1. Kalman-Bucy filtering and minimum mean square estimator under uncertainty
- Author
-
Ji, Shaolin, Kong, Chuiliu, Sun, Chuanfeng, and Zhang, Ji-Feng
- Subjects
Mathematics - Optimization and Control ,Mathematics - Probability - Abstract
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., Comment: 24 pages
- Published
- 2020