KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY

doi:10.1137/20M137954X

CSpace

	KALMAN-BUCY FILTERING AND MINIMUM MEAN SQUARE ESTIMATOR UNDER UNCERTAINTY
	Ji, Shaolin 1; Kong, Chuiliu 2,3; Sun, Chuanfeng 4; Zhang, Ji-Feng 2,3
	2021
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	59 期号:4 页码:2669-2692
摘要	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.
关键词	Kalman-Bucy filtering minimum mean square estimator drift uncertainty convex operator minimax theorem backward stochastic differential equation
DOI	10.1137/20M137954X
收录类别	SCI
语种	英语
资助项目	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研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000692322700012
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59249
专题	中国科学院数学与系统科学研究院
通讯作者	Kong, Chuiliu
作者单位	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
推荐引用方式 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.