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Variance Decay Property for Filter Stability
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DOI：10.1109/TAC.2024.3413573.png)
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Abstract
En 中文
This article is concerned with the problem of nonlinear (stochastic) filter stability for 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 & eacute; inequality (PI) is introduced for the nonlinear filter. PI is related to both the ergodicity of the Markov process and 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.
Keywords:
Hidden Markov models
Asymptotic stability
Nonlinear filters
Filtering theory
Stability criteria
Mathematical models
Optimal control
Nonlinear filtering
optimal control
stochastic systems
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
