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