A robust Kalman-Bucy filtering problem
A robust Kalman-Bucy filtering problem
复制标题
鲁棒卡尔曼-布西滤波问题
DOI：
10.1016/j.automatica.2020.109252
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发表时间：
2020-12-01
期刊：
影响因子：
6.4
通讯作者：
Sun, Chuanfeng
中科院分区：
文献类型：
--
作者：
Ji, Shaolin;Kong, Chuiliu;Sun, Chuanfeng
研究了模型不确定性下的广义Kalman-Bucy模型及其鲁棒性问题。我们发现这个鲁棒问题等价于一个次线性算子下的估计问题。通过Girsanov变换和极大极小定理，证明了在新的概率测度下，该问题可以转化为经典的Kalman-Bucy滤波问题。得到了控制最优估计量的方程。此外，在一定条件下，最优估计可分解为经典最优估计和与模型不确定性参数有关的一项。(c)2020爱思唯尔有限公司保留所有权利。
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.