论文标题
在不确定性下的Kalman-bucy过滤和最低均方根估计器
Kalman-Bucy filtering and minimum mean square estimator under uncertainty
论文作者
论文摘要
在本文中，我们研究了不确定性下的广义Kalman-Bucy过滤问题。考虑了信号过程和观察过程的漂移不确定性，对不确定性的态度的特征是凸操作员（凸风险度量）。通过解决凸操作员下的最小均方根估计问题来计算最佳滤波器或最小均方根估计器（MMSE）。在本文的第一部分中，在G-Hoppection中研究了该估计问题，这是一个特殊的凸操作员。对于这种情况，我们证明存在最坏的事先。基于此最坏情况，我们在G-Hoppection下获得了Kalman-Bucy滤波方程。在本文的第二部分中，我们研究了一般凸操作员下的最低均方根估计问题。推导MMSE的存在和唯一性结果。
In this paper, we study a generalized Kalman-Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation process is considered and the attitude to uncertainty is characterized by a convex operator (convex risk measure). The optimal filter or the minimum mean square estimator (MMSE) is calculated by solving the minimum mean square estimation problem under a convex operator. In the first part of this paper, this estimation problem is studied under g-expectation which is a special convex operator. For this case, we prove that there exists a worst-case prior. Based on this worst-case prior we obtained the Kalman-Bucy filtering equation under g-expectation. In the second part of this paper, we study the minimum mean square estimation problem under general convex operators. The existence and uniqueness results of the MMSE are deduced.
