Tropospheric delay determination by Kalman filtering VLBI data

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.

Determination of a terrestrial reference frame via Kalman filtering of very long baseline interferometry data

“…A Kalman filter approach has been successfully used by the ITRS combination center at NASA Jet Propulsion Laboratory (JPL) for their JTRF2008 solution, providing station coordinates at weekly intervals together with secular velocities and seasonal signals . For the analysis of very long baseline interferometry (VLBI, Schuh and Behrend, 2012;Schuh and Böhm, 2013) observations, Kalman filtering was introduced by Herring et al (1990), and recently applied in studies by Nilsson et al (2015), Soja et al (2015), and Karbon et al (2015).…”

Water vapour radiometry in geodetic very long baseline interferometry telescopes: assessed through simulations

“…Therefore, today the wet delays at all stations in an experiment are normally estimated from the VLBI data themselves, see e.g. Soja et al (2015). Stand-alone WVR observations at specific sites are mainly used to verify these estimates, see e.g.…”

Application of Kalman filtering in VLBI data analysis

“…The ZWD are modeled as random walk processes, and in this work, we assumed a PSD of 58 cm 2 /day for the process noise, as suggested (Herring et al 1990). For a description of how to estimate the PSD for the different parameters and the effect of using these values, see Soja et al (2015). The tropospheric gradients are modeled as first-order Gauss-Markov processes, and we assumed a time constant of 3 h and a process noise PSD of 0.025 cm 2 /day in the present study.…”

“…For a more detailed study of the ZWD from the Kalman filter, see Soja et al (2015). A comparison of gradients from different techniques, including the Kalman filter and LSM VLBI solutions, is described by (Heinkelmann et al: Atmospheric delay gradients with high temporal resolution, submitted to J. Geodesy).…”

“…This paper gives a general introduction to the Kalman filter and its performance for estimation of various parameters. More specific details on how the tropospheric delays are modeled in the Kalman filter, as well as a thorough analysis of the accuracy of estimated tropospheric parameters, are given in the accompanying paper (Soja et al 2015). Furthermore, a more detailed investigation on the EOP estimation is presented in (Karbon et al: EOP estimated from VLBI with a Kalman filter, in preparation).…”