1. error sources affecting high accuracy GNSS positioning
overview of GPS
error sources affecting high accuracy GNSS positioning

2. What is GPS?
GPS, or Global Positioning System, is able to show you your position on the Earth anytime, in any weather, anywhere.
The three parts of GPS are:
Satellites
Receivers
Software

3. GPS Satellites
                                                                                                                                
The GPS Operational Constellation consists of 24 satellites that orbit the Earth in very precise orbits twice a day. GPS satellites emit continuous navigation signals.

4. The Signal from the Satellite
Microwave Radio Frequency
Effective Output 500W
Line of Sight
Pass through clouds, glass, plastic
Blocked by buildings, mountains, etc.
Weaker signals under trees
Satillite down to earth

5. Time Difference
The GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is.

6. Time Delay = Distance Signal travels at speed of light (c)
Time delay x c = distance
If delay = s then distance = 20,446 km
One sat and earth picture, one sphere graphic, work out math to give distance of 20,000 km
Delay = 68.2 ms

7. Time Delay = Distance
Therefore, we know we are located on a sphere 20,446 km from satellite
One sat and earth picture, one sphere graphic, work out math to give distance of 20,000 km

8. 3-D Trilateration
1 Satellite
2 Satellites
3 Satellites

9. Time Correction Error of 1/1000 second = 300 km
Atomic Clocks used in Satellites
Quartz Clock in GPS receiver
Needs to be corrected
Corrected by seeing fourth satellite
Atomic clocks are accurate to nano-seconds fact check. Add picture of timing corrections

10. More Satellites are Better
Receiver selects best signal
Geometry affects accuracy
Watch satellite page
If accruing signal from additional satellites good to wait
Able to watch accuracy improve
Screen capture of grays vs black satellites showing still in process of accruing signal from additional Satellites

11. GPS Signals
Each GPS satellite transmits data that indicates its location and the current time. All GPS satellites synchronize operations so that these repeating signals are transmitted at the same instant.
Physically the signal is just a complicated digital code, or in other words, a complicated sequence of “on” and “off” pulses.
Signal chosen because:
The complex pattern ensures that the receiver does not accidentally synchronize up to some other signal or so the receiver won’t accidentally pick up another satellite’s signal

12. Signal Components
Almanac (telemetry) updated location of all satellites
Unique Satellite identification code
Pseudorandom noise code – similar to a song
Work on second mouse click that will lock in the PRN signal once it has locked in.
Offset = 68.2 milliseconds

13. The GPS Signals GPS satellites transmit on two L-band frequencies:
L1 = MHz (19 cm wavelength)
L2 = MHz (24.4 cm wavelength)
These two carrier frequencies (sine waves) are modulated by two digital codes and a navigation message.
Code modulations are achieved by
BPSK (binary phase shift keying) method
QPSK (quadrature phase shift keying) method

14. The GPS Codes – C/A Code The Coarse Acquisition (C/A) Code
Modulated on the L1 carrier only
For each satellite, a unique pseudorandom code of 1023 bits
The chip rate is Mbps*
In distance domain, one chip is 293 m
Code looks like noise, but is generated mathematically, hence “PRN Code” (pseudorandom noise)
Available to all users
* A “chip” is the length of time to transmit 0 or 1 in a binary pulse code. The chip rate is the number of chips per second.

15. The GPS Codes – P Code Precision (P) Code
Modulated on both L1 and L2 carriers
Encrypting the P code w/ secret W code results in Y code
Referred to as anti-spoofing (A-S)
Also called P(Y) code
P code chip rate is Mbps - 10x faster than C/A
In distance domain, one chip is 29.3 m
P code sequence is very long - A unique pseudorandom noise (PRN) code of 2.35 x 1014 binary digits
266 day period; divided into 38 segments of 7 days each
Each satellite transmits a unique 1-week segment of P-code, initialized every 0000

16. The GPS Navigation Message
Navigation (telemetry) data messages are modulated on both L1 and L2 carriers at a rate of 50 kbps.
In distance domain, one chip is 5950 km
Consists of 25 frames of 1,500 bits each, or 37,500 bits total
Complete transmission takes 750 seconds, or 12.5 minutes
Navigation message includes:
Coordinates of the GPS satellites in time
Satellite health, clock correction, almanac & atmospheric data
Info about other satellites

17. Execution of Surveys; Sources of Error
Errors may be characterized as random, systematic, or blunders
Random error represents the effect of unpredictable variations in the instruments, the environment, and the observing procedures employed
Systematic error represents the effect of consistent inaccuracies in the instruments or in the observing procedures
Blunders or mistakes are typically caused by carelessness and are detected by systematic checking of all work through observational procedures and methodology designed to allow their detection and elimination

18. GPS Errors & Biases (1) GPS errors include:
Satellite errors
Receiver errors
Signal propagation errors
Various schemes can be employed to reduce or even eliminate these errors

19. GPS errors include: Satellite errors
GPS Errors & Biases
GPS errors include: Satellite errors
orbit error
center-of-mass to L1 antenna phase center
L1-L2 antenna phase center offset
atomic clock error
selective availability (SA)
Satellite geometry, DOP
Transmission multipath
Satellite inter-channel bias

20. Ephemeris Error Satellite orbits are modeled (predicted)
Modeling not perfect – Ephemeris error on the order of 2 m to 5 m
Between-receiver differencing does not entirely remove ephemeris error, but better over short baselines (<10 km).
Two receivers located closely see about the same orbit error
In relative positioning, the ratio of ephemeris error to SV range is proportional to the baseline error to baseline length ratio
Expected baseline error is 2.5 mm for a 5 m ephemeris error for a 10 km baseline
Precise ephemeris data can be downloaded and applied during post-processing.

21. Satellite Clock Errors
Block II/IIA SVs carry 4 clocks
2 Rubidium and 2 Cesium atomic clocks
Block IIR carry Rubidium clocks only
Ru & Cs clocks are not perfect – some drift
Drift error corresponds to a range error ~2.6 to 5.2 m
Or ~8.6 to 17.3 ns per day
SV time monitored by control segment
Amount of drift is calculated and transmitted in the navigation message
Still leaves an error of several nanoseconds (where one nanosecond equates to a range error of ~ 30 cm)
Best removed by differencing techniques

22. Selective Availability
SA added by DoD with the Block II SVs in 1990
Motivated by C/A code receiver accuracies which approached P-code receiver accuracies
Even though P-code designed to be 10x more accurate
SA dithered the SV clock time (delta error) & slowly varied the orbital error (epsilon error)
SA discontinued in 2001
Too many schemes developed to get around SA
For short baselines, DGPS effectively cancelled SA
Eliminating SA improves autonomous accuracies
22 m horizontal, 33 m vertical, 95% of the time
DGPS accuracy not improved, but can lower transmission rate of differential correctors

23. Satellite Distribution
When the satellites are all in the same part of the sky, readings will be less accurate.

24. Satellite Geometry (1) Good geometry when satellites are spread out
Measures of geometry
DOP – Dilution of Precision (no dimensions) computed from approximate receiver & satellite coordinates
PDOP – Position Dilution of Precision
HDOP – Horizontal Dilution of Precision
VDOP – Vertical Dilution of Precision
TDOP – Time dilution of Precision

25. Satellite Geometry (2) The lower the DOP the better
Recommended PDOP < 5
Recommended HDOP < 2.5
DOPs are easy to predict using receiver approximate position & ephemeris predictions (SV almanacs).

26. GPS errors include: Receiver errors
GPS Errors & Biases
GPS errors include: Receiver errors
receiver noise
receiver clock
Antenna phase center
L1-L2 phase center offset
L1-L2 phase center variation
Circular polarization
Receiver inter-channel bias
Stability
Antenna height
Mark stability
Earth tides
Ocean tide loading
Atmospheric loading
Crustal motion

27. Receiver Clock Errors
Receivers use inexpensive crystal clocks, so experience much larger clock drift.
Can be treated as an unknown in the solution estimation process
Better yet, can be removed with differencing techniques.

28. ANTENNA HEIGHT
ARP
MARK
The height is measured vertically (NOT slant height) from the mark to the ARP in meters.
ARP = Antenna Reference Point, shown at
I promised we would talk more about antenna heights.
The height of the antenna is measure vertically from the from the mark, to the Antenna Reference Point which is almost always the center of the bottom-most, permanently attached piece o f the antenna.
Some antennas have a short pipe or extension to them.
If in doubt you can find photo’s and diagrams of each antenna (that we have calibrated) at the URL shown.
So if you leave the antenna height as “0” this will be the height OPUS returns.

29. The antenna phase centers are located somewhere around here.
ANTENNA TYPE
The antenna phase centers are located somewhere around here.
phase ctr.
The antenna offsets are the distance between the phase centers and the ARP
ARP
You do not need to know these offsets. They are passed to the processing software through the antenna type
This is a close up of the last slide. You can see where the ARP is.
When you enter the correct Antenna type OPUS knows the antenna offsets and passes them to the software to determine the ARP
NGS uses the ARP rather than the phase center. The ARP is a known point on the antenna whereas the phase center varies depending on the elevation angle from the antenna to the satellite.
The Antenna Reference Point (ARP) is almost always located in the center of the bottom surface of the antenna.
Incorrect or missing antenna type  big vertical errors

30. Antenna Phase Center Variation
Phase Center Variation (mm)
This shows the difference in vertical position of the L1 Phase Center as the satellite gains altitude.
You can see the phase pattern changes by 15 mm as the satellite climbs in its orbit
Elevation Angle (deg.)

31. Antenna Phase Center Variation
SV 20
SV 20
SV 14 .
SV 14
Different
Phase Patterns
Note that SV elevation and varying phase patterns affect signal interpretation differently
Antenna
Type B
Antenna
Type A
But where the problem comes in is that different types of antennas have different phase pattern.
This is the point in space where the antenna thinks it is receiving the signal. And it is different for the L1 & the L2.
So the satellites elevation and the varying phase patterns affect signal interpretation.

32. Antenna Phase Center Variation
The antenna phase center does not coincide with the physical center of the antenna’s active element.
In fact, the phase center can vary with SV elevation and azimuth.
Antenna phase center errors typically on order of a few centimeters.

33. Antenna Phase Center Variation
Use correct antenna type/calibration parameters for acquisition and processing.
NGS Antenna Calibration web site
For short baseline surveying, use the same antenna on each receiver
Orient each antenna in the same direction
Differencing techniques will cancel phase center variations

34. GPS errors include: Signal Propagation errors
GPS Errors & Biases
GPS errors include: Signal Propagation errors
Ionospheric effects
Dry troposphere delay
Wet troposphere delay
multipath

35. Line of Sight Transmissions
Line of sight is the ability to draw a straight line between two objects without any other objects getting in the way. GPS transmission are line-of-sight transmissions.
Obstructions such as trees, buildings, or natural formations may prevent clear line of sight.

36. Light Refraction
Sometimes the GPS signal from the satellite doesn’t follow a straight line.
Refraction is the bending of light as it travels through one media to another.

37. Atmospheric Error Sources
Ionosphere
Greatest at 1400 (local time)
Typical 5 to 15 m at zenith
Extreme 0.15 to 50 m at zenith
Higher frequencies have less effect
Error correction by dual frequency
“Wet” Troposphere
10% of total effect
Model accuracy only 10 to 50%
Need humidity along path
About 20 cm at zenith
Hydrostatic (“Dry”) Troposphere
90% of total effect
Model accuracy only 2 to 5%
Need surface atmospheric pressure and temperatures
Accurate pressure is critical
About 2.2 m at zenith

38. GPS Signal Delays Caused by the Atmosphere
TEC
IPWV

39. Atmosphere based Ionospheric Delay (Advance)
Ionosphere
> 10 km
< 10 km

40. Ionospheric Delay (1) The ionosphere is
A region of earth’s atmosphere where uv and x-ray radiation from sun cause gas ionization.
Extends from 50 km to ~1,000 km altitude
Ionosphere is a dispersive medium – it bends GPS signals and changes propagation speed of signal.
Bending (signal refraction) causes negligible range errors
Propagation speed changes cause significant range errors
Speeds up carrier phase beyond speed of light, so ranges appear short
Slows down PRN code, so ranges appear long
Ionosphere is not homogenous – described in layers within which electron densities vary.
Total Electron Count (TEC) varies with time of day, time of year, 11-year solar cycle, geographic location.

41. Ionospheric Delay (2) Ionospheric delay is frequency dependant
L2 ( MHz, 24.4 cm) is greater than L1 delay ( MHz, 19 cm)
Range errors on the order of 5 to 15 meters, but can be as high as 150 m during extreme solar events at midday and near the horizon
Differencing techniques over short baseline distances can effectively remove much of the ionospheric delay.
Dual-frequency receivers combine L1 & L2 carrier phase measurement for iono-free solutions
But increases measurement noise, so not always reliable
Loose integers of cycle ambiguities
Single frequency receivers must use empirical models in post-processing or from real-time sources.

42. Troposphere Delay Ionosphere troposphere
The more air molecules the slower the signal (dry delay)
High pressure
Low temperature
90% of total delay
relatively constant and easy to correct for
The more water vapor in the atmosphere the slower the signal (wet delay)
High humidity
10% of total delay
Highly variable and hard to correct for
Ionosphere
troposphere

43. Tropospheric Delay
The troposphere extends from earth’s surface up to about 50 km altitude
It is considered electrically neutral
Non-dispersive medium for RF below 15 GHz
Varies with temperature, pressure, and humidity
So minimized at receiver’s zenith (~2.3 m error), maximum at low elevations (~20-28 m error at 5° elevation)
Separated into dry (90%) and wet component
Dry component can be predicted ok.
Wet component cannot be predicted that well
Tropospheric delay cannot be removed with differencing techniques
Use standard meteorological data as default.
1010 mb, 20° C, 50% rel humidity

44. Sunspot cycle Sunspots follow a regular 11 year cycle
We are just past the peak of the current cycle
Sunspots increase the radiation hitting the earth's upper atmosphere and produce an active and unstable ionosphere

45. Signal Interference
Sometimes the signals bounce off things before they hit the receivers.

46. Multipath chain link fences vehicles road signs
Multiple signal paths between the satellite and receiver
caused by reflected signals within the receiver environment
chain link fences
vehicles
road signs
To reduce the errors associated with multipathing use a ground plain and avoid sites near reflective surfaces
B>

47. Multipath Errors (1)
A major error source for both pseudorange and code-phase measurements
Occurs when the GPS signal arrives at the antenna from a reflected path.
The reflected path is longer, so the receiver-to-satellite range appears greater.
Reflected signal interferes with the direct signal at the receiver antenna
Function of objects around antenna
Varies with SV geometry

48. Multipath Errors (2)
Multipath affects both carrier-phase and pseudorange measurements
Carrier-phase multipath max value is ¼ cycle, or about 4.8 cm on L1
Pseudorange multipath can theoretically reach tens of meters for C/A code measurements.
Pseudorange multipath mitigated w/ receiver technology
Since multipath is a function of SV geometry, it’s characteristics repeat every sidereal day
Assuming a static receiver configuration
This means it can be correlated from one day to the next in the position solution residual estimate

49. Multipath Errors (3) To reduce effects of multipath
Select a receiver antenna location free of obstructions or reflecting surfaces
Use an antenna w/ a groundplane, or a choke ring antenna
Choke ring features ¼ wavelength slots in a concentric pattern to attenuate reflected signals
In static observations, conduct data acquisition over multiple days during different time blocks

50. Multipath
Satellite signal arriving at receiver via multiple paths due to reflection (Leick 1995)
Quasi-periodic signal; 5 to 50 minutes
Maximum multipath is a fraction of wavelength (L1 = 19 cm; L2 = 24 cm) typically 2 to 5 cm
Geometric relationship between satellite, antenna, and surroundings
Same pattern in same satellite geometry on consecutive days

51. h ø ø Figure 1 Multipath Description
Multipath Delay :
(meters)
T = 2hSinø c
Multipath Freq. :
(Cycles/hr)
d(T )ƒ~ hCosø
dt  h
d ø ~ 2 rad.
dt hr. ø ø
Figure 1
Multipath Description
August Ionospheric refraction and Multipath Effects in GPS Carrier Phase Observations
Yola Georgiadou and Alfred Kleusberg
IUGG XIX General Assembly Meeting, Vancouver, Canada

52. Differential Correction
Differential correction is a technique that greatly increases the accuracy of the collected GPS data. It involves using a receiver at a known location - the "base station“- and comparing that data with GPS positions collected from unknown locations with "roving receivers."
ISU Base Station -

53. Differential GPS Positioning

54. DGPS Radio Beacon Systems

55. DGPS Radio Beacon Systems
Accuracy of DGPS method between <1 m and <3 m, depending on base-rover distance, transmission rate (“age of correctors”), and quality of C/A code receiver.
Higher accuracy w/ short baseline distances, higher transmission rates, and carrier-smoothed C/A code ranges.
Range is limited by VHF signal

56. WAAS-Wide Area Augmentation System

57. WAAS-Wide Area Augmentation System
Satellite based augmentation system
Developed by FAA & DOT for precision flight approaches
Approximately 25 ground reference stations across the US that monitor GPS satellite data.
Two master stations, located on either coast, collect data from the reference stations and create a GPS correction message.

58. WAAS-Wide Area Augmentation System
This correction accounts for GPS satellite orbit and clock drift plus signal delays caused by the atmosphere and ionosphere.
The corrected differential message is then broadcast through one of two geostationary satellites, or satellites with a fixed position over the equator.
The information is compatible with the basic GPS signal structure, which means any WAAS-enabled GPS receiver can read the signal.
Better than 3 m error 95% of the time.

59. Postprocessing / Real-time
Before
After

60. Carrier Phase Positioning
Resolving the integer ambiguity allows phase
measurements to be related to distances Nl
Distance
Nl = Integer Ambiguity
Dl = First Partial
Wavelength Dl
Distance = Nl + Dl

61. Carrier Phase Differencing( ) 2 1 N - + D = l p
Difference
Phase
Distance
Phase Difference

62. Datasheet Basics what's on a datasheet
The NGS Data Sheet
See file dsdata.txt for more information about the datasheet.
DATABASE = Sybase ,PROGRAM = datasheet, VERSION = 7.56
National Geodetic Survey, Retrieval Date = NOVEMBER 20, 2007
AE8289 ***********************************************************************
AE8289 CBN This is a Cooperative Base Network Control Station.
AE8289 TIDAL BM This is a Tidal Bench Mark.
AE8289 DESIGNATION
AE8289 PID AE8289
AE8289 STATE/COUNTY- MN/ST LOUIS
AE8289 USGS QUAD - DULUTH (1993)
AE8289
AE *CURRENT SURVEY CONTROL
AE8289 ___________________________________________________________________
AE8289* NAD 83(2007) (N) (W) ADJUSTED
AE8289* NAVD (meters) (feet) ADJUSTED
AE8289 EPOCH DATE
AE8289 X , (meters) COMP
AE8289 Y ,373, (meters) COMP
AE8289 Z ,624, (meters) COMP
AE8289 LAPLACE CORR (seconds) DEFLEC99
AE8289 ELLIP HEIGHT (meters) (02/10/07) ADJUSTED
AE8289 GEOID HEIGHT (meters) GEOID03
AE8289 DYNAMIC HT (meters) (feet) COMP
AE Accuracy Estimates (at 95% Confidence Level in cm)
AE8289 Type PID Designation North East Ellip AE
AE8289 NETWORK AE
AE8289 MODELED GRAV , (mgal) NAVD 88
AE8289 VERT ORDER - FIRST CLASS II
AE8289.The horizontal coordinates were established by GPS observations
AE8289.and adjusted by the National Geodetic Survey in February 2007.
what's on a datasheet
Position
Accuracy
How to locate and identify
help files (dsdata.txt, glossary, …)

63. W GEODETIC CONTROL BASICS: 1) Position? 2) Accuracy?
95% confidence interval W
NAD 83(2007) (N) (W)

64. A horizontal plane parallel with the ellipsoid
horizontal accuracy
radius
north a a b W W
east W
NGS 2007
textbook
FGDC 1998
A horizontal plane parallel with the ellipsoid

65. vertical accuracy W 95% confidence interval
--- NAVD (meters)

66. tie to adjacent stations?
old vs new accuracies
old order
(1st order class II)
new order
(1 cm)
distance dependent?
YES
angles, distances, leveling have proportional errors. NO
“rigid” GNSS network.
tie to adjacent stations?
ties are required.
local accuracy is computed.
accuracy metric?
TECHNIQUE
equipment resolution, design, technique, closure.
STATISTICS
observation quality, adjustment results.

67. Datasheet W North = 0.86 cm East = 0.69 cm Ellip = ± 1.45 cm
FZ1046 ***********************************************************************
FZ *CURRENT SURVEY CONTROL
FZ1046 ___________________________________________________________________
FZ1046* NAD 83(2007) (N) (W) ADJUSTED
FZ1046* NAVD (meters) (feet) LEVELING
FZ1046
FZ Accuracy Estimates (at 95% Confidence Level in cm)
FZ1046 Type PID Designation North East Ellip FZ
FZ1046 NETWORK FZ1046 E
FZ1046 VERT ORDER - THIRD ?
North = 0.86 cm
East = 0.69 cm
(N) (W) (meters) W
Ellip = ± 1.45 cm

68. using local & network accuracies
Network = CORS %w %a wz xy wx yz
“%z”
“aw”
“bx” ad bc cd ab
“%d” z w a d y x b c
“%y”
“%x”
“%b”
“%c”

69. using local & network accuracy horizontal example
0.0 cm
CORS
CORS
network 5.5 cm
North East
North East Ellip
network 0.86 cm
local
2 cm
“local”
5.91 cm
“network” 5.85 cm

70. Readjustment: What changed?