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Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
The Global Positioning System
Technology, Applications and
PhysicsStephen A. Wood
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
GPS Basics
Orbiting satellites broadcast precise time
Receiver on earth measures transit times
Need >= 4 satellite signals to obtain 3D position and resolve time ambiguity
Consumer receiver accuracy < 20 m
Errors at different locations are correlatedVarious services calculate and distribute/sell corrections to basic GPS signals (Differential GPS) << 1m
Wide Area Augmentation System operated as part of standard GPS (Aviation)
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
GPS “Constellation”
24+ satellites in 6 orbital planes55 degree inclination
20183 km above earth surface
Period 11 hr 58 min, ½ sidereal day
L1 = 1575.42 MHz, L2 = 1227.60 MHz
Prototypes launched 1978. Declared fully operational in 1995.
New Block IIR sats replacing older ones10 year life
2 cesium + 2 rubidium clocks
Can operate autonomously for 180 days
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Accuracy
Stationary Garmin Etrex Legend on Dashboard
Position recorded every 60 seconds
5.7m
8.2m
4.3m
8.0m
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
“Selective Availability”
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
GPS Signals
C/A Code: 1023 chip pseudo random code. 1Khz
All satellites on same carrier, but unique C/A codes
1 data bit = 20 codes. 50 bits/s
1 chip = 290 meter
1023 chips = 300 km
Data updated from ground
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Receiving GPS signalsAll satellites on same carrier.
Doppler shift ± 20 KHz
Receivers mostly digital
Downmixing
sin Î 1 t sin Î 2 t =12
cos Î 1 Î 2 t12
cos Î 1ƒ Î 2 t
Filter high freq. Phase shifts preserved
Feasible to digitize and correlate in software
1575.42-1546.78 = 28.64
sin Î 3 t ƒ Ë CA sin Î 4 t ƒ Ë CA Œcos Î 3 Î 4 t ƒ Ë Ë
22.9MHz 5.7MHz -> Band pass filter
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Analog GPS Receiver
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
GPS Applications
High Precision crane guidance at shipyards
Synchronization of clocksK2K Neutrino Oscillation: Tag events to 20ns
Precision Farming
Geodetic Measurements
Wind speed above ocean. Radar scatterometer
Surveying
Indoor GPS
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Precision Farming
Base Station receiver broadcasts differential signal
Tractor with 3 DGPS receivers. <1” positioning
Benefits:Optimize Plowing. No overlap. Pull wider plows. Exactly reproduce rows each year. Drip line placement.
Grade/Level fields
Broaden labor pool
24x7 plowing
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Geodetic MeasurementsSubduction pushes edge of North American Plate inland
Movement went backward aseismically for one month in 1999
6.7
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Geodetic Measurements
Carrier Phase GPS relative to reference siteSolid Earth Tide, pole tide + ocean loading corrections
Hourly estimation of tropospheric delay
Precise IGS satellite orbits
Ionospheric-free phase solutions
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
GPS Applications
Car Navigation
Hiking
Parking
Tombstones
Geocaching
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
A Friend Built a Sail Boat
Used a low cost consumer receiver to log trip
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Errors/Corrections
SatelliteTroposphere
Ionosphere
Relativity
Solar Wind/Eclipses
GroundPolar Motion 15m
Fluctuation in rotation period 1ms → 0.5m
Coordinate systems
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
WGS-84
WGS-84 defines ellipsoid and geoid.
Geoid is Mean Sea LevelGeoid extends under land using gravity measurements
What does your GPS receiver use?
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Dielectric Constant in Ionosphere
Refer to Jackson Dielectric Constant
Radio frequencies and free electrons
» Î =1Î p
2
Î 2Î p
2 =4 ÆÇe 2
m
Çmax H 10 12 e / m 3
10 MHz
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Propagation in Ionosphere
Plane wave solution of Maxwell's equations:=Dispersion relation
Phase and Group velocity≈Delay/Advancement from c
Units: TEC TECU
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Ionosphere
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Variation in delay
Electron density varies from 1 to 100 TECUDiurnal variation + solar “weather”
Angle of satellite from zenith
L1 1.57542 GHz L2: 1.2276 GHz0.5 – 55 ns 0.9 – 90 ns
Receivers have ionosphere model
Dual frequency receivers measure delay
DGPS/WAAS broadcast corrections
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Why are GPS signals polarized?
GPS signals are Right Hand Circularly Polarized
Dielectric constant in magnetic field is polarization dependent. ≈×−
@TEC=100TECU 0.07ns40 degrees of phase
Could confuse carrier phase detection
Probably other reasons to polarize
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Relativistic Effects
Special Relativity (Second order doppler shift)Sat clocks appear to run at
4km/sec
General RelativityGravitational Blue Shift speeds up clocks
Eccentric OrbitsCause daily variations
See Physics Today, May 2002. “Relativity and the Global Positioning System”
15 ms/day
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Sagnac Effect
Light propagating opposite directions in a rotating system
+/- 200 ns on earth
Issue for synchronizing clocks at different longitude
Many interpret Sagnac effect (and confirmation by GPS) as disproof of Special Relativity Theory
Linear motion relative, rotational motion absolute
SRT to weird
Deep seated need for “Geocentricity”
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Other Systems/Future
GLONASS (Global Navigation Satellite System)Soviet/Russian system, 10/24 satellites in operation
Each satellite has it's own frequency (FDMA)
EGNOS – European version of WAASBroadcasts corrections to GPS/GLONASS
GALILEOAdvantages over GPS
In part a symbol of European Pride. US Not thrilled.
GPS upgrades
Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi
Homework
List ways in which a GPS receiver can be used to measure the height of a building.