12.540 Principles of the globa Positioning System Lecture 20 Pre of. thomas herring 04/2802 12540Lec19 GPS Models and processing Summary modeling aspects Processing methods erencing of data Cycle slip detection Bias fixing and cycle slip repair 12540Lec19
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
Rank deficiencies Ranks deficiencies are combinations of parameters that can not be separately estimated In GPs. there are several rank deficiencies UTl, Longitudes of all the stations and the nodes of the satellite orbits, effectively can not be separated In theory, orbit perturbations by the moon/sun on the GPs orbits could be used to align the orbits in a solar system frame, but effect is too small to be useful (I think: never really tested) Separation is solved by adopting UT1-AT from VLBI, and coordinates Longitude is standard problem because choice of Greenwich as origin is arbitrary 0428/2 12540Lec19 Rank deficiencies Other rank deficiencies Pole, position can not separated from over all rotation of coordinates. Again resolved either by adopting polar motions none day or on average having zero rotation of the coordinates relative to an initial frame In principle could be separated by gravity field perturbations but effect is too small All station and satellite clocks can not be simultaneously estimated. Again there is sensitivity due moon/sun rturbations but these are too small. Later we will see how differencing data, implicitly eliminates this problem ). Solutio if clocks are explicitly estimated, is to adopt one clock as eference or set an average of the clock differences to be 12540Lec19
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
Rank deficiencies Velocity rank deficiency: It is not possible to separate"absolute"station 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 notions) lERS polar motion is referred to a no-net-rotation geologic frame(Nuvel-1A) There are some other rank deficiencies with nutations and orbits, but the apriori nutation series is very well defined by VLBI 0428/2 12540Lec19 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 and two effects can not separatee gle on the satellite be mapped to an off-bore-sight Interestingly, if the GPS satellites could be"rocked (so no longer pointing at the center of the Earth), the two effects could be separated Even with low precision satellite phase center positions can be estimated assuming"point" antenna
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
Estimated Satellite Z-offsets offset Hannay ke ring model Apriori Block IMlA offset Block 04/2802 12540Lec19 Time series estimates Block r satellites n PRN 7±0D6m 2002 12540Lec19
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 10 15 20 25 30 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
Zoom of absolute series only Block IIR satellites. Absolute PC model only PRN11Abs144±0.03 PN24Ab91100 200082001.02001.22001.4200162001820020200222002.4 0428/2 12540Lec19 Effects on radial orbit position of satellite Apriori orbit: No satellite or choke ring PC, sites constrained Orbit Adjustment relative to constrained model H Abs Mean -0.0140 03 RMS 0.15 eRel Mean -0.0140 03 RMS 0.15 mg 0.21 m Rel Mean 0. 1240.02 RMS 0.13 mo 0.18 m 2000004000y012200620020 12540Lec19
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 DSemimajor 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
Summary of phase center The effects of ground antenna phase center model only satellite phase center estimates are large(3.6 Block I/la definitely different from Block IIR and som indication of differences between satellites within the 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), 04/2802 12540Lec19 Scale effects From the different analyses and VLBI analysis we can estimate scale and its rate of change Soln Scale+ Srate + Abs 604 0.25 024006 Rel 11990.250.220.06 VLBI -0.21 0.04 -0.02001 Scale in ppb and scale rate ppb/yr (1ppb=6mm) 12540Lec19
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
Processing methods The clock and local oscillator phase variations are the biggest deviations in the model of GPS phase and range data These terms can be explicitly handled by estimation of clock variations(but if done brut-force in least squares with sequential LSQ or a Kalman filter an be attacked is a very large estimation problem). C When multiple sites see the same satellite, the satellite clocks can also be estimated, but at every epoch of measurement, one clock needs to be fixed or an ensemble average of cocks set to have zero mean adjustment 04/2802 12540Lec19 Differencing An alternative approach to explicit estimation is differencing data Single differences: two forms nc emanates menos drem sa sites that se Difference measurements from two satellites at the one site liminates the ground receiver cloc Double differences say eliter coins ape singled differences, but the ground and The local oscillator phases also cancel except the differer twt satellites aond woe stations s e his dierence shoulda be 12540Lec19
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
Differencing There are subtle problems with the exact times that measurements are made with differencing In the receivers, the measurements of range and 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 04/2802 12540Lec19 Light propagation time and differencing 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 Non-synchronized receiver sampling can cause 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: Feigl, K. L, R.w. King, T. A. Herring, and M. Rotchacher, A scheme for reducing the effect of selective a ty on precise geodetic meas ents from the global Positioning System, Geophys. Res. Left, 1289-1292 12540Lec19
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: 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
Cycle slip detection When processing phase, cycles slips are a potential 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 rinex file. The have a large offset from the range values (initial ambiguity, which in double differences should be a integer value) When the receiver looses lock(typically range will be missing but not always), a cycle slip occurs and this must be re-fixed to an integer or left as an unknown parameter 0428/2 12540Lec19 Cycle slip detection When o-minus-c is computed in one-ways for phase variations are dominated by clocks in receiver Multiple techniques are used to detect cycle slips Ln phase- Ln range(n=1, 2). Removes geometry but affected by ionospheric delay (opposite sign on phase and range) and noise in range measurements L1 phase -L2 phase. Some times called wide-lane. Affected by ion-delay but is common detector Double difference phase residuals: On short baselines moves ionosphere and if good apriori positions are known should be a smooth function of time often used to estimate number of cycles in sip and resolve to integer value Melbourne-Webena wide lane(ML-WL)(see over) 12540Lec19
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
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 0428/2 12540Lec19 MW Wide lane From the equations for range and phase with the phase offsets for cycle offsets you can derive MW-WL=M-N2=2-91+(P+P)f-f2 The MW-WL should be constant if there are no cycle slips. When the phase and range values are double differences, N2-N, should be integer. The factor that scales range is -0 1 and so range noise is reduced Average values of the Mw-WL are used to esimate L1/L2 phase difference independent of ion-delay and geometry changes 12540Lec19
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, N2-N1 should be integer. • The factor that scales range is ~0.1 and so range noise is reduced. • geometry changes. MW -WL = N1 - N2 = f L 2 - f L1 + (P1 + P2 ) fL1 - fL 2 fL1 + fL 2 Average values of the MW-WL are used to esimate L1/L2 phase difference independent of ion-delay and 10
