12. 540 Principles of the Global Positioning System Lecture 22 Prof. Thomas Herring 12540Lec22 KinematiC GPS The style of gps data collection and processing suggests that one or more GPs stations is moving(e.g, car, aircraft) To obtain good results for positioning as a function of time requires that the ambiguities be fixed to integer values Track is the MIT implementation of this style of processing
05/07/03 12.540 Lec 22 1 12.540 Principles of the Global Positioning System Lecture 22 05/07/03 12.540 Lec 22 2 Kinematic GPS processing Prof. Thomas Herring • The style of GPS data collection and processing suggests that one or more GPS stations is moving (e.g., car, aircraft) • To obtain good results for positioning as a function of time requires that the ambiguities be fixed to integer values • Track is the MIT implementation of this style of 1
Styles of kinematic GPS Kinematic GPS techniques go by a number of names with features that are often receiver specific Kinematic GPS: Early term which implies that there is no loss of lock while the receiver is moving. In survey mode, if loss of ock occurs the antenna must be returned to a point of know ocation Rapid Static GPS: Technique that uses range and phase to resolve ambiguities. No need to maintain lock while receiver \is ping. Surveying where position during static portion all that RTK Real-time kinematic: Kinematic solution with real-time radio telemetry link. Analysis is done on-the-fly. Very popular now with surveyors because results know instar 12540Lec22 General aspects The success of kinematic processing depends on separation of sites The MIT software allows multiple stations to be used in the positioning(may by kinematic or static For separations 10 km, usually easy(most RTK systems work at these distances) 10>100 km more difficult but often successful Depends on quality of data and ionospheric activity >100 km very mixed results
05/07/03 12.540 Lec 22 3 Styles of kinematic GPS • Kinematic GPS techniques go by a number of names with features that are often receiver specific. of lock while the receiver is moving. In survey mode, if loss of lock occurs the antenna must be returned to a point of known location. resolve ambiguities. No need to maintain lock while receiver moving. Surveying where position during static portion all that is needed. radio telemetry link. Analysis is done on-the-fly. Very popular now with surveyors because results know instantly. – Kinematic GPS: Early term which implies that there is no loss – Rapid Static GPS: Technique that uses range and phase to – RTK Real-time kinematic: Kinematic solution with real-time 05/07/03 12.540 Lec 22 4 General aspects • The success of kinematic processing depends on separation of sites • The MIT software allows multiple stations to be used in the positioning (may by kinematic or static) • For separations < 10 km, usually easy (most RTK systems work at these distances). • 10>100 km more difficult but often successful. Depends on quality of data and ionospheric activity. • >100 km very mixed results 2
Issues with length As site separation increases, the differential ionospheric delays increases, atmospheric delay differences also increase making modeling of phase data more difficult For short baselines(<10 km), ionospheric delay can be treated as zero and l 1 and l2 resolved separately For longer baselines this is no longer true and ambiguities must be resolved with lc (and often the MW WL L1-L2 number of cycles) Track features Track uses the melbourne -Webena wide Lane to resolve l1-l2 and then a combination of techniques to determine l1 and l2 cycles separately For short baselines uses a search technique and floating point estimation with L1 and L2 separately For long baselines uses floating point estimate with LC and ionospheric delay constraint
05/07/03 12.540 Lec 22 5 Issues with length 05/07/03 12.540 Lec 22 6 Track features separately. separately • As site separation increases, the differential ionospheric delays increases, atmospheric delay differences also increase making modeling of phase data more difficult • For short baselines (<10 km), ionospheric delay can be treated as ~zero and L1 and L2 resolved separately • For longer baselines this is no longer true and ambiguities must be resolved with LC (and often the MW WL L1-L2 number of cycles) • Track uses the Melbourne-Webena Wide Lane to resolve L1-L2 and then a combination of techniques to determine L1 and L2 cycles • For short baselines uses a search technique and floating point estimation with L1 and L2 • For long baselines uses floating point estimate with LC and ionospheric delay constraint 3
Ambiguity resolution Basic problem is determine the integer number of cycles in the carrier phase double differences Two generic classes of approach Searching methods: T wo basic types Search over integer ambiguities checking RMS fit of phase residuals Search over position, minimizing a fit function that does not jer part of an ity(e.g. Cosine of phase Estimation and then resolution using statistical testing Statistical Resolution The most common method now is estimation with statistical assessment of fitting to integer Generic classes of cases: NNNNN.01+0.01 Pretty clearly can be resolved NNNNN. 35+0.40 Highest probability answer is nnnnn but NNNNN+1 also has >10% of being correct. Since 10-100 ambiguities need to be resolved 1-10 of them would be incorrect in the above case NNNNN.01+0.55 clearly close to an integer but+1 value also very likely NNNNN. 35+0.01 should be resolvable to integer but value is ar from integer
05/07/03 12.540 Lec 22 7 Ambiguity resolution differences. – Searching methods: Two basic types • Search over integer ambiguities checking RMS fit of phase residuals • Search over position, minimizing a fit function that does not depend on integer part of ambiguity (e.g.. Cosine of phase residuals) – Estimation and then resolution using statistical testing. • Basic problem is determine the integer number of cycles in the carrier phase double • Two generic classes of approach: 05/07/03 12.540 Lec 22 8 • The most common method now is estimation with statistical assessment of fitting to integer. • Generic classes of cases: NNNNN+1 also has >10% of being correct. Since 10-100 ambiguities need to be resolved 1-10 of them would be incorrect in the above case. very likely far from integer, Statistical Resolution – NNNNN.01±0.01 Pretty clearly can be resolved – NNNNN.35±0.40 Highest probability answer is NNNNN but – NNNNN.01±0.55 clearly close to an integer but +1 value also – NNNNN.35±0.01 should be resolvable to integer but value is 4
Statistical resolution Uncertainties of ambiguities are always uncertain Formal estimates come for inversion but these depend on data noise characteristics(most importantly correlations in data) Many kinematic surveys done with high sampling rates(0. 1-1Hz) so white noise assumptions generate very small error estimates Most testing methods use a"contrast or "ratio"style test (ie, ratio of x2 with best and next best choice of ambiguities and an impact on x2 of setting the value to n integer. Covers last case shown--no integer seems correct implying modeling errors 12540Lec22 LAMBDA Method In addition to individual values Each ambiguity that is resolved effects other estimates and thus there is a cascading effect The LAMBDa Method tries to account for these correlations by projecting the ambiguities into ar orthogonal space. Use of eigenvectors and eigenvalues discussed in earlier classes) Method is from a linear operator that preserves nteger values and transforms ambiguities so that estimates are nearly un-correlated.(Eigenvectors ould make estimates uncorrelated, by integers would be preserved)
05/07/03 12.540 Lec 22 9 Statistical resolution • Formal estimates come for inversion but these depend on data noise characteristics (most importantly correlations in data). • rates (0.1-1Hz) so white noise assumptions generate very small error estimates. • test (ie., ratio of c2 with best and next best choice of ambiguities and an impact on c2 of setting the value to an integer. Covers last case shown--no integer seems correct implying modeling errors.) Uncertainties of ambiguities are always uncertain. Many kinematic surveys done with high sampling Most testing methods use a “contrast” or “ratio” style 05/07/03 12.540 Lec 22 10 LAMBDA Method • In addition to individual values: Each ambiguity that is resolved, effects other estimates and thus there is a cascading effect. • The LAMBDA Method tries to account for these correlations by projecting the ambiguities into an orthogonal space. (Use of eigenvectors and • Method is from a linear operator that preserves estimates are nearly un-correlated. (Eigenvectors would make estimates uncorrelated, by integers would not be preserved). eigenvalues discussed in earlier classes). integer values and transforms ambiguities so that 5