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.

中文翻译：

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鲁棒的Kalman-Bucy滤波问题

本文研究了模型不确定性下的广义Kalman-Bucy模型以及相应的鲁棒问题。我们发现，该鲁棒问题等效于亚线性算子下的估计问题。通过Girsanov变换和极小极大定理，我们证明了该问题可以在新的概率测度下重新构造为经典的Kalman-Bucy滤波问题。得到控制最优估计器的方程。此外，在某些情况下，最优估计器可以分解为经典最优估计器和与模型不确定性参数有关的项。