@inproceedings{73f60264bf684d58b4bd1e9b1108dcbe,
title = "Backward Map for Filter Stability Analysis",
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 Poincar{\'e} 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 Poincar{\'e} constant is positive if and only if the HMM is detectable.",
author = "Kim, {Jin Won} and Joshi, {Anant A.} and Mehta, {Prashant G.}",
note = "This work is supported in part by the AFOSR award FA9550-23- 1-0060, the NSF award 2336137 (Joshi, Mehta) and the DFG grant 318763901/SFB1294 (Kim).; 63rd IEEE Conference on Decision and Control, CDC 2024 ; Conference date: 16-12-2024 Through 19-12-2024",
year = "2024",
doi = "10.1109/CDC56724.2024.10886772",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4070--4077",
booktitle = "2024 IEEE 63rd Conference on Decision and Control, CDC 2024",
address = "United States",
}