1. Ruth Neilan and Jan Kouba IGS Central Bureau at JPL
Introduction to GPS
Ruth Neilan and Jan Kouba
IGS Central Bureau at JPL
Pasadena, California
USA

2. Content Space Segment Control Segment User Segment and Ground Segment
GPS System Description
Space Segment
Control Segment
User Segment and Ground Segment
GPS Signals
Observations, Observation Model
Pseudorange, Carrier Phase
GPS Positioning
Navigation/Point Positioning
Relative Positioning/Differencing
GPS Denial of Accuracy
GPS Error Sources
GPS Future Developments

3. GPS System Description
GPS (Global Positioning System)
also called NAVSTAR (NAVigation System, Timing And Ranging)
The GPS consists of 3 main segments:
Space Segment: the constellation of satellites
Control Segment: operation and monitoring of the GPS System
User Segment: all GPS receivers and processing software's
We might add a 4th segment:
Ground Segment:
permanent civilian networks of reference sites, associated analyses and archives (e.g. IGS)

4. GPS Space Segment
The space segments nominally consists of 24 satellites, currently:
28 (24+4 spares) active GPS satellites (26 Block II, 2 Block IIR)
Constellation design: at least 4 satellites in view from any location at any time to allow navigation (solution for 3 position + 1 station clock unknowns)
“Right Time, Right Place, Any Time, Any Place”
GPS Orbit characteristics:
Semi-Major Axis (Radius): 26,600 km
Orbital Period : h 58 min
Orbit Inclination: degrees
Number of Orbit Planes: 6 (60 degree spacing)
Number of Satellites: (4 spares)
Approximate Mass: kg, 7.5 year lifespan
Data Rate (message): bit/sec
PRN (Pseudo-Random Noise) Codes: Satellite-dependent Codes
Transmit, Frequencies L-Band L1: MHtz L2: MHtz

5. GPS Space Segment
Speed of satellites relative to the Earth center approximately 4 km/s, relative to the user up to 2.8 km/s.
GPS satellites repeat their ground tracks after: 1 sidereal day = 23 h 56 min = 2 orbital periods. The same geometry is reached 4 minutes earlier every day.
2:1 commensurability of GPS revolution period with Earth rotation leads to resonance effects with gravity field (many maneuvers necessary).
Satellites equally distributed in each of the six orbit planes.

6. GPS Space Segment
Currently: 26 Block II, 2 Block IIR, no Block I satellites are active.
Picture of a Block II Satellite

7. US Air Force and NIMA Control and Tracking Stations
GPS Control Segment
US Air Force and NIMA Control and Tracking Stations
Hermitage
MCS Colorado Springs
Bahrain
Kwajalein
Hawaii
Ascension
Ouito
Diego Garcia
Smithfield
Buenos Aires
US Airforce Tracking Sites
US Airforce Upload Sites
See also map at <
MCS – Master Control Station
US NIMA Tracking Sites

8. GPS User and Ground Segment
User Segment:
All GPS receivers on land, on sea, in the air and in space.
Extremely broad user community with applications of the GPS for:
Navigation
Surveying
Geodynamics and geophysics
Remote sensing (troposphere and ionosphere)
Time and frequency transfer
etc.
Ground Segment:
IGS global network; IGS products reference frame for coordinates, orbits, and Earth rotation.
Regional permanent networks (Europe, Japan, US, ...): densification of the reference frame.

9. GPS Signals Signals driven by an atomic clock
Fundamental Frequency at MHz
Two carrier signals (sine waves):
L 1 : f= MHz, ( =19 cm ), generated by MHz x 154
L 2 : f= MHz, (  =24 cm), generated by MHz x 120
Bits encoded on carrier by phase modulation:
C/A-code (Clear Access / Coarse Acquisition): MHz ( =300 m ), 10.23/10
P-code (Protected / Precise): MHz ( = 30 m ) at fundamental frequency
Navigation Message: (system time, “Broadcast” orbits, satellite clock corrections, almanacs, ionospheric information, etc.), 50 bps on both L1 and L2

10. Observations and Models
Pseudorange measurements by delay correlation time difference (Tr-Ts) of the received satellite and receiver replica codes
Prs = c (Tr-Ts) = rs + c (tr - ts)
Phase differences (r-  s) (initially ambiguous), analogously by comparing the received satellite and receiver generated phases:
Lrs =  (r-  s) = rs + c (tr - ts) + brs
Where: c is the speed of light; rs is the receiver to satellite distance;  is the wavelength; tr and ts are the receiver and satellite clock errors; brs is the initial (non-integer) phase bias.

11. Navigation/Point Positioning
Typical noise on pseudorange or phase measurements is < 1% of the wavelengths: for C/A pseudorange: < 3m; for P-code: < .3 m and for phase measurements: < 2 mm
Basic Observation model (equation):
rs + c (tr - ts) + brs + …
Where ‘…’ indicates additional error sources
for pseudoranges (when brs =0) contains 4 unknowns (xr, yr, zr, tr) : 3 for the receiver position and one for receiver clock error, and
rs =((xs-xr)2 +(ys-yr)2 +(zs-zr)2)
satellite positions and clock errors (xs, ys, zs, ts) are obtained from the navigation (broadcast) message
at least four (typically 6) simultaneous pseudorange observations are needed for receiver position and clock determination (at m, nsec level)
for phases an initial phase bias unknown brs per each observed (continuous) satellite arc must be introduced. After that (subject to an initial phase/clock datum), phase navigation is completely analogous to pseudorange navigation.

12. Relative Positioning by Differencing
Single differencing : by subtracting simultaneous phase observations from station A and B to the same satellite S
[ As + c (tA - ts) + bAs + …]–[ Bs + c (tB - ts) + bBs + … ]= ABs + c tAB + bABs
nearly eliminates satellite clocks, receivers must be synchronized within 1 msec
reduces some common errors, in particular for short baselines A-B, such as errors due to orbit, ionosphere or troposphere
solutions for the station clock difference tAB still required
Double differencing: by subtracting two single differences (between stations A,B) to the satellites i and j.
ABij + NABij
where ABij = ABi - ABj and the double difference phase ambiguity NABij = bABi- bABj is an integer! (all phase instrumental biases cancel out)
station clock differences are nearly eliminated! Only 3 relative position unknowns needed after the initial integer ambiguities are resolved

13. Basic Concepts tobs A = observed time delay from SV signal
GPS Positioning: Simplified Concepts, Basic Error Sources
GPS
tobs A = observed time delay from SV signal
transmit to station A signal reception
TR = Time signal received at A
Ts = Time signal trasmitted from SV
tgeo = delay due to geometry, distance
tClk A = apparent delay due to user clock offset
tsv = apparent delay due to satellite clock offset
tiono = dispersive delay due to ionosphere
tatm(wet/dry) = delay due to troposphere
tmult = delay due to multipath (m), signal reflection Ts
tobs A A m TR
tobs A = = (TR - Ts ) = tgeo+ tClk A - tsv + tiono + tatm(wet/dry) + tmult +...

14. Differencing Techniques
Single Differencing: reduces common errors, SV Clock nearly cancels, appropriate for short baselines
GPS
dts
rA = observed distance, including errors
rAs = correct ‘true’ distance SV to station
((xS-xA)2+(yS-yA)2+(zS-zA)2)1/2
dtA or B = station clock error
dts = satellite clock error
tAB= difference in station clock offsets
c = speed of light
b = initial phase bias SV to station
B = baseline rB rA
DrAB =rA- rB B B
dtB A
dtA
DrAB = rA- rB = [rAs + c (dtA - dts) + bAs +…]-[ Bs + c (dtB - dts) + bBs +…]
= DrABs + c tAB + bABs

15. Differencing Techniques
GPSi
GPSj
rBj
rBi
rAi
rBj
Double Differencing: station clock offsets nearly cancel, only 3 relative positions needed, (x,y,z) B B A
DrABij = DrABi - DrABj
bABij = DbABi - DbABj = DNABij >> an integer phase ambiguity

16. GPS Denial of Accuracy
Selective Availability (SA): intentional degradation of accuracy
Increased navigation errors (based on broadcast orbits/clocks) from several meters to more than 30 m !
Epsilon: navigation message contained intentional orbit errors; apparently not used; no effect when using IGS precise orbits.
Dither: satellite clock was dithered; same effect as a satellite clock error; eliminated (mitigated) when using relative (differential) positioning; no effect when using IGS precise clocks (but only at the epochs of the IGS precise clock)
cm phase navigation/positioning with IGS precise orbits and clocks!
Switched off permanently on May 2, 2000 WK 1060, Day of Year 123) at 04:00UT as directed by the President of the US.
Anti-Spoofing (AS): denial of precise P-code
Encryption of the more precise P-code on L1 and L2 (a key available only to authorized users)
Modern GPS receivers can still perform precise code (< .3m)and phase (<2mm) measurements on L1 and L2
Somewhat increased noise level for code measurements and for L2 carrier phase measurements even for modern GPS receivers.

17. GPS Error Sources Satellite orbits Satellite clocks
IGS Final or Rapid orbits (available within 24h) virtually eliminate orbit errors (<.1m) for post-processing at any epoch
In real-time the broadcast orbit errors (~3m) can be reduced (< 1m) by DGPS (Differential GPS) or by using IGS Predicted or the Ultra-Rapid orbits
Satellite clocks
for relative positioning double differencing nearly eliminates satellite clock errors
IGS Final or Rapid satellite clocks (available within 24h) virtually eliminate satellite clock errors (<.1m) for post-processing (currently only at the 5 min epoch sampling)
in real time the broadcast clock errors (SA) reduced by DGPS
Tropospheric refraction
virtually eliminated by estimating corrections to a model (also used in GPS meteorology); or at IGS stations, by using the IGS tropospheric delay products!
nearly eliminated (< .1m) by using a model with measured met data
reduced by a nominal model and/or differential positioning (e.g. DGPS)

18. GPS Error Sources Ionospheric refraction
for dual frequency receivers, the use of (P1, P2) or (L1, L2) virtually eliminates ionospheric refraction (also used for ionospheric delay determination/monitoring, e.g. by IGS, the IGS ionospheric delay products )
For single frequency receivers, the use of IGS ionospheric delay products (available within a few weeks) significantly reduces ionospheric refraction errors
For single frequency receivers, ionospheric refraction errors reduced in differential (relative) positioning (e.g. DGPS) for baselines up to 100 km
Antenna phase center variations
virtually eliminated in relative positioning over moderate baseline lengths (<500km) when using the same antenna types
antenna phase center corrections (e.g. IGS antenna phase center tables) must be used for different antenna types and precise positioning (<.1m)
Multipath
difficult to mitigate, errors can reach a few cm for the phase and up to a meter or more for pseudorange positioning/navigation
reduced by improved site selections and hardware (receiver/antenna) designs

19. Future Developments GPS Modernization
C/A on L2, improve codeless, cross correclation receiver processing
3rd frequency, L5 at MHz with full access to frequencies available for civilian use
improved satellite designs, longer life, Hydrogen Maser frequency standards
Spectrum protection for GPS signals remains an issue, conflict with satellite communications interests
Need space-to-space allocation for GPS use
Full and guaranteed access (in peace time) to civilian use
guaranteed by the Presidential Decision Directive (PDD), March 1996:
SA switched off on May 2, 2000, GPS WK 1060, 123 doy at 04:00UT
no SA should allow cm interpolation of the IGS clock solutions and instantaneous cm positioning/navigation at any instant at any time with no base (DGPS) stations required
with no SA most DGPS’ should become obsolete and redundant

20. References
Websites
GPS Links from IGS:
U.S. Coast Guard Navigation Information Center:
U.S. Department of Transportation:
NIMA Satellite Geodesy:
UNAVCO:
GPS Environmental & Earth Science Information System:
GPS Joint Program Office
Books:
Institute of Navigation, Global Positioning System, Vol. I, Papers published in NAVIGATION, ISBN: , 1980 (Spilker, Van Dierendonck, etc.
American Institute of Aeronautics and Astronautics (AIAA), Global Positioning System: Theory and Applications, Volume I & II, Progress in Astronautics and Aeronautics ISBN or Order Number: , 1996
Kleusberg, A. P. Teunissen,ed. GPS for Geodesy, Lecture Notes in Earth Sciences, Springer-Verlag, ISBN , 1996
Springer, T.A., “Modeling and Validating Orbits and Clocks Using the Global Positioning System”, Doctoral Thesis, University of Bern, Switzerland, November 1999

21. QUESTIONS? Ruth E. Neilan
IGS Central Bureau Jet Propulsion Laboratory,
Pasadena, California, USA