Applying Kalman filtering to investigate tropospheric effects in VLBI

Transcription

1 Applying Kalman filtering to investigate tropospheric effects in VLBI Benedikt Soja, Tobias Nilsson, Maria Karbon, Robert Heinkelmann, James Anderson, Li Liu, Cuixian Lu, Julian A. Mora-Diaz, Virginia Raposo-Pulido, Minghui Xu, Santiago Belda and Harald Schuh Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences Geodetic Week 2014, Berlin October 7, 2014

2 Motivation for Kalman filtering VLBI data Capable of real-time analysis of continuous observations VLBI Global Observing System (VGOS): e-vlbi, observations 24/7 Efficient handling of large number of observations VGOS: increase in number of observations by 1-2 orders of magnitude Ease of including different data sets in the estimation GGOS: combination of space-geodetic techniques Stochastic modeling (focus of this presentation) tum.de ivscc.gsfc.nasa.gov raege.net 2

3 Kalman filter overview Prediction x k = F k x k 1 + w k P k = F k P k 1 F k T + Q k Correction x k = x k + K k (z k H k x k ) P k = (I K k H k )P k K k = P k H k T (H k P k H k T + R k ) 1 Forward + backward + smoothing Extension of the GFZ version of VieVS (Böhm et al., 2012) FWF project VLBI-ART (VLBI Analysis in Real-Time) 3

4 Kalman filter solution Estimation of: Station coordinates (NNT+NNR constraints) Radio source positions (NNR) Full set of EOP Clock (optional: clock rate) ZWD + gradients IERS Conventions 2010 Stochastic modeling random walk, integrated random walk (clock), first order Gauss-Markov (gradients) Option to use adaptive factor (Adaptive KF) 4

5 Previous results CONT11 Zenith wet delays (ZWD) from KF and LSM: good agreement KF with better baseline length repeatabilities Comparison with ZWDs from water vapor radiometers (WVR): KF up to 15% better than LSM 5

6 Station-dependent noise ZWD time series from CONT campaigns, using KF and LSM Computing Allan Standard Deviation (ASD) Assuming random walk: ASD ~ τ 1/2 Estimating Power Spectral Densities: PSD = ASD 2 τ τ PSD necessary to compute the covariance matrix of the prediction error Prediction x k = F k x k 1 + w k Correction x k = x k + K k (z k H k x k ) P k = F k P k 1 F T k + Q k P k = (I K k H k )P k Wettzell / CONT14 K k = P k H T k (H k P k H T k + R k ) 1 6

7 CONT02 PSD 7

8 CONT05 PSD 8

9 CONT08 PSD 9

10 CONT11 PSD 10

11 CONT14 PSD 11

12 PSD changing over time Stations participating in >3 CONT sessions Average: PSD decreasing except CONT02 Possible reasons Measurements of higher quality lower PSD? CONT sessions during different seasons (May, Aug, Sep, Oct)? Weather at certain stations? Atmospheric circulation patterns? 12

13 Comparison of PSD values Average PSD values PSD [cm 2 /d] Herring, 1992 (VLBI) 58 Schüler, 2001 (GNSS) 6 CONT sessions KF 20 CONT sessions LSM 22 CONT11: comparison to PSDs from water vapor radiometer data IVS 1999 Annual Report PSD [cm 2 /d] Onsala Tsukuba WVR CONT11 KF CONT11 LSM IVS 2005 Annual Report 13

14 Effects on station coordinates Baseline length repeatabilities computed KF station coordinates averaged over 1 day Station-based vs. average PSD Example: CONT14 vs. 17 cm 2 /d Station-based approach always better by 2-3% 14

15 Effects on station coordinates Comparison of different global models PSD [cm 2 /d] Herring 58 CONTs 20 CONT14 17 Schüler 6 Larger PSD smaller repeatability ZWD absorbing noise from other estimated parameters? Improvement using larger PSDs for other parameters? 15

16 Summary Kalman filter used to analyze recent CONT sessions Stochastic properties of ZWD investigated Temporal and spatial differences studied Station-based noise better baseline length repeatabilities Outlook Tropospheric gradients comparisons (WVR, GNSS, ray tracing) Integration of external data in the KF Keep fine-tuning the KF (noise for stations, clocks,...) 16

17 Thanks for your attention! Acknowledgements VLBI data: IVS WVR data: Onsala Space Observatory, Sweden & GSI, Japan Project funding: FWF (VLBI-ART) 17