A Bayesian framework for robust Kalman filtering under uncertain noise statistics

In this paper, we propose a Bayesian framework for robust Kalman filtering when noise statistics are unknown. The proposed intrinsically Bayesian robust Kalman filter is robust in the Bayesian sense meaning that it guarantees the best average performance relative to the prior distribution governing unknown noise parameters. The basics of Kalman filtering such as the projection theorem and the innovation process are revisited and extended to their Bayesian counterparts. These enable us to design the intrinsically Bayesian robust Kalman filter in a similar way that one can find the classical Kalman filter for a known model.

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