Stochastic Detectability and Mean Bounded Error Covariance of the Recursive Kalman Filter with Markov Jump Parameters |
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Authors: | Eduardo F. Costa Alessandro Astolfi |
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Affiliation: | 1. Departamento de Matemática Aplicada e Estatística – ICMC – USP , S?o Carlos, SP, Brazil efcosta@icmc.usp.br;3. Electrical and Electronic Engineering Department, Imperial College London, London, United Kingdom and Dipartimento di Informatica, Sistemi e Produzione , University of Rome “Tor Vergata,” , Roma, Italy |
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Abstract: | In this article, we study the error covariance of the recursive Kalman filter when the parameters of the filter are driven by a Markov chain taking values in a countably infinite set. We do not assume ergodicity nor require the existence of limiting probabilities for the Markov chain. The error covariance matrix of the filter depends on the Markov state realizations, and hence forms a stochastic process. We show in a rather direct and comprehensive manner that this error covariance process is mean bounded under the standard stochastic detectability concept. Illustrative examples are included. |
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Keywords: | Detectability Kalman filtering Markov jump systems Stochastic systems |
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