VieLSM and VieLSMscan version 2 1 Kamil Teke
- Slides: 32
Vie_LSM and Vie_LSM_scan (version 2. 1) Kamil Teke and Johannes Böhm Vie. VS User Workshop 9 – 10 September, 2013 Vienna
Introduction “vie_lsm” is a module of “Vie. VS”, which estimates geodetic parameters with least squares adjustment from VLBI observations. All the parameters can be estimated as continuous piece-wise linear offsets (CPWLO) in sub-daily and daily temporal resolution. Vie. VS User Workshop 2013 2
Estimated parameters are: Clocks (offset (cm), rate (cm/day), quadratic term (cm/day 2), CPWLO (cm)), Zenith wet delays (cm) as CPWLO, Troposphere gradients (cm) as CPWLO, EOP (mas and ms) as CPWLO, Antenna coordinates in TRF (cm) as one offset per session or as CPWLO, Source coordinates in CRF (declinations in mas and right ascensions in ms) as CPWLO. Vie. VS User Workshop 2013 3
continuous piece-wise linear offsets (CPWLO) Vie. VS User Workshop 2013 4
Partial derivatives of the delay model w. r. t. a sub-daily parameter Vie. VS User Workshop 2013 5
design matrix of real observation equations design matrix of pseudo-observation equations (constraints) bc is a zero vector (due to NNT and NNR conditions parameter vector (estimates) variance-covariance matrix of the estimates Vie. VS User Workshop 2013 6
Estimation Settings The first solution is meant to remove large clock offsets (and rates and quadratic terms) for numerical reasons. (Clock offsets can be several kilometers. ) 7
Parametrization for least squares Vie. VS User Workshop 2013 8
VLBI clock error quadratic polynomial for each clock CPWLO for each clock e. g. at each UTC integer hour (t 1 and t 2) total clock error at epoch t Vie. VS User Workshop 2013 9
Parametrization for relative clock errors This combination adds relative constraints on the clock offsets. Actually, observation equations are added to the design matrix which tell that the difference between two adjacent piecewise linear clock offsets is zero a certain standard deviation . (These constraints are mainly important to bridge gaps without observations to avoid singularity of the normal equation system. ) 10
Troposphere delay reduced from observations a priori to the adjustment estimated Vie. VS User Workshop 2013 estimated 11
Parametrization for ZWD and gradients 12
Parametrization for EOP If you want to estimate one constant value per session, the recommendation is to set the parameterization as shown above. Very strong relative constraints of 1 e-4 m(a)s/day take care that the estimates are the same over the session. Example: The session is from 18 UT to 18 UT. Then, three piecewise linear offsets are set up for each EOP. (They are set up a midnight before the session, at midnight during the session, and at midnight after the session. ) The strong constraints take care that all three estimates per session are the same. 13
Parametrization for Station Coordinates 14
Parametrization for Source Coordinates 15
Session-wise parameterization Vie. VS User Workshop 2013 16
Session-wise parameterization 17
Session-wise parameterization 18
Session-wise parameterization 19
Session-wise parameterization Case 1: NNT/NNR (one coordinate offset per session) 20
Session-wise parameterization Case 2: Fix some station coordinates (one coordinate offset per session) 21
Session-wise parameterization Case 3: Fix some station coordinates (CPWLO coordinates) 22
Session-wise parameterization 23
Session-wise parameterization 24
Session-wise parameterization 25
vie_lsm scan-wise update 26
Scan-wise update of normal equation system Claudia Tierno Ros, Third Vie. VS user workshop, 11 -13 September, 2012 27
Scan-wise update of normal equation system Claudia Tierno Ros, Third Vie. VS user workshop, 11 -13 September, 2012 28
Command window – vie_lsm 29
Command window – vie_lsm 30
Conclusions vie_lsm corrects clock breaks and detects outlier observations. vie_lsm provides SINEX input and datum free normal equations for global solutions (vie_glob). CPWLO estimates of Vie. VS are in a good agreement with those derived from other space geodetic techniques. Scan-wise update of normal equation system ensures a successful process of the future sessions with lots of observations. Vie. VS User Workshop 2013 31
Thank you so much for your attention! Vie. VS User Workshop 2013 32
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