A generalized Kalman filter with its precision in recursive form when the stochastic model is misspecified

Journal article (2021)

Authors

P.J.G. Teunissen University of Melbourne, Mathematical Geodesy and Positioning - CEG , Curtin University
Amir Khodabandeh University of Melbourne
D.V. Psychas Mathematical Geodesy and Positioning - CEG
Research Group
Mathematical Geodesy and Positioning (CEG) (TU Delft)
Copyright: © 2021 P.J.G. Teunissen, A. Khodabandeh, D.V. Psychas
DOI
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https://doi.org/10.1007/s00190-021-01562-0
Kalman filter Stochastic model Minimal detectable bias (MDB) Error-variance matrices Generalized filter Predicted residual
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Published Date

2021

Language

English

Faculty

Civil Engineering & Geosciences

Department

Geoscience and Remote Sensing

Research Group

Mathematical Geodesy and Positioning

Abstract

In this contribution, we introduce a generalized Kalman filter with precision in recursive form when the stochastic model is misspecified. The filter allows for a relaxed dynamic model in which not all state vector elements are connected in time. The filter is equipped with a recursion of the actual error-variance matrices so as to provide an easy-to-use tool for the efficient and rigorous precision analysis of the filter in case the underlying stochastic model is misspecified. Different mechanizations of the filter are presented, including a generalization of the concept of predicted residuals as needed for the recursive quality control of the filter.