04/28/02 12.540 Lec 19 1 12.540 Principles of the Global Positioning System Lecture 20 Prof. Thomas Herring 04/28/02 12.540 Lec 19 2 GPS Models and processing – ? Rank deficiencies – Processing methods: ? Differencing of data ? Cycle slip detection ? Bias fixing and cycle slip repair ? Summary: Finish up modeling aspects 1 04/28/02 12.540 Lec 19 3 Rank deficiencies ? that can not be separately estimated. ? In GPS, there are several rank deficiencies: satellite orbits, effectively can not be separated. orbits could be used to align the orbits in a solar system frame, setting the mean longitude change of stations to ITRF coordinates. Longitude is standard problem because choice of Greenwich as origin is arbitrary. Ranks deficiencies are combinations of parameters – UT1, Longitudes of all the stations and the nodes of the – In theory, orbit perturbations by the moon/sun on the GPS but effect is too small to be useful (I think: never really tested) – Separation is solved by adopting UT1-AT from VLBI, and 04/28/02 12.540 Lec 19 4 Rank deficiencies ? Other rank deficiencies: – Pole position can not separated from over all rotation of coordinates. Again resolved either by adopting polar motions on one day or on average having zero rotation of the coordinates relative to an initial frame. but effect is too small. estimated. Again there is sensitivity due moon/sun perturbations but these are too small. (Later we will see how differencing data, implicitly eliminates this problem). Solution, if clocks are explicitly estimated, is to adopt one clock as reference or set an average of the clock differences to be zero. – In principle could be separated by gravity field perturbations – All station and satellite clocks can not be simultaneously 2 04/28/02 12.540 Lec 19 5 Rank deficiencies – motions from secular drift of pole and secular UT1- AT changes. (Remember pole has drifted 10 meters in 100 years--10 cm/yr comparable to plate motions). – IERS polar motion is referred to a no-net-rotation geologic frame (Nuvel-1A). 04/28/02 12.540 Lec 19 6 Subtle rank deficiencies ? Phase center patterns for satellites and ground receivers can not separately determined using just GPS antennas. ? Because the satellites point towards the center of the Earth; a given elevation angle at a GPS receiver can be mapped to an off-bore-sight angle on the satellite and two effects can not separated. ? (so no longer pointing at the center of the Earth), the two effects could be separated. ? Even with low precision satellite phase center ? Velocity rank deficiency: It is not possible to separate “absolute” station ? There are some other rank deficiencies with nutations and orbits, but the apriori nutation series is very well defined by VLBI Interestingly, if the GPS satellites could be “rocked” positions can be estimated assuming “point” antenna 3 4 04/28/02 12.540 Lec 19 7 Estimated Satellite Z-offsets -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5 1015202530 Z-offset No Choke ring phase center Z offset Hannover Choke ring model Satellite Z-phase center position (m) PRN Block IIR Block IIR Apriori Block II/IIA offset 04/28/02 12.540 Lec 19 8 Time series estimates -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1999 2000 2001 2001 2002 2002 2003 PRN 11 Abs 1.44±0.03 m PRN 14 Abs 1.71±0.06 m PRN 28 Abs 1.45±0.07 m PRN 11 Rel -2.14±0.04 m PRN 14 Rel -1.87±0.06 m PRN 28 Rel -2.18±0.05 m Z Phase center offset (m) Year Block IIR satellites 04/28/02 12.540 Lec 19 9 Zoom of Absolute series only 0.5 1.0 1.5 2.0 2.5 3.0 2000.8 2001.0 2001.2 2001.4 2001.6 2001.8 2002.0 2002.2 2002.4 Z Phase center offset (m) Year PRN 11 Abs 1.44±0.03 m PRN 14 Abs 1.71±0.06 m PRN 28 Abs 1.45±0.07 m Block IIR satellites. Absolute PC model only 04/28/02 12.540 Lec 19 10 Effects on radial orbit position of satellite -0.4 -0.2 0.0 0.2 0.4 0.6 2000.0 2000.4 2000.8 2001.2 2001.6 2002.0 s 0.20 m s 0.21 m No Satellite PC Rel s 0.18 m D Semimajor Axis PRN 11 (m) Year Apriori orbit: No satellite or choke ring PC, sites constrained Abs Mean -0.01±0.03 RMS 0.15 m Rel Mean -0.01±0.03 RMS 0.15 m Mean 0.12±0.02 RMS 0.13 m Orbit Adjustment relative to constrained model 5 04/28/02 12.540 Lec 19 11 Summary of phase center ? The effects of ground antenna phase center model only satellite phase center estimates are large (~3.6 meters) ? Block II/IIA definitely different from Block IIR and some same type (differences are a few centimeters) ? Radial orbit changes are small (<1 cm on average). Interestingly better agreement of loose solution with constrained when satellite PC estimated (10 cm differences), indication of differences between satellites within the Scale effects ? From the different analyses and VLBI analysis we can estimate scale and its rate of change: Soln Scale +- Srate +- Abs -6.04 0.25 -0.24 0.06 Rel 11.99 0.25 -0.22 0.06 VLBI -0.21 0.04 -0.02 0.01 ? Scale in ppb and scale rate ppb/yr (1ppb=6mm) 04/28/02 12.540 Lec 19 12 6 04/28/02 12.540 Lec 19 13 Processing methods ? biggest deviations in the model of GPS phase and range data. ? These terms can be explicitly handled by estimation of is a very large estimation problem). Can be attacked with sequential LSQ or a Kalman filter. ? When multiple sites see the same satellite, the satellite clocks can also be estimated, but at every or an ensemble average of cocks set to have zero mean adjustment. The clock and local oscillator phase variations are the clock variations (but if done brut-force in least squares epoch of measurement, one clock needs to be fixed, 04/28/02 12.540 Lec 19 14 Differencing ? An alternative approach to explicit estimation is differencing data. ? Single differences: two forms: satellite. Eliminates error due to satellite clock. Eliminates the ground receiver clock. ? Double differences: satellites clocks are eliminated. in the number of cycles of phase between the combination of two satellites and two stations. This difference should be an integer. – Difference measurements from two sites that see the same – Difference measurements from two satellites at the one site: – By differencing a pair a single differences, but the ground and – The local oscillator phases also cancel except the differences 7 04/28/02 12.540 Lec 19 15 Differencing ? There are subtle problems with the exact times that ? phase to all the satellites can be made at exactly the same (within electronics noise) ? But signals measured at the same time receivers separated by large distances must have been transmitted from the satellite at different times due to the light propagation time.. measurements are made with differencing. In the receivers, the measurements of range and 04/28/02 12.540 Lec 19 16 ? This effect can lead to 20 ms differences in the transmission times. When SA was on and satellite clocks had frequency drifts of ~1Hz, this lead to errors of 0.02 cycles (~4mm). Not such a problem anymore and even with SA was not severe. ? problems. Normally receivers stay with in 1 ms of GPS time (by resetting their clock counters). Older receivers could be off by up to 80 ms: nobreakspace Light propagation time and differencing Non-synchronized receiver sampling can cause Feigl, K. L, R. W. King, T. A. Herring, and M. Rotchacher, A scheme for reducing the effect of selective availability on precise geodetic measurements from the Global Positioning System, Geophys. Res. Lett., 1289–1292, 1991. 8 04/28/02 12.540 Lec 19 17 Cycle slip detection ? problem. You can look at this in HW2 data set. The L1 and L2 phase values are in the L1 and L2 slots in The have a large offset from the range should be a integer value) ? missing but not always), a cycle slip occurs and this parameter 04/28/02 12.540 Lec 19 18 Cycle slip detection ? variations are dominated by clocks in receiver. ? Removes geometry but affected by ionospheric delay (opposite sign on phase and range) and noise in range measurements Some times called wide-lane. Affected by ion-delay but is common detector removes ionosphere and if good apriori positions are known, should be a smooth function of time. Often used to estimate When processing phase, cycles slips are a potential the rinex file. values (initial ambiguity, which in double differences When the receiver looses lock (typically range will be must be re-fixed to an integer or left as an unknown When o-minus-c is computed in one-ways for phase, Multiple techniques are used to detect cycle slips: – Ln phase - Ln range (n=1,2). – L1 phase - L2 phase. – Double difference phase residuals: On short baselines, number of cycles in sip and resolve to integer value. – Melbourne-Webena wide lane (ML-WL) (see over) 9 04/28/02 12.540 Lec 19 19 MW wide lane ? Very useful combination of data that is often used in kinematic GPS where receiver coordinates are changing. ? The MW WL should equal number of cycles of phase between between L1 and L2 and is calculated, effectively, be computing the expected L1 and L2 phase difference from the pseudorange data. 04/28/02 12.540 Lec 19 20 MW Wide lane ? From the equations for range and phase with the phase offsets for cycle offsets you can derive: ? The MW-WL should be constant if there are no cycle slips. When the phase and range values are double differences, N 2 -N 1 should be integer. ? The factor that scales range is ~0.1 and so range noise is reduced. ? geometry changes. MW -WL = N 1 - N 2 =f L 2 -f L1 + (P 1 + P 2 ) f L1 - f L 2 f L1 + f L 2 Average values of the MW-WL are used to esimate L1/L2 phase difference independent of ion-delay and 10 04/28/02 12.540 Lec 19 21 Ambiguity resolution ? The MW-WL is often used to get N1-N2 and then N1 squares fit to the phase data. ? If the sigma of the estimate is small, and the estimate is close to an integer then it can be resolved to an integer values. ? position estimate by typically a factor of two and makes it similar to the North sigma. Bias fixing has little effect on North and Up sigma except for short sessions. 04/28/02 12.540 Lec 19 22 is estimated, as non-integer value, from the least- Fixing ambiguities, improves the sigma of the east Summary ? Today’s lecture examined: ? rank deficiencies ? Differencing of data to eliminate clock errors ? Cycle slip detection and bias fixing (also called ambiguity resolution). 11