Geodesy by radio interferometry: The application of Kalman Filtering to the analysis of very long baseline interferometry data

Abstract

We discuss the application of Kalman filtering techniques to the analysis of very long baseline interferometry (VLBI) data. The VLBI observables are geometrically related to the geodetic and astrometric parameters which can be determined from them. However, contributions to the observables from the clocks at, and the atmospheres above, the VLBI sites must be accounted for if reliable estimates of geodetic and astrometric parameters are to be obtained. Here an implementation of a Kaiman filter to account for stochastic behavior on those parameters which vary during the course of a VLBI experiment is discussed. Both the nature of the stochastic processes which should be used in the model for the VLBI data and the implementation of the Kaiman filter estimator are considered. From the results obtained, we conclude that the Kaiman filter is appropriate for analyzing VLBI data. The choice of stochastic model does not unduly affect the estimates of the geodetic parameters and the quality of these estimates is higher than that for conventional weighted least squares estimators.

Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data

“…[ 1994,1997] report similar improvements using a larger VLBI data set. They also used a linear, piecewise continuous parameterization rather than the stochastic approach adopted by Herring [1992]. Both studies suffered from the lack of reliable statistics for the magnitudes and variations of the delays due to atmospheric azimuthal asymmetry.…”

Integrated satellite interferometry: Tropospheric noise, GPS estimates and implications for interferometric synthetic aperture radar products

“…The deterministic approach sets limits on the range of the delay, and possibly its rate of change, over some time interval, and its value during that interval is estimated as a constant in the least squares inversion. The stochastic hpproach makes use of the statistical properties of the process in a Kalman filter (or other related optimal filters) estimation scheme [Gelb, 1974;Herring et al, 1990]. The tropospheric delay is typically modeled as a random walk (fi = 2) process or as several first-order Gauss-Markov processes [Herring et al, 1990].…”

“…The stochastic hpproach makes use of the statistical properties of the process in a Kalman filter (or other related optimal filters) estimation scheme [Gelb, 1974;Herring et al, 1990]. The tropospheric delay is typically modeled as a random walk (fi = 2) process or as several first-order Gauss-Markov processes [Herring et al, 1990].…”

New constraints on current deformation in Asia from continuous GPS measurements at Ulan Baatar, Mongolia

“…We included 7 global IGS stations (TSKB, USUD, TAIW, Klq3, SHAO, XIAN, IRKT) to serve as ties with the 1TRFX)6 (Sillard et al, 1998). The least squares adjustment vector and its corresponding variancecovariance matrix for station positions and orbital elements estimated for each independent daily solution were then passed to a Kalman filter (GLOBK, Herring et al, 1990) and combined with global SINEX (Solution Independent Exchange format) files from the IGS daily processing routinely done at SIO in order to estimate station positions and velocities in 1TRFX)6. All parameters were kept loose at this stage, constraints were only applied at the next stage to impose the reference frame.…”