stephen wood, jlab, nov 13, 2002 /home/saw/slides/gps/gpstalk.sxi the global positioning system...

Stephen Wood, JLAB, Nov 13, 2002 /home/saw/SLIDES/GPS/gpstalk.sxi

The Global Positioning System

Technology, Applications and

PhysicsStephen A. Wood


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)


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


Accuracy

Stationary Garmin Etrex Legend on Dashboard

Position recorded every 60 seconds

5.7m

8.2m

4.3m

8.0m


“Selective Availability”


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


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


Analog GPS Receiver


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


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


Geodetic MeasurementsSubduction pushes edge of North American Plate inland

Movement went backward aseismically for one month in 1999

6.7


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


GPS Applications

Car Navigation

Hiking

Parking

Tombstones

Geocaching


A Friend Built a Sail Boat

Used a low cost consumer receiver to log trip


Errors/Corrections

SatelliteTroposphere

Ionosphere

Relativity

Solar Wind/Eclipses

GroundPolar Motion 15m

Fluctuation in rotation period 1ms → 0.5m

Coordinate systems


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?


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


Propagation in Ionosphere

Plane wave solution of Maxwell's equations:=Dispersion relation

Phase and Group velocityâ‰ˆDelay/Advancement from c

Units: TEC TECU


Ionosphere


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


Why are GPS signals polarized?

GPS signals are Right Hand Circularly Polarized

Dielectric constant in magnetic field is polarization dependent. â‰ˆÃ—âˆ’

@TEC=100TECU 0.07ns40 degrees of phase

Could confuse carrier phase detection

Probably other reasons to polarize


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


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”


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


Homework

List ways in which a GPS receiver can be used to measure the height of a building.

stephen wood, jlab, nov 13, 2002 /home/saw/slides/gps/gpstalk.sxi the global positioning system...

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