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Variance Decay Property for Filter Stability

Authors :
Kim, Jin Won
Mehta, Prashant G.
Source :
IEEE Transactions on Automatic Control, 2024
Publication Year :
2023

Abstract

This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance decay property which is used to conclude filter stability. For this purpose, a new notion of the Poincar\'e inequality (PI) is introduced for the nonlinear filter. PI is related to both the ergodicity of the Markov process as well as the observability of the HMM. The proofs are based upon a recently discovered minimum variance duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE).<br />Comment: 16 pages

Details

Database :
arXiv
Journal :
IEEE Transactions on Automatic Control, 2024
Publication Type :
Report
Accession number :
edsarx.2305.12850
Document Type :
Working Paper
Full Text :
https://doi.org/10.1109/TAC.2024.3413573