KMS Of Academy of mathematics and systems sciences, CAS
| KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY | |
| Ji, Shaolin1; Kong, Chuiliu2,3; Sun, Chuanfeng4; Zhang, Ji-Feng2,3 | |
| 2021 | |
| Source Publication | SIAM JOURNAL ON CONTROL AND OPTIMIZATION
 |
| ISSN | 0363-0129 |
| Volume | 59Issue:4Pages:2669-2692 |
| 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 P-theta*. Based on this P-theta* 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. |
| Keyword | Kalman-Bucy filtering minimum mean square estimator drift uncertainty convex operator minimax theorem backward stochastic differential equation |
| DOI | 10.1137/20M137954X |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Key R\&D Program of China[2018YFA0703900] ; National Natural Science Foundation of China[11971263] ; National Natural Science Foundation of China[11871458] ; National Natural Science Foundation of China[11701214] ; Natural Science Foundation of Shandong Province[ZR2017BA032] |
| WOS Research Area | Automation & Control Systems ; Mathematics |
| WOS Subject | Automation & Control Systems ; Mathematics, Applied |
| WOS ID | WOS:000692322700012 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59249 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Kong, Chuiliu |
| Affiliation | 1.Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 250100, Shandong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100149, Peoples R China 4.Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China |
| Recommended Citation GB/T 7714 | Ji, Shaolin,Kong, Chuiliu,Sun, Chuanfeng,et al. KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2021,59(4):2669-2692. |
| APA | Ji, Shaolin,Kong, Chuiliu,Sun, Chuanfeng,&Zhang, Ji-Feng.(2021).KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,59(4),2669-2692. |
| MLA | Ji, Shaolin,et al."KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 59.4(2021):2669-2692. |
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