Abstract
The troposphere is one of the most important error sources for space geodetic techniques relying on radio signals. Since it is not possible to model the wet part of the tropospheric delay with sufficient accuracy, it needs to be estimated from the observational data. In the analysis of very long baseline interferometry (VLBI) data, the parameter estimation is routinely performed using a least squares adjustment. In this paper, we investigate the application of a Kalman filter for parameter estimation, specifically focusing on the tropospheric delays. The main advantages of a Kalman filter are its real-time capability and stochastic approach. We focused on the latter and derived stochastic models for VLBI zenith wet delays, taking into account temporal and location-based differences. Compared to a static noise model, the quality of station coordinates, also estimated in the Kalman filter, increased as a result. In terms of baseline length and station coordinate repeatabilities, this improvement amounted to 2.3 %. Additionally, we compared the Kalman filter and least squares results for VLBI with zenith wet delays derived from GPS (Global Positioning System), water vapor radiometers, and ray tracing in numerical weather models. The agreement of the Kalman filter VLBI solution with respect to water vapor radiometer data was larger than that of the least squares solution by 6–15 %. Our investigations are based on selected VLBI data (CONT campaigns) that are closest to how future VLBI infrastructure is designed to operate. With the aim for continuous and near real-time parameter estimation and the promising results which we have achieved in this study, we expect Kalman filtering to grow in importance in VLBI analysis.
Highlights
Very long baseline interferometry (VLBI, Schuh and Behrend 2012; Schuh and Böhm 2013), among other space geodetic techniques, has been successfully used in the past to estimate tropospheric parameters, in particular zenith wet delays (ZWD) and horizontal delay gradients (e.g., Heinkelmann et al 2011)
ZWD noise characterization To determine the power spectral density (PSD), ZWD time series were derived for all five CONT campaigns and all participating stations, using both the Kalman filter (KF) and least squares method (LSM) approach
For the initial KF solution, a PSD of = 56 cm2/day, taken from Herring et al (1990), was used. This value is larger than others from literature (e.g., = 6 cm2/day, Schüler 2001) and gives the observations more weight compared to the predictions
Summary
Very long baseline interferometry (VLBI, Schuh and Behrend 2012; Schuh and Böhm 2013), among other space geodetic techniques, has been successfully used in the past to estimate tropospheric parameters, in particular zenith wet delays (ZWD) and horizontal delay gradients (e.g., Heinkelmann et al 2011). The standard method for parameter estimation in operational VLBI analysis is the least squares adjustment, called least squares method (LSM). Another option is the use of a Kalman filter (KF, Kalman 1960). Pioneering work about the application of a Kalman filter in VLBI analysis was performed by Herring et al (1990), with the focus on tropospheric investigations by Tralli et al (1992).
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