The GPS/GNSS Signal (2)

Center for Research and Application for Satellite Remote Sensing
Yamaguchi University
The GPS/GNSS Signal (2)

• GNSS and trilateration rely on measurement of distances to fix position
• Range is the GNSS term for distance
• Trilateration measure distance from controls on ground
• GNSS ranging measure distance from orbiting satellites
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GNSS and Trilateration

• GNSS signals are broadcast in the microwave part of the electromagnetic spectrum
• It is passive system because only the satellites transmit and the users only receive them
• There is no limit to the number of users without danger of overburdening the system
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One-way ranging
A Passive System

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The Electromagnetic Spectrum

• Distance is a function of the speed of light (c), signal frequency (f), and elapsed
time (t)
• The GNSS signals do not return to the satellite
• A clock in the satellite marks the time it departs from the satellite and a clock in
the receiver can mark the moment it arrives
• The range depends on the time it takes a GNSS signal to make a trip from the
satellite to the receiver.
• Therefore the satellite must tell the receiver the exact time it left the satellite
Time

• In GNSS, the control points are the satellites themselves but it is
somewhat complicated because the satellite is always moving.
• The GNSS signal must communicate to its receiver:
1) what time it is on the satellite;
2) the instantaneous position of a moving satellite;
3) some information about atmospheric correction; and
4) satellite identification and where to find the other satellites.
Control Points

• In order to communicate the needed information by the receiver,
codes are used and carried by carrier waves.
• A carrier has at least one of characteristics such as phase,
amplitude, or frequency that may be changed (modulated) to carry
information.
• The 2 GPS carrier waves are radio waves that are part of the L-band
(390 MHz – 1550 MHz)
The Navigation Code

Modulation types

• A wavelength with a duration of 1 second or 1 cycle per second has a frequency of
1 hertz (Hz)
• The lowest sound human ears can detect has a frequency of about 25 Hz and the
highest is about 15,000 Hz or 15 kilohertz (KHz)
• Most modulated carriers used in GPS have frequencies that are measured in
million cycles per second or megahertz (MHz)
• The fundamental frequencies of GPS are:
L1 at 1575.42 MHz (λ=19.0 cm)
L2 at 1227.60 MHz (λ=24.4 cm)
L5 at 1176.45 MHz (λ=25.48 cm) (new addition)
Wavelength

• GPS codes are binary, strings of zeroes and one, the language of
computers
• 3 basic GPS codes:
• 1) Navigation code,
• 2) Precise code (P code) and
• 3) Coarse Acquisition code (C/A code)
• Navigation code has a frequency of 50 Hz and is modulated into both L1
and L2 carriers.
Codes

Navigation Message

• Information in the Navigation message deteriorates with time.
• For example, every 2 hours the data in subframes 1, 2 and 3, the
ephemeris and clocks parameters, are updated.
• The data in subframes 4 and 5, the almanacs, are renewed every 6
days.
• These updates are provided by the government uploading facilities.
Navigation Message

• Subframe 1 contains the time-sensitive information.
• Drifts of each satellite clock are carefully monitored by the Control Segment
and is eventually uploaded into subframe 1 of where it is known as the
broadcast clock correction.
• One of the 10 words in subframe 1 provides information about the Age of Data
Clock or AODC.
Subframe 1

• Each GPS satellite carries 4 atomic clocks : 2 cesium
and 2 rubidium. Block IIR satellites are all rubidium
• Galileo satellite has 4 atomic clocks: 2 rubidium and 2
hydrogen maser
• GLONASS satellite has 3 Cesium clocks
• Beidou satellites has rubidium and hydrogen maser
• QZSS 1st generation satellites carry rubidium but next
satellites will be atomic-less clock.
• IRNSS satellites has 3 rubidium clocks
• The clocks in any one satellite are completely
independent from each other
Atoms emitting a
microwave frequency
Hydrogen maser
Rubidium
Satellite clocks

• Subframes 2 and 3 contain information about the position of the satellite, with
respect to time (ephemeris).
• There are 6 orbital elements: a (semi major axis), e (eccentricity), Ω (longitude of the
ascending node), ω (argument of perigee), i (inclination) and v (true anomaly).
• This information is used to calculate the ECEF, WGS84 coordinates of the satellite at
any moment.
• The broadcast ephemeris also deteriorates with time.
• As a result one of the important portion of the Navigation message is called IODE or
Issue of Data Ephemeris.
Subframes 2 and 3

• The broadcast ephemeris is a
prediction of the satellite
location at some time later
• They are the results of least-
squares curve fitting analysis
of the satellite’s actual orbit.
The Broadcast Ephemeris

Ephemeris and clock data parameters
decoded from subframes 1, 2 and 3
Ephemeris and clock data parameters
• EPHEMERIS FOR SATELLITE 2 :
• PRN number for data .................. 2
• Issue of ephemeris data .............. 224
• Semi-Major Axis (meters) ............. 2.65603E+07
• C(ic) (rad) .......................... 1.88127E-07
• C(is) (rad) .......................... -1.00583E-07
• C(rc) (meters) ....................... 321.656
• C(rs) (meters) ....................... 87.6875
• C(uc) (rad) .......................... 4.36418E-06
• C(us) (rad) .......................... 2.70829E-06
• Mean motion difference (rad/sec) ..... 5.04521E-09
• Eccentricity (dimensionless) ......... 0.0139305
• Rate of inclination angle (rad/sec) .. 4.11089E-10
• Inclination angle @ ref. time (rad) .. 0.950462
• Mean Anomaly at reference time (rad) . -2.62555
• Corrected Mean Motion (rad/sec) ...... 0.000145859
• Computed Mean Motion (rad/sec) ....... 0.000145854
• Argument of perigee (rad) ............ -2.56865
• Rate of right ascension (rad/sec) .... -8.43857E-09
• Right ascension @ ref time (rad) ..... 1.75048
• Sqrt (1 - e^2) ....................... 0.999903
• Sqr root semi-major axis, (m^1/2) .... 5153.67
• Reference time ephemeris (sec) ....... 240704

• Subframe 4 addresses atmospheric correction.
• It contains the almanac data for satellites with pseudorandom noise
(PRN) numbers from 25 through 32.
• It also contains a flag that tells the receiver when a security system
known as antispoofing or AS has been activated by the Control
Stations.
Subframe 4

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https://www.trimble.com/gps_tutorial/howgps-error.aspx
The atmosphere

GPS Satellite Ionospheric
Model Parameter
Decoded from Subframe 4
Ionospheric parameters:
Alpha[0] : 1.397E-08
Alpha[1] : 2.235E-08
Alpha[2] : -1.192E-07
Alpha[3] : -1.192E-07
Beta[0] : 1.044E+05
Beta[1] : 9.83E+04
Beta[2] : -1.966E+05
Beta[3] : -3.932E+05
GPS Satellite Ionospheric Model Parameter

• Subframe 5 contains almanac data for satellites with PRN numbers
from 1 through 24.
• Once, the receiver finds its first satellite, it can look at the
ephemerides to figure the position of more satellites to track.
Subframe 5

• Subframe 1 contains information about the health of the satellites.
• Subframes 4 and 5 also include health data of all the satellites
• inform users of any satellite malfunctions
• tell the receiver that all signals from the satellite are good and reliable
• tell the receiver which satellites have tracking problems or other difficulties.
• tell the receiver that the satellite will be out of commission in the future it
will be undergoing a scheduled orbit correction.
• Satellites are vulnerable to clock breakdown.
• This is the reason why satellites carry as many as 4 clocks.
Satellite Health

• Like the Navigation Message, the P and C/A code are impressed on
the L1 and L2 GPS carrier waves by modulation
• They carry raw data from which GPS receivers derive their time and
distance.
The P and C/A Codes

• The P and C/A code are complicated; in fact they appear to be nothing
but noise at first.
• They are known as pseudorandom noise, or PRN codes.
• But these codes have been carefully designed and capable of repetition
and replication.
PRN

P Code
• It is generated at a rate of 10.23 million bits per second and is available on both L1
and L2.
• Each satellite repeats its portion of the P code every 7 days, and the entire code is
renewed every 37 weeks.
• Each satellite is assigned one particular week of the 37-week-long P code, thus the
receiver can identify the satellite.
• For example SV 14 is so named because it broadcasts the 14th week of the P code.

• The C/A code is generated at 1.023 million bits per second, 10 times
slower than the P code.
• Satellite identification: each satellite broadcast a completely unique C/A
code on its L1 frequency
C/A Code

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Codes modulated on carrier waves

• The C/A code is the vehicle for the SPS (Standard Positioning
Service) – civilian use
• The P code provides the same service for PPS (Precise Positioning
Service) – military use
SPS and PPS

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https://www.gps.gov/
Latest report on Range, Horizontal and Vertical Accuracy

Global Vertical Error Histogram
31

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Global Horizontal Error Histogram

• GNSS Ranging
• One-way ranging
• The elapsed time is measured by 2 clocks: one in the
satellite and another in the receiver.
• Perfect synchronization of clocks is physically impossible.
• A discrepancy of 1 microsecond can create a range error
of 300 meters.
The Production of a Modulated Carrier Wave

• Phase angles are important to the
modulation of the carrier by phase
that is the method of attaching the
codes to the GPS carriers.
• 0, 90, 180, 270, and 360 are known as
phase angles in a single wavelength.
• The oscillators of GPS satellite create
very constant wavelengths, because
like clocks or oscillators, they're
known as frequency standards.
Phase angles

• Time measurement devices used in GPS are more correctly called
oscillators or frequency standards.
• The rate of all the components of GPS signals are multiples of the
standard rate of the oscillators, 10.23 MHz known as the
fundamental clock rate (Fo).
• L1- 154 x 10.23 MHz =1575.42 MHz
• L2- 120 x 10.23 MHz =1227.60 MHz
• The codes are also based on Fo.
• 10.23 code chips of the P code occur every microseconds or the
chipping rate is 10.23 Mbps exactly the same as Fo, 10.23 MHz.
Frequency standard

• The frequency of a modulated carrier, measured in hertz, can indicate the
elapsed time between the beginning and end of a wavelength.
• The length is approximately:
where
λ = the length of each complete wavelength (m)
ca = the speed of light corrected for atmospheric effects
f = frequency in hertz
If c=299 792 458 m/s and L1 frequency =1,575.42 MHz, What is its
wavelength?
Wavelength

• Binary biphase modulation is the kind of phase modulation used to
encode a carrier in GPS.
• Each zero (0) and one (1) is known as a code chip.
• 0-normal state
• 1-mirror image state.
• The modulations from 0 to 1 and from 1 to 0 are accomplished by
instantaneous 180⁰ changes in phase.
Encoding by Phase Modulation

• The chipping rate of the C/A code is 10 times slower than the P code, a tenth
of Fo, 1.023 Mbps
• 10 P code chips occur in the time it takes to generate 1 C/A code, allowing P
code derived pseudoranges to be much more precise.
• This is the reason C/A code is known as coarse acquisition code.
• Even though both codes are broadcast on L1, they are distinguishable from
one another by their transmission in quadrature.
• That means that the C/A code is phase shifted 90⁰ from P code.
Encoding by Phase Modulation

Code Modulation
of the L1 Carrier
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• Observable - the thing being measured
• Observation - the measurement
2 types of observables:
• Pseudorange
• instantaneous point positioning; low accuracy;
• ranging based on codes
• Carrier phase
• high precision survey
• Ranging based on the carrier waves
The Observables

• A pseudorange observable is based on a
time shift.
• This time shift is symbolized by dτ, d tau.
• This is the time elapsed between the
instant a GPS signal leaves a satellite and
the instant it arrives at a receiver.
• The elapsed time is known as the
propagation delay.
• A pseudorange is measured by a receiver
by comparing a replica of the code
generated by the receiver itself with the
code it receives from the satellite.
Pseudoranging

• The code sent by the satellite usually do not line up with the replica code
generated by the receiver.
• Lining up the code from the satellite with the replica in the GPS receiver is called
autocorrelation.
• It depends on the transformation of code chips to code states.
• The formula used to derive the code states (+1 and -1) from code chips (0 and 1) is:
code state=1-2x
where x is the code chip value.
• For example a normal code state of +1 corresponds to a chip value of 0. A mirror
code state of -1 corresponds to a chip value of 1.
Autocorrelation

Q1: If a tracking loop of 10 code states generated in a receiver does not match the
10 code states received from the satellite, how does the receiver know?
A1: The sum of the products of the code of each of the receivers 10 code states
with each of the 10 code states from the satellite, when divided by 10, does not equal
1.
Q2: How does the receiver know when a tracking loop of 10 replica code states does
match 10 code states from the satellite?
A2: The sum of the products of the code of each of the receivers 10 code states
with each of the 10 code states from the satellite, when divided by 10, is exactly 1.
Autocorrelation

• Once correlation of the two codes is achieved with a delay lock loop,
it is maintained by a correlation channel within the GPS receiver, and
the receiver is sometimes said to have achieved lock, or to be locked
on to the satellites.
• If the correlation is interrupted, the receiver is said to have lost lock.
• As long as the lock is present, the Navigation Message is available to
the receiver.
Lock on to the satellites

• One reason the time shift, dτ, cannot reveal the true range, ρ, of
the satellite at a particular instant is the lack of perfect
synchronization between the clock in the receiver and the clock in
the satellite.
• Hence, a small part of dτ contains clock errors too.
• There are 2 clock offsets that bias every satellite to receiver
pseudorange observable.
• This is the reason it is called a pseudorange.
Imperfect Oscillators

Pseudorange Equation

• Carrier phase ranging is the center of high accuracy surveying
applications.
• It depends on the carrier waves themselves, the unmodulated L1
and L2.
• The foundation of the carrier phase measurement is the
combination of the unmodulated carrier itself received from a GPS
satellite with replica of that carrier generated within the receiver.
Carrier phase ranging

The phase difference between the
incoming signal and the replica wave
generated by the receiver reveals the
fractional part of the carrier phase
measurement.
When two waves reach exactly the same phase angle they said to be in phase,
coherent or phase locked.
When two waves reach the same angle at different times, they are out of phase or
phase shifted.
Phase Difference

• The carrier phase observable is sometimes called the reconstructed
carrier phase or carrier beat phase.
• A beat is the pulsation resulting from the combination of 2 waves
with different frequencies.
• A beat is created when a carrier generated within a receiver and a
carrier received from a satellite are combined.
• How could a beat be created when the carrier from satellite and the
carrier generated within the receiver are supposed to be identical?
Beat

• If a GPS satellite is moving toward an observer its carrier wave
comes into the receiver with a higher frequency than it had at the
satellite.
• If it is moving away, its carrier wave comes into the receiver with a
lower frequency than it had at the satellite.
• Since the GPS is always moving with respect to the observer, any
signal received is always Doppler-shifted.
Doppler Effect

Doppler effect

• A carrier phase observation cannot rely on the travel
time for 2 reasons:
1) the receiver has no codes with which to tag any
particular instant on the incoming continuous carrier
wave.
2) since the receiver cannot distinguish one cycle from
any other, it has no way of knowing the initial phase of
the signal when it left the satellite.
Carrier Phase Approximation

Cycle ambiguity problem
While the determination of the
fractional part of a wavelength
can be solved, the number of full
wavelengths (N) is still a problem
Components of the carrier phase observable

Φ = carrier phase measurement
N = cycle ambiguity
λ = wavelength
εφ = receiver noise
Carrier phase formula

End of GNSS Lecture 2

The GPS/GNSS Signal (2)

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