Modelling GPS Observables for Time Transfer

Transcription

1 Modelling GPS Observables for Time Transfer Marek Ziebart Department of Geomatic Engineering University College London

2 Presentation structure Overview of GPS Time frames in GPS Introduction to GPS observables Modelling the observables Applications, accuracies, issues

3 GPS segments I: Space Segment ~30 satellites in orbit, six orbital planes, 55 inclination Orbit near circular, 26,000km semi-major axis Satellites move ~4kms -1, orbital period ~12 hours On board rubidium and caesium clocks Thermally stabilised bus Several generations of satellite on orbit

4 GPS segments II: Control Segment Limited network (5) of tracking and uplink stations (about to grow) Ensemble of atomic clocks at Master Control Station, Colorado Springs -> defines system time System time steered to remain an integer number of seconds offset from UTC Control segment determines predicted satellite trajectories and clock behaviour

5 GPS Segments III: User Segment

6 Satellite clocks Freely running drift steadily from system time, not steered Satellite oscillators detuned before launch to offset first order relativistic time dilation Satellite clock offset and drift from system time estimated by control segment and made available to user via satellite navigation message

7 General context of problem In positioning getting accurate absolute position is generally difficult Where is my receiver?

8 Relative positioning is far easier Measure multiple ranges to satellites Rover at unknown point Compute relative position vector Reference receiver placed at known point New point for which We need to calculate position Point with known co-ordinates

9 Determining absolute time from GPS is complex What is the UTC time by my clock?

10 Determining relative time from GPS is more straightforward My clock is 4 seconds slower than yours.

11 Time frames in GPS GPST (Colorado) UT1/UTC link between orbital reference frame (inertial space) and Earth-centred, Earth-fixed terrestrial frames TDB, TDT, GAST, TAI User time frame (timing laboratories in this case)

12 GPS signals 19 cm and 24 cm (L-band) wavelength carriers Pseudo-random noise (PRN) codes (30 m and 300 m chip spacing) Navigation Message predicted orbit, predicted clock behaviour, offset from UTC

13 GPS observables L1 and L2 carrier phase L1 and L2 Doppler count C/A, P1 and P2 pseudoranges L2C as of yesterday

14 Basic mathematical model: Pseudoranges P i = x x + r s r s P δ t c δt c + I + T + M + ε satellite clock offset from system time receiver clock offset from system time satellite antenna phase centre position ground antenna phase centre position measured pseudorange

15 Basic mathematical model: signal errors ionospheric delay multipath P i = x x + t c t c I T M r s δ + δ ε r s dry and wet tropospheric delay Target parameter noise

16 Basic mathematical model: Phase Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ phase multipath phase ambiguity measured phase

17 Modelling I: Receiver position ε δ δ = Φ Φ M T I N c t c t x x s r s r i Position of antenna phase centre at the instant of measurement Ideally treated as a known quantity

18 Instantaneous antenna phase centre position Elevation dependent phase centre variations (L1, L2) Mean L1/L2 phase centre offset L2 phase centre offset L1 phase centre offset antenna reference point (ARP) antenna pre-amplifier vector from ground mark to ARP ground mark Earth and ocean tide correction Published mean coordinates of station

19 Kinematic Earth tide variation, Lhasa: 1 day, perihelion Earth tide correction (m) m range (on this day) time (MJD)

20 Modelling II: Transmitter position Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Position of satellite transmit antenna phase centre at the instant of signal transmission Known to varying degrees of accuracy Requires knowledge of orbit and satellite attitude (Block IIA only)

21 Orbit accuracies and latency Broadcast ephemeris: 2-5m accuracy, real-time access IGS predicted : cm accuracy, quasi-real-time IGS rapid : ~5 cm radial accuracy, on the day IGS final : <5 cm radial accuracy, two weeks latency Note: 30 cm orbit error => 1 ns time error

22 Modelling III: Satellite Clock Error Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Crude estimate of satellite clock error broadcast in navigation message Precise applications require estimation of residual offset Parameterised as offset, drift and ageing Can be eliminated by common view differencing

23 Difference between OSPF broadcast satellite clock offset and final IGS solution satellite clock error (m) Circa 3 metres (10 ns) PRN number

24 Common view differencing Φ 1 - Φ 2 eliminates satellite clock errors Φ 1 Φ 2

25 Modelling IV: Phase ambiguity Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Integer number of cycles biasing the phase range observable Constant parameter for a phase connected arc Can be determined from a single epoch of data

26 Atmospheric models Ionosphere: Troposphere: from 9km 100km depth to at 1000km poles, 16km Driving at parameter: equator driving electron parameters: content, Neutral solar gas UV density, flux, solar water cycle, vapour coupling distribution with solar magnetic field

27 Modelling IV: Ionospheric refraction Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Dispersive (frequency dependent) effect for microwaves Highly variable, chaotic delay (2m -> 80m) Can be eliminated (to first order) using dual frequency ionosphere-free combination

28 Modelling IV: Tropospheric delays Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Dry and wet components Total delay ~2-3m Dry component modelled successfully using surface meteorological data Wet component driven by water vapour density most approaches estimate the delay

29 Wet component Tropospheric delay estimation Most up to date approaches estimate Zenith delay and two horizontal gradient parameters Slowly varying effect can be modelled using a random walk in time Still a major source of uncertainty ~5-10 cm

30 Modelling V: Multipath Φ i = x r x s + δ t c δt c + N + I + T + M + ε r s Φ Signal degradation due to the physical environment of the receiver and the transmitter High and low frequency noise/bias Hot area of research

31 Approaches to dealing with Multipath Hardware mitigation: ground planes, choke rings, antenna gain pattern Correlator windows Smart choice of antenna siting Modelling: sidereal filter (GPS constellation geometry repeats daily) Ray tracing Statistical approaches

32 Data pre-processing: pseudoranges Read RINEX Gross error check Ionosphere-free combination Cycle slip detection Tropospheric delay Multipath detection Phase Smoothing Test Data

33 Pseudo-range time estimation: single station -4.0E E-08 Receiver Clock Offset (Seconds) -6.0E E E E E-07 averaged clock offset (OSPF) averaged clock offset (SP3) IGS clock (truth model) ~3m -1.1E E Seconds of Hour

34 Project tracking network = atomic clocks (H-masers, caesium, rubidium) = conventional quartz clocks

35 Pseudo-range time estimation: network approach -8.80E E E-08 estimated clock offset (seconds) -9.40E E E E E E E E-07 averaged clock offset IGS receiver clock (truth model) Global network solution, GLPS, clocks only, weighted RMS scatter: ~0.2m or ~1ns -1.10E Time (minutes)

36 Receiver clock offset (Goldstone H-maser, USA): Carrier phase solution 0.0E E-08 Estimated accuracy: ~0.1ns -2.0E E E E E E E E receiver clock offset (seconds) Time (seconds of day)

37 Conclusions and Outlook Many ways of using GPS observables in time transfer 1 ns real-time accuracy with pseudo-ranges and networks is feasible 0.1 ns post-processed results are routine (two week latency) 0.1 ns daily solution may be feasible now Careful modelling of observables underpins all applications many ways to fail, many ways to improve performance