This document discusses GPS error sources and techniques for improving GPS accuracy, including: - The troposphere causes delays in GPS signals and is a source of error. Techniques like WAAS and LAAS use reference stations and satellites to correct for tropospheric delays. - Good satellite geometry with low PDOP provides the most accurate GPS positioning. Dilution of precision metrics like PDOP indicate satellite geometry quality. - Ambiguity resolution techniques using dual or triple frequency carrier phase and code data can fix integer ambiguities and improve positioning accuracy to centimeter-level.

1. GNSS Surveying, GE 205
Kutubuddin ANSARI
kutubuddin.ansari@ikc.edu.tr
Lecture 4, March 15, 2015
GPS Error-2

2. • The troposphere is the lowest
layer of the atmosphere that
lies next to the Earth’s
surface.
• Most of the air that makes up
the atmosphere is found in the
troposphere
• It extends to about 14
kilometers (around 9 miles)
above the Earth and is where
virtually all weather takes
place.
2. Troposphere

3. Troposphere
• As you move up into the
troposphere the temperature
decreases.
• At the top of this layer the air
temperature is about - 60°C.
• Environmental Lapse rate 6.5
0
C/km

4.  The troposphere is the electrically neutral atmospheric
region that can be extend up to about 50 km from the
surface of the earth.
 The troposphere is a non-dispersive medium for radio
frequencies below 15 GHz, as a result, it delays the GPS
carriers and codes identically.
 That is, the measured satellite to receiver range will be
longer than the actual geometric range, which means
that a distance between two receivers will be longer
than the actual distance.
Tropospheric Delay

6. The above equation in terms of Zenith Total Delay (ZTD) can be
expressed with sum of a hydrostatic part Zenith Hydrostatic
Delay (ZHD) and a wet part Zenith Wet Delay (ZWD)
ZTD= ZHD + ZWD
About 90 % of the troposphere refraction arise from the dry and
about 10% from the wet component.

7. Precipitable Water Vapor (PWV)
Precipitable water vapor (PWV) is the amount of
water vapor present in a column above the surface of
the Earth
Measured in units of inches or millimeters
It represents the maximum amount of water that
could fall down to the surface as precipitation if all
the water vapor converted into a liquid or a solid

8. • ZWD is proportional to PWV as:
ZWD=Q.PWV
where factor Q is depending by the vertical mean temperature Tm,
• Q is a dimensional quantity variable in space and time, however in
mean is equal to 6.5.
• The Zenith Total Delay (ZTD), is the sum of ZHD and ZWD:
ZTD= ZHD + Q.PWV
• Generally 10 mm PWV corresponds to approximately 65 mm of
ZWD .
Precipitable Water Vapor (PWV)

9. Mapping function
Basic form of mapping function was deduced by
Marini (1972) and matches the behavior of the
atmosphere at near-zenith and low elevation angles.
Form is with constants (k):
1
2
3
1
( )
sin( )
sin( )
sin( )
sin( )
m
k
k
k
ε
ε
ε
ε
ε
=
+
+
+
+L
where is elevation angleε

10. Relation with Temperature
A multiple linear regression method and neural network method
are performed to retrieve the relation between PWV verses
temperature . The PWV has lower correlations with tropospheric
temperature. To check what type of prelateship PWV constrains
with temperature, let us consider an equation of PWV with
atmospheric temperature (T) has been given by:
PWV aT b= +
If is error between observed and modeled value of PWV then theϵ
equation can be written by least square method in following form:
2 2
= (PWV )aT bε ∑ − −

11. To calculate the value of a and b, let the partial derivatives of error
with respect to a and b are zero:
2 2
= 0 = 0and
a b
ε ε∂ ∂
∂ ∂
After solving the equation the two equations can be obtained in
following form:
2
0
0
PWV a T nb
PWV T a T b T
Σ − Σ − =
Σ × − Σ − Σ =
Where n is number of observations. The values of constants a and b
will explain the modelled relationship among PWV and temperature
Relation with Temperature

12. Sources of GPS Error
Source Amount of Error
 Satellite clocks: 1.5 to 3.6 meters
 Orbital errors: < 1 meter
 Ionosphere: 5.0 to 7.0 meters
 Troposphere: 0.5 to 0.7 meters
 Receiver noise: 0.3 to 1.5 meters
 Multipath: 0.6 to 1.2 meters
 Selective Availability (see notes)
 User error: Up to a kilometer or more

13. Geometry Measure

14. N
S
W E
Ideal Satellite Geometry

15. S
N
W E
Poor Satellite Geometry

16. Good Satellite Geometry

17. Poor Satellite Geometry

18. Good Satellite Geometry

19. Poor Satellite Geometry

20. GPS Satellite Geometry
• Satellite geometry can affect the quality of GPS signals
and accuracy of receiver trilateration
• Dilution of Precision (DOP) reflects each satellite’s
position relative to the other satellites being accessed
by a receiver
• There are five distinct kinds of DOP

21. Dilution Of Precision
PDOP = Position Dilution Of Precision (Commonly Used)
GDOP = Geometric Dilution Of Precision
VDOP = Vertical Dilution Of Precision
HDOP = Horizontal Dilution Of Precision
TDOP = Time Dilution Of Precision

22. • It’s usually up to the GPS receiver to pick satellites
which provide the best position triangulation.
• Some GPS receivers allow DOP to be manipulated by
the user.
• Position Dilution of Precision (PDOP) is the DOP
value used most commonly in GPS to determine the
quality of a receiver’s position.
GPS Satellite Geometry

23. Dilution Of Precision (DOP)
Good DOP
Poor DOP

24. when measuring
must have good
DOP and good
visibility
…may not
always be
possible
Dilution Of Precision (DOP)

25. The cofactor matrix Q
1
( )
T
Q A A −
=
1
1 0 1 0 1 0
1 1
2 0 2 0 2 0
2 2 2
3 0 3 0 3 0
3 3 3
4 0 4 0 4 0
4 4 4
x x y y z z
c
x x y y z z
c
A
x x y y z z
c
x x y y z z
c
ρ ρ ρ
ρ ρ ρ
ρ ρ ρ
ρ ρ ρ
− − − 
− − − 
 
 − − −
− − − 
 =
 − − −
− − − 
 
 − − −
− − − 
  
( ) ( ) ( )
2 2 2
0 0 0x x y y z zρ = − + − + −

26. The cofactor matrix Q

27. When the topocentric local coordinate system with its
axes along the local north, east, and up .
The cofactor matrix Q

28. QUALITY PDOP
Very Good 1-3
Good 4-5
Fair 6
Suspect >6
How to check?

29. Wide Area Augmentation
System (WAAS)

30. •The WAAS is an air navigation system to expand the GPS, with
the goal of improving its accuracy, integrity, and availability.
•The WAAS specification requires it to provide a position
accuracy of 7.6 meters or better for both lateral and vertical
measurements.
•The ground segment is composed of multiple Wide-area
Reference Stations (WRS). These ground stations monitor and
collect information on the GPS signals, then send their data to
three Wide-area Master Stations (WMS).
• 38 WRS stations , 20 in USA, 7 in Alaska, 1 in Hawaii, 1 in
Puerto Rico, 5 in Mexico, and 4 in Canada
Wide Area Augmentation System

31. • The space segment consists of multiple geosynchronous of
communication satellites which broadcast the correction
messages generated by the WAAS Master Stations for reception by
the user segment
•The user segment is the GPS and WAAS receiver, which uses the
information broadcast from each GPS satellite to determine its
location and the current time, and receives the WAAS corrections
from the Space segment
Wide Area Augmentation System

32. •The signals from GPS satellites are received by Wide Area Reference
Stations (WRS) sites.
•The GPS information collected by the WRS sites is forwarded to the
WAAS Master Station (WMS).
•At the WMS, the WAAS augmentation messages are generated.
These messages contain information that allows GPS receivers to
remove errors in the GPS signal, allowing for a significant increase in
location accuracy and reliability.
How It Works ?

33. •The augmentation messages from the WMS to be transmitted to
Geostationary communications satellites.
•The Receivers receive the WAAS augmentation message from
Geostationary communications satellite and processes to estimate
the position .
•WAAS also provides indications to receivers of where the GPS
system is unusable due to system errors or other effects.
How It Works ?

35. ±3m
±15m
•With Selective Availability set to
zero, and under ideal conditions,
a GPS receiver without WAAS
can achieve fifteen meter
accuracy most of the time.
•Under ideal conditions a WAAS
equipped GPS receiver can
achieve three meter accuracy.
•Precision depends on good
satellite geometry, open sky view,
and no user induced errors.
How good is WAAS?

36. Local Area Augmentation
System (LAAS)

37. •The Local Area Augmentation System (LAAS) is an all-weather
aircraft landing system based on real-time differential correction
of the GPS signal
•Basically LAAS is complement of the WAAS with seamless
satellite based navigation system. Practical terms, this means that
at locations where the WAAS is unable to meet existing navigation
the LAAS is used to fulfill those requirements.
•The International Civil Aviation Organization (ICAO) calls this
type of system is a Ground Based Augmentation System (GBAS).
Local Area Augmentation System (LAAS)

38. Local Area Augmentation System (LAAS)

39. •Local reference receivers located around the airport
send data to a central location at the airport.
•This data is used to formulate a correction
message, which is then transmitted to users.
•A receiver on an aircraft uses this information to
correct GPS signals, which then provides a standard
display for Landing System.
How It Works ?

40. Ambiguity Resolution

41. The pseudorange is the "distance" between the GPS
satellite at some transmit time and the receiver at some
receive time. Because the transmit time and the receive
time are different, it is impossible to measure the true
range between the satellite and the receiver. The basic
definition of the pseudorange observable is:
Code Pseudorange
R c tρ= + ∆

42. Phase Pseudorange
Another observable, based on the carrier phase of the
signal, does not require the actual information being
transmitted. The basic definition of the phase
observable is:
where N is the
integer number of
cycles
R c t Nφ ρ λ= + ∆ +

43. Ambiguity
The integer number of cycles, N, is typically not known
and varies for every receiver-satellite combination. As
long as the connection between the receiver and the
satellite is not broken, N remains constant while the
fractional beat phase changes over time.
Because of the ambiguous nature of N, it is referred to
as the ambiguity and can either be solved for by using
the code pseudoranges, or estimated.

44. Ambiguity Resolution
1. Single-Frequency Phase Data
The ambiguity is denoted by N. As soon as the
ambiguity is determined as an integer value, the
ambiguity is said to be resolved or fixed.
When phase (Φ)measurements for only one
frequency are available, the most direct approach is
as follows-
1 1 Iono
f Nφ ρ δ
λ λ
= + ∆ + − ∆

45. 2. Dual-frequency phase data
This situation for the ambiguity resolution improves
significantly when using dual frequency phase data.
There are many advantages implied in dual-frequency
data because of the various possible linear combinations
that can be formed like the wide-lane and narrow-lane
techniques. Denoting the phase data referring to the
frequencies f1 and f2 by Φ1 and Φ2 then-
Wide Lane = Φ1 − Φ2
Narrow Lane = Φ1 + Φ2

46. ( ) ( )
1 1 1 2 2 2
1 2
21 1 2
21 1 2 21 1 2
21 21 21
1 2
1 1
1 1 2 21 1 2
21 21
,
Let ide lane = -
,
1 1
= a f + N - b
f
N
b b
af N af N
f f
w
and f f f N N N
f
f f
N a f f
f f
φ φ
φ φ φ
φ
φ φ
= + − = + −
= − = −
 
− ÷
 
⇒ = − + − +
2. Dual-frequency phase data
The phase models in the modified form

47. 3. Combining dual-frequency carrier phase
and code data
The models for dual-frequency carrier phases and code
ranges, both expressed in cycles of the corresponding
carrier, can be written in the form-

48. From the above equations
3. Combining dual-frequency carrier phase
and code data

49. 4. Combining triple-frequency carrier
phase and code data
The technique based on three carriers is denoted as
three carrier ambiguity resolution (TCAR).

50. After the successful computation of the N1 ambiguity,
the same procedure may be applied accordingly to get
the other two carrier ambiguities N2 and N3.
4. Combining triple-frequency carrier
phase and code data