The Global Positioning System And Relativity: A 10%
The Global Positioning Systemand Relativity: A 10% test ofgeneral relativity everydayProf. Thomas HerringDepartment of Earth, Atmosphereand Planetary Sciences8.224 Seminar Fall 2001.http://www-gpsg.mit.edu/ tah02/24/20038.224 Seminar1
Overview Original design of the Global PositioningSystem (GPS) Use by “non-authorized” users Selected applications Relativistic effects02/24/20038.224 Seminar2
GPS Original Design Started development in the late 1960sas NAVY/USAF project to replaceDoppler positioning system Aim: Real-time positioning to 10meters, capable of being used on fastmoving vehicles. Limit civilian (“non-authorized”) users to100 meter positioning.02/24/20038.224 Seminar3
GPS Design Innovations:– Use multiple satellites (originally 21, now 28)– All satellites transmit at same frequency– Signals encoded with unique “bi-phase,quadrature code” generated by pseudo-randomsequence (designated by PRN, PR number):Spread-spectrum transmission.– Dual frequency band transmission: L1 1.575 GHz, L2 1.227 GHz Corresponding wavelengths are 190 mm and244 mm02/24/20038.224 Seminar4
Latest Block IIR satellite(1,100 kg)02/24/20038.224 Seminar5
Measurements Measurements:– Time difference between signal transmission fromsatellite and its arrival at ground station (called“pseudo-range”, precise to 0.1–10 m)– Carrier phase difference between transmitter andreceiver (precise to a few millimeters)– Doppler shift of received signal All measurements relative to “clocks” inground receiver and satellites (potentiallyposes problems).02/24/20038.224 Seminar6
Measurement usage “Spread-spectrum” transmission:Multiple satellites can be measured atsame time. Since measurements can be made atsame time, ground receiver clock errorcan be determined (along with position).rrr Signal V(t, x ) Vo sin[2 ( ft k .x ) C(t)]C(t) is code of zeros and ones (binary).Varies discretely at 1.023 or 10.23 MHz02/24/20038.224 Seminar7
Measurements Since the C(t) code changes the sign of thesignal, satellite can be only be detected if thecode is known (PRN code) Multiple satellites can be separated by“correlating” with different codes (only thecorrect code will produce a signal) The time delay of the code is the pseudorange measurement.02/24/20038.224 Seminar8
PositionDetermination(perfectclocks). Three satellitesare needed for 3-Dposition with perfectclocks. Two satellitesare OK if height isknown)02/24/20038.224 Seminar9
Positiondetermination:with clock errors:2-D case Receiver clock isfast in this case, soall pseudo-rangesare short02/24/20038.224 Seminar10
Positioning For pseudo-range to be used forpositioning need:– Knowledge of errors in satellite clocks– Knowledge of positions of satellites This information is transmitted bysatellite in “broadcast ephemeris” “Differential” positioning (DGPS)eliminates need for accurate satelliteclock knowledge.02/24/20038.224 Seminar11
GPS security: SA To stop non-authorized users from getting thefull accuracy of GPS, the military until May2000 “corrupted” the GPS signals. Selective Availability (SA) “dithered” theclocks by time equivalent of 100 meters. Turned off because ineffective(Example shown later)02/24/20038.224 Seminar12
GPS security: AS To ensure that military systems were notcorrupted by false GPS transmission, Antispoofing (AS) in enabled on all satellites At L1 frequency: GPS satellites use two C(t)sequences: Course Acquisition C/A code andPrecise Positioning code (P code) P-code in modified under AS to the Y-codewhich only authorized user know02/24/20038.224 Seminar13
Satellite constellation Since multiple satellites need to be seenat same time (four or more):– Many satellites (original 21 but now 28)– High altitude so that large portion of Earthcan be seen (20,000 km altitude —MEO)02/24/20038.224 Seminar14
Current constellation Relative sizescorrect (inertialspace view) “Fuzzy” lines notdue to orbitperturbations, butdue to satellitesbeing in 6-planesat 55o inclination.02/24/20038.224 Seminar15
Satellite Availability (smallest number above15o minimum elevation)Satellite Availability02/24/20038.224 Seminar16
Positioning accuracy Best position accuracy with pseudorange is about 20 cm (differential) andabout 5 meters point positioning. For many applications we want betteraccuracy For this we use “carrier phase” where“range” measurement noise is fewmillimeters02/24/20038.224 Seminar17
Carrier phase positioning To use carrier phase, need to makedifferential measurements between groundreceivers. Simultaneous measurements allow phaseerrors in clocks to be removed i.e. the clockphase error is the same for two groundreceivers observing a satellite at the sametime (interferometric measurement).02/24/20038.224 Seminar18
Phase positioning Use of carrier phase measurementsallows positioning with millimeter levelaccuracy and sub-millimeter ifmeasurements are averaged for 24hours.02/24/20038.224 Seminar19
200SAonPseudorange Point PositioningNorth (m)100Examples ofpositioningresults0-100Scatter 21 m and 23 m-2008101214 16 18Time (hrs)2022240.102.0Phase Differential PositioningPseudorange Differential Positioning0.05North (m)North (m)1.00.00-0.05-1.0Scatter 0.008 m and 0.002 mScatter 0.20 m and 0.15 m-2.0810 1202/24/2003-0.1014 16 18Time (hrs)2022248.224 Seminar8101214 16 18Time (hrs)20222420
Summary Use of differential measurements withcarrier phase allows very preciseposition determination (independentlargely of security features). We use these measurements in Earthscience for deformation studies andatmospheric studies02/24/20038.224 Seminar21
Tectonic Deformation Results “Fixed GPS” stations operate continuouslyand by determining their positions each daywe can monitor their motions relative to aglobal coordinate system Temporary GPS sites can be deployed onwell defined marks in the Earth and themotions of these sites can be monitored(campaign GPS)02/24/20038.224 Seminar22
Example of motions measured inPacific/Asia region Fastest motionsare 100 mm/yr Note convergencenear JapanMore at http://www-gpsg.mit.edu/ fresh/MIT IGS AAC.html02/24/20038.224 Seminar23
Motion after Earthquakes. Example from HectorMine, CAContinued motion tells us about material characteristicsand how stress is re-distributed after earthquake30Difference from Mean (mm)20Time of Hector mine earthquake220 mm offset removed10RMS Scatter aboutlinear trend 0.8 mm0-10-20Pre-Hector MinePost Hector .02002.52003.0Year02/24/20038.224 Seminar24
Relativistic effects General relativity affects GPS in three ways– Equations of motions of satellite– Rates at which clock run– Signal propagation In our GPS analysis we account for thesecond two items Orbits only integrated for 1-3 days andequation of motion term is considered small02/24/20038.224 Seminar25
Clock effects GPS is controlled by 10.23 MHz oscillators On the Earth’s surface these oscillators areset to 10.23x(1-4.4647x10-10) MHz (39,000ns/day rate difference) This offset accounts for the change inpotential and average velocity once thesatellite is launched. The first GPS satellites had a switch to turnthis effect on. They were launched with“Newtonian” clocks02/24/20038.224 Seminar26
Propagation and clock effects Our theoretical delay calculations aremade in an Earth centered, non-rotatingframe using a “light-time” iteration i.e.,the satellite position at transmit time isdifferenced from ground station positionat receive time. Two corrections are then applied to thiscalculation02/24/20038.224 Seminar27
Corrections terms Propagation path curvature due to Earth’spotential (a few centimeters)2GMRr Rsln3cRr Rs Clock effects due to changing potentialGMe a sin E2c For e 0.02 effect is 47 ns (14 m)02/24/20038.224 Seminar28
Effects of Selective AvailabilityPRN 03 (June 14)800Clock SA (ns) 1999Clock NoSA (ns) 2000Clock error (ns)6004002000-200002/24/20034812Time (hrs)8.224 Seminar16202429
Relativistic EffectsPRN 03 Detrended; e 0.0250Clock - trend (ns)GR Effect (ns)Clock error (ns)250-25-50002/24/20034812Time (hrs)8.224 Seminar16202430
Tests of General Relativity In the parameterized post-Newtonianformulation, the time delay expressionbecomes:GM (1 )e a sin E22c In PPN, is the gravitational term. In generalrelativity 1 The clock estimates from each GPS satelliteallow daily estimates of02/24/20038.224 Seminar31
Using GPS to determine Each day we can fit a linear trend and onceper-revolution sin and cos terms to the eachof the 27-28 GPS satellites. Comparison between the amplitude andphase (relative to sin(E)) allows and estimateof gamma to be obtained Quadrature estimates allows error bound tobe assessed (cos(E) term) Problem: Once-per-orbit perturbations arecommon. However should not beproportional to eccentricity.02/24/20038.224 Seminar32
Initial “quick” resultsAmplitudecomparison onlyConsistent withGR to 10%Only 1 week ofdata: Data afterMay 2000 couldbe used.02/24/20038.224 Seminar33
Conclusions GPS dual-use technology: Applications incivilian world widespread– Geophysical studies (mm accuracy)– Engineering positioning ( cm in real-time)– Commercial positioning: cars, aircraft, boats (cmto m level in real-time) Relativistic effects are large but largelyconstant However due to varying potentials andvelocities effects can be seen Some effects are incorporated by convention Need to keep in mind “negligible effects” asaccuracy improves02/24/20038.224 Seminar34
The Global Positioning System and Relativity: A 10% test of general relativity everyday . Overview Original design of the Global Positioning System (GPS) Use by “non-authorized” users Selected applications Relativistic effects. 02/24/2003 8.224 Seminar 3 . – Engineering
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