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A robust Kalman-Bucy filtering problem
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DOI：10.1016/j.automatica.2020.109252.png)
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Abstract
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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. (c) 2020 Elsevier Ltd. All rights reserved.
Keywords:
Kalman-Bucy filters
Model uncertainty
Robust estimation
Minimum mean square estimator
Minimax theorem
Sublinear operator
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