Adjustment Models for Multivariate Geodetic Time Series with Vector-Autoregressive Errors

authored by
Boris Kargoll, Alexander Dorndorf, Mohammad Omidalizarandi, Jens-André Paffenholz, Hamza Alkhatib

In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

Geodetic Institute
External Organisation(s)
Anhalt University of Applied Sciences
Clausthal University of Technology
Journal of Applied Geodesy
No. of pages
Publication date
Publication status
Peer reviewed
ASJC Scopus subject areas
Modelling and Simulation, Engineering (miscellaneous), Earth and Planetary Sciences (miscellaneous)
Electronic version(s) (Access: Open)

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