be available globally to general
users. When all the currently planned GNSS systems are
deployed, the users will benefit from the use of a total
constellation of 75+ satellites, which will significantly
improve all the aspects of positioning, especially availability
of the signals in so-called urban canyons.
• The general designer of Compass navigation system is Sun
Jiadong, who is also the general designer of its
predecessor, the original Beidou navigation system.

BEIDOU
• Frequencies for Compass are allocated in four bands: E1, E2, E5B, and E6
and overlap with Galileo.
• The fact of overlapping could be convenient from the point of view of the
receiver design, but on the other hand raises the issues of inter-system
interference, especially within E1 and E2 bands, which are allocated for
Galileo's publicly regulated service.
• However, under International Telecommunication Union (ITU) policies, the
first nation to start broadcasting in a specific frequency will have priority to
that frequency, and any subsequent users will be required to obtain
permission prior to using that frequency, and otherwise ensure that their
broadcasts do not interfere with the original nation's broadcasts.

BEIDOU
• It now appears that Chinese Compass satellites will start transmitting
in the E1, E2, E5B, and E6 bands before Europe's Galileo satellites and
thus have primary rights to these frequency ranges.
• Although little was officially announced by Chinese authorities about
the signals of the new system, the launch of the first Compass
satellite permitted independent researchers not only to study general
characteristics of the signals but even to build a Compass receiver.

Other Systems – IRNSS
Indian Regional Navigational Satellite System
• an autonomous regional satellite navigation system being developed
by Indian Space Research Organisation (ISRO)
• would be under the total control of Indian government.
• The government approved the project in May 2006, with the
intention of the system to be completed and implemented by 2015
• will consist of a constellation of 7 navigational satellites.
• All the 7 satellites will be placed in the Geostationary orbit (GEO) to have a
larger signal footprint and lower number of satellites to map the region.
• It is intended to provide an all-weather absolute position accuracy of
better than 7.6 meters throughout India and within a region extending
approximately 1,500 km around it.
• A goal of complete Indian control has been stated, with the space segment,
ground segment and user receivers all being built in India.
• The first three satellitesIRNSS-1A, IRNSS-1B and IRNSS-1C of the proposed
constellation were precisely launched on 1 July 2013, 4 April 2014 and 16
October 2014 respectively from Satish Dhawan Space Centre.
• The next one IRNSS-1D of the proposed constellation is planned to be
launched by end of 2014 and ,
• the remaining three satellites IRNSS-1E, IRNSS-1F and IRNSS-1G are
planned to be launched by middle of 2015.

Other Systems – QZSS
Quasi-Zenith Satellite System
• is a proposed three-satellite regional time transfer system
and Satellite Based Augmentation System for the Global
Positioning System, that would be receivable within Japan
• With regards to its positioning, can only provide limited accuracy on
its own and is not currently required in its specifications to work in a
stand-alone mode
• Positioning service could collaborate with the geostationary
satellites in Japan's Multi-Functional Transport
Satellite(MTSAT), currently under development,
• which is a Satellite Based Augmentation System similar to the
U.S. Federal Aviation Administration's Wide Area Augmentation
System (WAAS).
• The first demonstration satellite was launched in September
2010
• targeted at mobile applications, to provide communications-
based services (video, audio, and data) and positioning
information.

Satellite Geodesy Lecture Notes MSU 2015.pptx

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