A robust Kalman-Bucy filtering problem

Shaolin Ji; Chuiliu Kong; Chuanfeng Sun

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arXiv · 1905.01791

A robust Kalman-Bucy filtering problem

Shaolin Ji·Chuiliu Kong·Chuanfeng Sun

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Abstract

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 estimate 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 model uncertainty.

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Shaolin Ji, Chuiliu Kong, Chuanfeng Sun. 2019-05-06. A robust Kalman-Bucy filtering problem. https://arxiv.org/abs/1905.01791

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