Backward Map for Filter Stability Analysis

Jin Won Kim, Anant A. Joshi, Prashant G. Mehta

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A backward map is introduced for the purposes of analysis of nonlinear (stochastic) filter stability. The backward map is important because filter-stability, in the sense of χ2 divergence, follows from a certain variance decay property associated with the backward map. To show this property requires additional assumptions on the hidden Markov model (HMM). The analysis in this paper is based on introducing a Poincaré Inequality (PI) for HMMs with white noise observations. In finite state-space settings, PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. It is shown that the Poincaré constant is positive if and only if the HMM is detectable.

Original languageEnglish (US)
Title of host publication2024 IEEE 63rd Conference on Decision and Control, CDC 2024
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4070-4077
Number of pages8
ISBN (Electronic)9798350316339
DOIs
StatePublished - 2024
Event63rd IEEE Conference on Decision and Control, CDC 2024 - Milan, Italy
Duration: Dec 16 2024Dec 19 2024

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference63rd IEEE Conference on Decision and Control, CDC 2024
Country/TerritoryItaly
CityMilan
Period12/16/2412/19/24

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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