L1-Optimal Filtering of Markov Jump Processes. II. Numerical Analysis of Particular Realizations Schemes

被引：5

作者：

Borisov, A. V. ^{[1
,2
,3
]}

机构：

[1] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Inst Informat Problems, Moscow, Russia

[2] Natl Res Univ, Moscow Aviat Inst, Moscow, Russia

[3] Moscow MV Lomonosov State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia

来源：

AUTOMATION AND REMOTE CONTROL | 2020年 / 81卷 / 12期

基金：

俄罗斯基础研究基金会;

关键词：

Markov jump process; stable estimate; maximum a posteriori probability estimate; numerical integration scheme;

D O I：

10.1134/S0005117920120024

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Part II of the paper deals with particular numerical schemes used to realize the filtering algorithm for Markov jump processes by indirect observations corrupted by Wiener noises. The orders of accuracy of these numerical schemes are determined. The cases of additive and multiplicative noises in observations are investigated separately: as shown below, the same schemes in these cases have different accuracy. For observations with additive noises, schemes of orders 1/2, 1 and 2 are proposed; for observations with multiplicative noises, schemes of orders 1 and 2. The theoretical results are illustrated with numerical examples.

引用

页码：2160 / 2180

页数：21

共 14 条

[1] L1-Optimal Filtering of Markov Jump Processes. I. Exact Solution and Numerical Implementation Schemes
Borisov, A. V.
[J]. AUTOMATION AND REMOTE CONTROL, 2020, 81 (11) : 1945 - 1962
[2] L1-Optimal Filtering of Markov Jump Processes. III. Identification of System Parameters
Borisov, A. V.
[J]. AUTOMATION AND REMOTE CONTROL, 2022, 83 (11) : 1773 - 1791
[3] Analysis and Estimation of the States of Special Jump Markov Processes. II. Optimal Filtration in Wiener Noise
A. V. Borisov
[J]. Automation and Remote Control, 2004, 65 : 741 - 754
[4] Analysis and estimation of the states of special jump Markov processes. II. Optimal filtration in Wiener noise
Borisov, AV
[J]. AUTOMATION AND REMOTE CONTROL, 2004, 65 (05) : 741 - 754
[5] Controllable Markov Jump Processes. II. Monitoring and Optimization of TCP Connections
Borisov, A. V.
Miller, G. B.
Stefanovich, A. I.
[J]. JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL, 2019, 58 (01) : 12 - 28
[6] Controllable Markov Jump Processes. II. Monitoring and Optimization of TCP Connections
A. V. Borisov
G. B. Miller
A. I. Stefanovich
[J]. Journal of Computer and Systems Sciences International, 2019, 58 : 12 - 28
[7] Analysis and filtration of special discrete-time Markov processes. II. Optimal filtration
Borisov, AV
Miller, GB
[J]. AUTOMATION AND REMOTE CONTROL, 2005, 66 (07) : 1125 - 1136
[8] Analysis and Filtration of Special Discrete-Time Markov Processes. II. Optimal Filtration
A. V. Borisov
G. B. Miller
[J]. Automation and Remote Control, 2005, 66 : 1125 - 1136
[9] Optimal Filtering of Markov Jump Processes Given Observations with State-Dependent Noises: Exact Solution and Stable Numerical Schemes
Borisov, Andrey
Sokolov, Igor
[J]. MATHEMATICS, 2020, 8 (04)
[10] Backward representation of Markov jump processes and related problems. II. Optimal nonlinear estimation
A. V. Borisov
[J]. Automation and Remote Control, 2006, 67 : 1466 - 1484

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