Satellite Navigation GPS measurements and error sources

Transcription

1 Satellite Navigation GPS measrements and error sorces Pictre: ESA AE4E08 Sandra Verhagen Corse , lectre 4 1

2 Today s topics Recap: GPS signal components Code Phase measrements psedoranges Carrier Phase measrements GPS measrements: example Otlook: error sorces Book: Section 5.1 2

3 Recap: GPS signal components All signals and time information are coherently derived from the same clock with a freqency of f 0 =10.23 MHz Signal components Freqency Wavelength / chiplength L1 carrier MHz (154*f 0 ) cm L2 carrier MHz (120*f 0 ) cm C/A code on L1 with Mbits/sec (0.1*f 0 ) 293 m P code on L1 and L Mbits/sec (f 0 ) 29.3 m Broadcast message 50 bits/sec 3

4 Recap: GPS signal components From: Misra and Enge 4

5 Recap: GPS signal components carrier f (t) +1-1 phase shift 180 o code and data Ct () Dt () signal St () 5

6 Code Phase measrements τ? transit time 70 to 90 ms t? tre GPS time at which code is received s ( ) t t τ emission time (imprinted on signal) t () t measred arrival time (clock reading) ρ ( ) s ( τ ) () t = c t t t t psedorange 6

7 Code Phase measrements ( ) = +δ () t t t t t receiver clock bias t ( ) = +δ () t t t t t t = t t 8

8 Code Phase measrements t t t t t ( ) = +δ () receiver clock bias t ( ) = +δ () t t t t t t = t Receiver clocks: drift! Deviation from GPS time limited to ±1 ms: continos clock steering reset (clock jmp!) when certain threshold is reached δt () t t 9

9 Code Phase measrements t t t t t ( ) = +δ () receiver clock bias s t t t t t ( ) s τ = ( τ) + δ ( τ) satellite clock bias estimated by control segment 10

10 Code Phase measrements t () t = t+δt () t s t t t t t ( ) s τ = ( τ) + δ ( τ) Unmodeled effects and errors ρ () t = c t () s ( ) t t t τ + ε ρ () t () ( ) s = c t+ δt ( ) t t τ δt t τ + ερ () t () s = cτ + c δt ( ) t δt t τ + ερ () t 11

11 psedorange () t c c t t t t () t ρ = τ + δ ( ) δ s ( τ) + ε ρ clock biases noise + errors distance traveled by signal 12

12 psedorange () t c c t t t t () t ρ = τ + δ ( ) δ s ( τ) + ε ρ clock biases noise + errors distance traveled by signal cτ = r(, t t τ ) + I () t + T () t ρ ρ geometric range ionosphere and troposphere delays 13

13 psedorange ρ = r+ I + T + c δt δt + ε s ρ ρ ρ psedorange measrement = biased and noisy measrement of the geometric range r Not to be stdied: part on Constrcting psedorange measrements in Section

14 psedorange measrements: example -clock 1 psedorange [m] Figre: Peter Bist 15

15 psedorange measrements: example -clock 2 psedorange [m] Figre: Peter Bist 16

16 psedorange measrements: example -clock 1 -clock 2 clock error [m] Figre: Peter Bist 17

17 Carrier Phase measrements φ [cyc] Very precise! 18

18 Carrier Phase measrements φ ( t ) φ() t 0 φ [cyc] f ( t t ) 0 = nmber of cycles since starting point of interval Carrier phase : φ() t = φ( t ) + f ( t t )

19 Carrier Phase measrements received φ generated Carrier phase measrement: Difference between phases of receiver-generated carrier signal and received carrier signal 20

20 Carrier Phase measrements received φ generated Carrier phase measrement: Difference between phases of receiver-generated carrier signal and received carrier signal Phase measrement + whole nmber of cycles traveled range Change in phase continosly measred (incl. fll cycles) 21

21 Carrier Phase measrements s φ() t = φ () t φ ( t τ) + N + εφ Recall: φ() t = φ( t ) + f ( t t ) 0 0 φ () t = φ ( t ) + f ( t t ) + f ( δt () t δt ( t )) clock biases φ ( t τ) = φ ( t ) + f ( t τ t ) + f ( δt ( t τ) δt ( t )) s s s s

22 φ() t = f τ ( s δ () ( )) δ τ + f t t t t + φ ( t ) φ ( t ) s 0 0 ( s δ ( ) 0) δ ( 0) f t t t t + N + ε φ Carrier Phase measrements s φ() t = φ () t φ ( t τ) + N + εφ ( ) φ () t = φ ( t ) + f ( t t ) + f δt () t δt ( t ) s s s s t = t0 + f t t0 + f t t t t0 ( ) φ ( τ) φ ( ) ( τ ) δ ( τ) δ ( ) -clock biases - initial phases - clock biases at t 0 - integer ambigity (constant) - noise and errors A 23

23 φ() t = f τ Carrier Phase measrements ( δ () s ( )) δ τ + f t t t t + A + λ A + ε φ c f = λ λ φ() t = c τ ( δ () s ( )) δ τ + c t t t t + λ ε φ cycles meters 24

24 Carrier Phase measrements λ φ() t = c τ ( δ () s ( )) δ τ + c t t t t + λ A + λ ε φ Φ = r+ I + T φ φ ( s δ ) δ + c t t + λ A + ε Φ Ambigities mst be resolved to take advantage of high precision phase measrements 25

25 GPS measrements: example Dataset Jne 1 st, GPS week :00-23:59 (GPS-time) 10 seconds interval Trimble 4700 receiver dal-freqency GPS (L1 & L2) choke-ring antenna at GNSS-observatory in Delft RINEX: Receiver Independent Exchange format data (delf1520) provided by H. van der Marel plots by Q. Le, photo by R. Kremers 26

26 Rinex version OBSERVATION DATA G (GPS) RINEX VERSION / TYPE teqc 2002Mar14 Atomatic GPS proces :15:24UTCPGM / RUN BY / DATE Linx Pentim II gcc Linx 486/DX+ COMMENT BIT 2 OF LLI FLAGS DATA COLLECTED UNDER A/S CONDITION COMMENT DELFT-16 MARKER NAME 13502M004 MARKER NUMBER H. VAN DER MAREL AGRS.NL (KAD,MD,TUD) OBSERVER / AGENCY TRIMBLE 4700 N1.30/S0.00 REC # / TYPE / VERS TRM UNAV ANT # / TYPE APPROX POSITION XYZ ANTENNA: DELTA H/E/N 1 1 WAVELENGTH FACT L1/2 7 L1 L2 C1 P2 D1 S1 S2 # / TYPES OF OBSERV INTERVAL COMMENT AGRS.NL - Active GPS Reference System for the Netherlands COMMENT H.vanderMarel@geo.tdelft.nl COMMENT COMMENT The coordinates in the RINEX header are given in the COMMENT system ETRS89 and were based on the ITRF96 soltion. COMMENT SNR is mapped to RINEX snr flag vale [1-9] COMMENT L1: 3 -> 1; 8 -> 5; 40 -> 9 COMMENT L2: 1 -> 1; 5 -> 5; 60 -> 9 COMMENT GPS TIME OF FIRST OBS END OF HEADER G 5G 1G 4G 2G14G30G 6G25G Satellite Navigation (AE4E08) Lectre

27 date time observed GPS satellites G 5G 1G 4G 2G14G30G 6G25G L1 [cyc] L2 [cyc] C1 [m] P2 [m] D1 [Hz] S1 [db-hz] S2 [db-hz] Rinex version 2

28 Rinex version 3 > G G G G G G G G G G G G E S S S24 date time no. observed GNSS 7 satellites > G G G G C1 [m] L1 [cyc] D [Hz] 8 S [db-hz] G G G G G G G01 Satellite Navigation (AE4E08) Lectre G E G: GPS E: Galileo S: SBAS

29 consider one GPS satellite a = m r = m skyplot: local azimth verss elevation of GPS satellite PRN 20 grond-track as observed in Delft over 24 hr period (Delft is at 52 degrees latitde North, the orbital plane has a 55 degrees inclination) 30

30 90 Elevation elevation angle - PRN20 80 elevation angle [degrees] time [hors of day] 31

31 Psedorange observation 2.8 x C1 - PRN range [meters] time [hors of day] 32

32 L1 carrier phase observation carrier phase is ambigos (jst starts at zero here) 0.5 x L1 - PRN range [cycles] time [hors of day] 33

33 L1 Doppler freqency observation 4000 D1 - PRN Doppler [Hz] time [hors of day] 34

34 55 Signal strength actally Carrier-to-Noise density ratio S1 - PRN20 Signal-to-Noise ratio [db-hz] time [hors of day] down to 25 db-hz, pretty good receiver 35

35 range [meters] Psedorange observations 2.9 x C1 - all PRNs they get longer as time proceeds? time [hors of day] 36

36 Receiver clock error 2.5 x 106 receiver clock error [m] [m] time [hors of day] oscillator in receiver has stability of abot 10-7 s/s 37

37 Noise and bias Noise: qickly varying, averages ot to zeros Bias: systematic / persistent over longer time, or otlier in observation 38

38 Normal distribtion assme satellite and receiver are not moving range measrement repeated 10,000 times flctations de to measrement noise relative freqecy ρ ρ 39

39 Normal distribtion assme satellite and receiver are not moving range measrement repeated 10,000 times flctations de to measrement noise generally, normal distribtion assmed relative freqecy ρ ρ 40

40 Normal distribtion A random variable has a normal or Gassian distribtion with parameters and x σ x x σ x 2 σ x : mean : standard deviation : variance Notation: 41

41 Standard deviation and RMS error Standard deviation: measre for flctations 2 ( x ) Empirical standard deviation: i x with n i= 1 n 1 P( x x σ ) = 68.3% P( x x 2 σ ) = 95.4% x x x 1 n xi n i = 1 = RMS error: n i= 1 ( x n x i 2 ) 42

42 Error sorces satellite: orbit clock instrmental delays signal path ionosphere troposphere mltipath receiver clock instrmental delays other spoofing interference 44

43 Smmary and otlook GPS: history and overview (Chapter 1, Sections 2.1, 2.2, 4.4) GPS signals (Section 2.3) Ftre GNSS (Chapter 3) GPS receivers (paper Braasch and Van Dierendonck) GPS measrements (Section 5.1) Homework (optional): on blackboard Next: error sorces and PVT estimation 45