Including uncertainty into the model of a KF to provide robust estimators

Shaolin Ji, Chuiliu Kong, Chuanfeng Sun, A robust Kalman–Bucy filtering problem, . Automatica, Volume 122, 2020, DOI: 10.1016/j.automatica.2020.109252.

A generalized Kalman–Bucy model under model uncertainty and a corresponding robust problem are studied in this paper. We find that this robust problem is equivalent to an estimated problem under a sublinear operator. By Girsanov transformation and the minimax theorem, we prove that this problem can be reformulated as a classical Kalman–Bucy filtering problem under a new probability measure. The equation which governs the optimal estimator is obtained. Moreover, the optimal estimator can be decomposed into the classical optimal estimator and a term related to the model uncertainty parameter under some condition.

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