Filtering of Stochastic Systems

Jan H. van Schuppen

doi:10.1007/978-3-030-66952-2_9

Filtering of Stochastic Systems

Jan H. van Schuppen^*

^*Corresponding author for this work

Mathematical Physics

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific

Abstract

Filter problems are formulated for stochastic systems which are not Gaussian systems. Both the estimation problem, the sequential estimation problem, and the filter problem are treated. A sufficient condition for the existence of a finite-dimensional filter system is formulated. The concept of a family of invariant conditional distributions is defined. It is described how to solve the filter problem by a measure transformation method. Cases treated include the Poisson–Gamma filter and the filter of an output-finite–state-finite stochastic system.

Original language	English
Title of host publication	Control and System Theory of Discrete-Time Stochastic Systems
Editors	J.H. van Schuppen
Publisher	Springer
Chapter	9
Pages	327-373
Number of pages	47
ISBN (Electronic)	078-0-030-66952-9
DOIs	https://doi.org/10.1007/978-3-030-66952-2_9
Publication status	Published - 2021

Publication series

Name	Communications and Control Engineering
ISSN (Print)	0178-5354
ISSN (Electronic)	2197-7119

Keywords

Filter problem
Poisson-Gamma filter

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10.1007/978-3-030-66952-2_9

Cite this

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AB - Filter problems are formulated for stochastic systems which are not Gaussian systems. Both the estimation problem, the sequential estimation problem, and the filter problem are treated. A sufficient condition for the existence of a finite-dimensional filter system is formulated. The concept of a family of invariant conditional distributions is defined. It is described how to solve the filter problem by a measure transformation method. Cases treated include the Poisson–Gamma filter and the filter of an output-finite–state-finite stochastic system.

KW - Filter problem

KW - Poisson-Gamma filter

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Filtering of Stochastic Systems

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