Kalman--Bucy Filtering and Minimum Mean Square Estimator under Uncertainty
| Autor: | Chuanfeng Sun, Ji-Feng Zhang, Chuiliu Kong, Shaolin Ji |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mean square
Control and Optimization Applied Mathematics Minimax theorem Probability (math.PR) Process (computing) Estimator Kalman filter Quantitative Biology::Genomics Signal Optimization and Control (math.OC) Convex operator FOS: Mathematics Filtering problem Applied mathematics Mathematics - Optimization and Control Mathematics - Probability Mathematics |
| Zdroj: | SIAM Journal on Control and Optimization. 59:2669-2692 |
| ISSN: | 1095-7138 0363-0129 |
| DOI: | 10.1137/20m137954x |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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