1. School of Engineering NTM2, Rumc, GPS, 1 References [1]Jean-Marie Zogg [HTW Chur], „GPS, Essentials of Satellite Navigation, Compendium“, Document: GPS-X-02007-D, https://www.u-blox.com/sites/default/files/gps_compendiumgps-x-02007.pdf. https://www.u-blox.com/sites/default/files/gps_compendiumgps-x-02007.pdf Chapter 1.1: The principle of measuring signal transit time Chapter 2.3.4: WGS-84 Chapter 4: GNSS technology: the GPS example Chapter 7.2: Sources of GPS error Chapter 8.2: Data interfaces [2]GPS SPS Signal Specification, 2nd Edition (June 2, 1995), http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm [3] beautiful visualisation of the satellites‘ positions by HSR / ICOM http://icom4u.hsr.ch/giove_a/index.htm [4]Parkinson, Spilker, „Global Positioning System: Theory and Applications“, Volume I/II, Progress in Astronautics and Aeronautics, Volume 163/164, 1996. Terms NAVSTAR GPS („Navigational Satellite Timing and Ranging - Global Positioning System) is a GNSS (Global Navigation Satellite System), developed by the US-DoD in 197x and fully operational since 1993. Other GNSS under „development“: Glonass (Ru), Galileo (EU), Beidou/Compass (China) GPS (Introduction)

2. School of Engineering GPS-Principle Assumptions 1.distance A between Tx is known. 2.Tx transmit synchronously, Rx can only measure TDOA (time difference of arrival). Determination of positions via Time-of-Fly measurements Conclusions with 2 Tx, x-position (and time) and with 4 Tx, x,y,z-positions (and time) can be determined! Source: [1] NTM2, Rumc, GPS, 2

3. School of Engineering TDOA measurement by code correlation GPS-Principle S1 Code S2 Code Tx1Tx2Rx D = (Δt∙c+A)/2 Code s 1 mit N Chip Tx1 Tx2 Rx t t t after correlation with code s 1 with code s 2 ∆τ∆τ T chip ∆τ2∆τ2 ∆τ1∆τ1 s1s1 s2s2 s2s2 s1s1 s2s2 S1 Code S2 Code NTM2, Rumc, GPS, 3

4. School of Engineering Worldwide Reference Ellipsoid WGS-84 Ellipsoid approximates true (complex) shape of the earth there are many different reference systems GPS works with geocentric WGS-84 reference system Source: [1] cartesian coordinates ellipsoidal coordinates (longitude, latitude, altitude) used for further processing 1° Grad = 60’ Bogenminuten. 1’ Bogenminute Breite = 1 Seemeile bzw. 1 nautischen Meile (NM) = 1.852 km. 1’ Bogenminute Länge = 1.852 km mal cos(Breitengrad). conversion into CH-1903 coordinates required [1] GPS-Principle NTM2, Rumc, GPS, 4

5. School of Engineering Basic equations x,y,z,t coordinates and time of user x i,y i,z i,t i coordinates and time of 4 satellites (x 1 -x) 2 + (y 1 -y) 2 + (z 1 -z) 2 = [c·(t 1 -t)] 2 (x 2 -x) 2 + (y 2 -y) 2 + (z 2 -z) 2 = [c·(t 2 -t)] 2 (x 3 -x) 2 + (y 3 -y) 2 + (z 3 -z) 2 = [c·(t 3 -t)] 2 (x 4 -x) 2 + (y 4 -y) 2 + (z 4 -z) 2 = [c·(t 4 -t)] 2 4 equations (c: speed of light) and 4 unknowns GPS-Principle Source: [1] NTM2, Rumc, GPS, 5

6. School of Engineering GPS-Subsystems (orbital data) 1 Master Control Station (Colorado) 5 Monitor Stations world wide 3 Ground Control Stations (with Satellite Uplink) Source: [1] NTM2, Rumc, GPS, 6

7. School of Engineering GPS-Space Segment 24 to 32 Satellites 55° at a height of 20‘180 km 6 different orbital planes (4-5 satellites per plane) time of circulation ≈ 12 h always ≥ 4 satellites visible everywhere on earth NTM2, Rumc, GPS, 7

8. School of Engineering [1] coverage area GPS-Space Segment Orbit and coverage area NTM2, Rumc, GPS, 8

9. School of Engineering GPS-Space Segment Link budget 25119 km (border of coverage area) L1 (1575.42 MHz) Coarse/Acquisition (C/A-) Code for civil use min. sensitivity specified in [2] [1] NTM2, Rumc, GPS, 9

10. School of Engineering Spectral power density of received signal and (thermal) noise floor Link Budget <= -130 dBm / MHz - source bandwidth 1 MHz ≈ 1/T chip [1] -174 signal before despreading -160 + 14 dB signal after despreading f – f L1 <= thermal noise + noise figure F NTM2, Rumc, GPS, 10

11. School of Engineering Satellite-Signal 1575.42 MHz T chip ≈ 1 / Bandwidth Source: [1] t / ms 1 2 20 C/A-code T bit 1023 T chip NTM2, Rumc, GPS, 11

12. School of Engineering 32 Gold- / PRN-codes with N = 1023 chips Generation with 2 LFSR, chip rate 1.023 Mchip/s satellite identified by PRN-number => CDMA GPS-Coarse/Acquisition-Codes NTM2, Rumc, GPS, 12 delayed PN-code due to tap-selection (=> cyclic shift) seed = [1 1 … 1]

13. School of Engineering GPS User Segment Correlation receiver Source [1] (Doppler-Shift ± 5000 Hz) (all GPS-codes ) Process-Gain 10·log 10 (1023) ≈ 30 dB SNR = -16 dB before despreading => SNR = +14 dB after despreading correlation time for data demodulation is 20 times longer Gain NTM2, Rumc, GPS, 13

14. School of Engineering GPS Navigation Message Source: [1] NTM2, Rumc, GPS, 14

15. School of Engineering Navigation message contains 25 frames and lasts 12.5 minutes a GPS-frame has 5 x 300 = 1500 bits and lasts 30 s Subframes 1-3 are identical for all the 25 frames subframe 1 contains clock data of transmitting satellite subframes 2 and 3 contain ephemeris data of transmitting satellite ephemeris data are highly accurate orbital data a receiver has the complete clock values and ephemeris data from the transmitting satellite every 30 seconds Time-To-First-Fix (cold start autonomous) at least 18-36 s => slow start-up is a system-inherent limitation of GPS Subframe 4-5 are different for all the 25 frames subframe 5 contains almanac data of first 24 satellites plus health almanac data are less accurate than ephemeris data subframe 4 contains almanac data of satellites 25-32 and difference between GPS and UTC time GPS Navigation Message NTM2, Rumc, GPS, 15

16. School of Engineering Accuracy without Selective Availability Source: [1] 95%- or 2σ-accuracy: 100 m95%- or 2σ-accuracy: 12 m Deactivation of SA (artificial degradation) in the year 2000 68% or σ-accuracy: 6 m NTM2, Rumc, GPS, 16

17. School of Engineering Improved GPS Main sources of GPS errors effect of the ionosphere (counter measures: DPGS and in the near future 2 frequency receiver) multipath (mainly in urban areas) effect of the satellite constellation (DOPs [Dilution of Precision]) transmission of correction factors Source: [1] NTM2, Rumc, GPS, 17 Differential GPS (DGPS)

18. School of Engineering EGNOS (European Geostationary Navigation Overlay System) 34 ground stations calculate correction signals (à la DGPS) for GPS correction in a radius of about 200 km around the reference station broadcast of correction signals via 3 geostationary satellites (C/A-Codes >32) 1-3 m accuracy Improved GPS Source: [1] NTM2, Rumc, GPS, 18

19. School of Engineering Improved GPS Achievable accuracy with DGPS and SBAS SBAS: satellite based augmentation systems [1] NTM2, Rumc, GPS, 19

20. School of Engineering Improved GPS Some Location Based Services are based on satellite navigation GPS-Rx not always „on“, e.g. because of current consumption time to first fix (cold start): 18-36 s (missing orbital data) Assisted GPS (A-GPS) delivery of missing orbital data via „fast“ channel, e.g. GSM/GPRS [1] NTM2, Rumc, GPS, 20

21. School of Engineering Data Interface to Peripherals NMEA-0183 data interface standardized by National Marine Electronics Association (NMEA) data telegram for serial interface Example: GGA data set (GPS fix data) $GPGGA,130305.0,4717.115,N,00833.912,E,1,08,0.94,00499,M,047,M,,*58 NTM2, Rumc, GPS, 21

22. School of Engineering Time Pulse Most GPS-Rx generate 1- 4 time pulses per s time puls is synchronized to UTC-time Accuracy 5 - 60 ns [1] GPS-time-pulse is often used to synchronize devices in a «large» area as e.g. base stations, gliders, … NTM2, Rumc, GPS, 22