The Global Positioning System (GPS)

1. The Global Positioning System(GPS)

2. Brief History of Navigation • PreHistory - Present: Celestial Navigation • Ok for latitude, poor for longitude until accurate clock invented ~1760 • 13th Century: Magnetic Compass • 1907: Gyrocompass • 1912: Radio Direction Finding • 1930’s: Radar and Inertial Nav • 1940’s: Loran-A • 1960’s: Omega and Navy Transit (SatNav) • 1970’s: Loran-C • 1980’s: GPS

3. Brief History of GPS • Original concept developed around 1960 • In the wake of Sputnik & Explorer • Preliminary system, Transit, operational in 1964 • Developed for nuke submarines • 5 polar-orbiting satellites, Doppler measurements only • Timation satellites, 1967-69, used the first onboard precise clock for passive ranging • Fullscale GPS development begun in 1973 • Renamed Navstar, but name never caught on • First 4 SV’s launched in 1978 • GPS IOC in December 1993 (FOC in April 1995)

4. GPS Tidbits • Development costs estimate ~$12 billion • Annual operating cost ~$400 million • 3 Segments: • Space: Satellites • User: Receivers • Control: Monitor & Control stations • Prime Space Segment contractor: Rockwell International • Coordinate Reference: WGS-84 ECEF • Operated by US Air Force Space Command (AFSC) • Mission control center operations at Schriever (formerly Falcon) AFB, Colorado Springs

5. Who Uses It? • Everone! • Merchant, Navy, Coast Guard vessels • Forget about the sextant, Loran, etc. • Commercial Airliners, Civil Pilots • Surveyors • Has completely revolutionized surveying • Commercial Truckers • Hikers, Mountain Climbers, Backpackers • Cars now being equipped • Communications and Imaging Satellites • Space-to-Space Navigation • Any system requiring accurate timing

6. How It Works (In 5 Easy Steps) • GPS is a ranging system (triangulation) • The “reference stations” are satellites moving at 4 km/s • A GPS receiver (“the user”) detects 1-way ranging signals from several satellites • Each transmission is time-tagged • Each transmission contains the satellite’s position • The time-of-arrival is compared to time-of-transmission • The delta-T is multiplied by the speed of light to obtain the range • Each range puts the user on a sphere about the satellite • Intersecting several of these yields a user position

7. Multi-Satellite Ranging A 3rd range constrains user to 1 of the 2 points. Which point is determined by “sanity” – 1 point obviously wrong. 1 range puts user on the spherical face of the cone. Intersecting with a 2nd range restricts user to the circular arcs. Pictures courtesy http://giswww.pok.ibm.com/gps

8. The GPS Constellation • 24 operational space vehicles (“SV’s”) • 6 orbit planes, 4 SV’s/Plane • Plus at least 3 in-orbit spares • Orbit characteristics: • Altitude: 20,180 km (SMA = 26558 km) • Inclination: 550 • Eccentriciy: < 0.02 (nominally circular) • Nodal Regression: -0.0040/day (westward) • The altitude results in an orbital period of 12 sidereal hours, thus SV’s perform full revs 2/day. • Period and regression lead to repeating ground tracks, i.e. each SV covers same “swath” on earth ~ 1/day.

9. Simulation: GPS and GLONASS Simulation

10. GPS Visibility • GPS constellation is such that between 5 and 8 SV’s are visible from any point on earth • Each SV tracked by a receiver is assigned a channel • Good receivers are > 4-channel (track more than 4 SV’s) • Often as many as 12-channels in good receivers • Extra SV’s enable smooth handoffs & better solutions • Which SV’s are used for a solution is a function of geometry • GDOP: Geometric Dilution of Precision • Magnification of errors due to poor user/SV geometry • Good receivers compute GDOP and choose “best” SV’s

11. Timing • Accuracy of position is only as good as your clock • To know where you are, you must know when you are • Receiver clock must match SV clock to compute delta-T • SVs carry atomic oscillators (2 rubidium, 2 cesium each) • Not practical for hand-held receiver • Accumulated drift of receiver clock is called clock bias • The erroneously measured range is called a pseudorange • To eliminate the bias, a 4th SV is tracked • 4 equations, 4 unknowns • Solution now generates X,Y,Z and b • If Doppler also tracked, Velocity can be computed

12. Position Equations Where: Pi= Measured PseudoRange to the ith SV Xi , Yi , Zi= Position of the ith SV, Cartesian Coordinates X , Y , Z = User position, Cartesian Coordinates, to be solved-for b = User clock bias (in distance units), to be solved-for The above nonlinear equations are solved iteratively using an initial estimate of the user position, XYZ, and b

13. GPS Time • GPS time is referenced to 6 January 1980, 00:00:00 • GPS uses a week/time-into-week format • Jan 6 = First Sunday in 1980 • GPS satellite clocks are essentially synched to International Atomic Time (TAI) (and therefore to UTC) • Ensemble of atomic clocks which provide international timing standards. • TAI is the basis for Coordinated Universal Time (UTC), used for most civil timekeeping • GPS time = TAI + 19s • Since 19 leapseconds existed on 1/6/1980 • GPS time drifts ahead of UTC as the latter is “held” (leapseconds) to accommodate earth’s slowing

14. More About Time • GPS system time referenced to Master USNO Clock, but now implements its own “composite clock” • SV clocks good to about 1 part in 1013 • Delta between GPS SV time & UTC is included in nav/timing message • Correction terms permit user to determine UTC to better than 90 nanoseconds (~10-7 sec) • The most effective time transfer mechanism anywhere • Satellite velocity induces relativistic time dilation of about 7200 nanosec/day • The 10-bit GPS-week field in the data “rolled-over” on August 21/22 1999 – some receivers probably failed!

15. GPS Signals • GPS signals are broadcast on 2 L-band carriers • L1: 1575.42 MHz • Modulated by C/A-code & P-code • L2: 1227.6 MHz • Modulated by P-code only • (3rd carrier, L3, used for nuclear explosion detection) • Most unsophisticated receivers only track L1 • If L2 tracked, then the phase difference (L1-L2) can be used to filter out ionospheric delay. • This is true even if the receiver cannot decrypt the P-code (more later) • L1-only receivers use a simplified correction model

16. For Signal-Heads Only • Antenna Polarization: RHCP • L1 • Center Frequency: 1.57542 GHz • Signal Strength: -160 dBW • Main Lobe Bandwidth: 2.046 MHz • C/A & P-Codes in Phase Quadrature • L2 • Center Frequency: 1.22760 GHZ • Signal Strength: -166 dBW • Code modulation is Bipolar Phase Shift Key (BPSK) • Total SV Transmitted RF Power ~45 W

17. PRN Codes • GPS signals implement PseudoRandom Noise Codes • Enables very low power (below background noise) • A form of direct-sequence spread-spectrum • Specifically a form of Code Division Multiple Access (CDMA), which permits frequency sharing • Codes are known “noise-like” sequences • Each bit (0/1) in the sequence is called a chip • Each GPS SV has an assigned code • Receiver generates equivalent sequences internally and matches signal to identify each SV • There are currently 32 reserved PRN’s

18. PRN Code Matching • Receiver slews internally-generated code sequence until full “match” is achieved with received code • Time data in the nav message tells receiver when the transmitted code went out • Slew time = time delay incurred by SV-to-receiver range • Minus clock bias and whole cycle ambiguities Receiver/Signal Code Comparison

19. Coarse Acquisition (C/A) Code • 1023-bit Gold Code • Originally intended as simply an acquisition code for P-code receivers • Modulates the L1 only • Chipping rate = 1.023 MHz (290 meter “wavelength”) • Sequence Length = 1023 bits, thus Period = 1 millisec • ~300 km range ambiguity: receiver must know range to better than this for position solution • Provides the data for Standard Positioning Service (SPS) • The usual position generated for most civilian receivers • Modulated by the Navigation/Timing Message code

20. Precise (P) Code • Generally encrypted into the Y-code • Requires special chip to decode • Modulates both L1 & L2 • Also modulated by Nav/Time data message • Chipping rate = 10.23 MHz • Sequence Length = BIG (Period = 267 days) • Actually the sum of 2 sequences, X1 & X2, with sub-period of 1 week • P-code rate is the fundamental frequency (provides the basis for all others) • P-Code (10.23 MHz) /10 = 1.023 MHz (C/A code) • P-Code (10.23 MHz) X 154 = 1575.42 MHz (L1). • P-Code (10.23 MHz) X 120 = 1227.60 MHz (L2).

21. Code Modulation Image courtesy: Peter Dana, http://www.colorado.Edu/geography/gcraft/notes/gps/gps_f.html

22. Navigation Message • In order to solve the user position equations, one must know where the SV is. • The navigation and time code provides this • 50 Hz signal modulated on L1 and L2 • The SV’s own position information is transmitted in a 1500-bit data frame • Pseudo-Keplerian orbital elements, fit to 2-hour spans • Determined by control center via ground tracking • Receiver implements orbit-to-position algorithm • Also includes clock data and satellite status • And ionospheric/tropospheric corrections

23. The Almanac • In addition to its own nav data, each SV also broadcasts info about ALL the other SV’s • In a reduced-accuracy format • Known as the Almanac • Permits receiver to predict, from a cold start, “where to look” for SV’s when powered up • GPS orbits are so predictable, an almanac may be valid for months • Almanac data is large • Takes 25 subcommutations of subframes 4,5 • 12.5 minutes to tranfer in entirety

24. Selective Availability (SA) • To deny high-accuracy realtime positioning to potential enemies, DoD reserves the right to deliberately degrade GPS performance • Only on the C/A code • By far the largest GPS error source • Accomplished by: • “Dithering” the clock data • Results in erroneous pseudoranges • Truncating the nav message data • Erroneous SV positions used to compute user position • Degrades SPS solution by a factor of 4 or more • Long-term averaging is the only effective SA compensator • FAA and Coast Guard needs are pressuring DoD to eliminate • ON 1 MAY 2000: SA WAS DISABLED BY DIRECTIVE

25. How Accurate Is It? • Remember the 3 types of Lies: • Lies, Damn Lies, and Statistics… • Loosely Defined “2-Sigma” Repeatable Accuracies: • All depend on receiver quality • SPS (C/A Code Only) • S/A On: • Horizontal: 100 meters radial • Vertical: 156 meters • Time: 340 nanoseconds • S/A Off: • Horizontal: 22 meters radial • Vertical: 28 meters • Time: 200 nanoseconds • PPS (P-Code) • Slightly better than C/A Code w/o S/A (?)

26. Differential GPS • A reference station at a known location compares predicted pseudoranges to actual & broadcasts corrections: “Local Area” DGPS • Broadcast usually done on FM channel • Corrections only valid within a finite range of base • User receiver must see same SV’s as reference • USCG has a number of DGPS stations operating • Base stations worldwide collect pseudorange and SV ephemeris data and “solve-for” time and nav errors • “Wide Area” DGPS • Not yet (?) available in realtime • DGPS can reduce errors to < 10 meters

27. Carrier Phase Tracking • Used in high-precision survey work • Can generate sub-centimeter accuracy • The ~20 cm carrier is tracked by a reference receiver and a remote (user) receiver • The carrier is not subject to S/A and is a much more precise measurement than pseudoranges. • Requires bookeeping of cycles: subject to “slips” • Ionospheric delay differences must be small enough to prevent full slips • Requires remote receiver be within ~30km of base • Usually used in post-processed mode, but RealTime Kinematic (RTK) method is developing

28. Available Receivers • Garmin, Magellan, Lowrance, DeLorme, Trimble, etc. • Basic 6-12 channel receivers ~$100 • Usually includes track & waypoint entry • With built-in maps ~$150 • Combination GPS receiver/cell phone ~$350 • Survey-quality: $1000 and up • Carrier tracking • FM receiver for differential corrections • RS232 port to PC for realtime or post-processing • Military Standard: $10000+ ??