Backward Map for Filter Stability Analysis
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909341260447744 |
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| author | Kim, Jin Won Joshi, Anant A. Mehta, Prashant G. |
| author_facet | Kim, Jin Won Joshi, Anant A. Mehta, Prashant G. |
| contents | In this paper, a backward map is introduced for the purposes of analysis of the nonlinear (stochastic) filter stability. The backward map is important because the filter-stability in the sense of $\chisq$-divergence follows from showing a certain variance decay property for the backward map. To show this property requires additional assumptions on the model properties of 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backward Map for Filter Stability Analysis Kim, Jin Won Joshi, Anant A. Mehta, Prashant G. Probability Optimization and Control In this paper, a backward map is introduced for the purposes of analysis of the nonlinear (stochastic) filter stability. The backward map is important because the filter-stability in the sense of $\chisq$-divergence follows from showing a certain variance decay property for the backward map. To show this property requires additional assumptions on the model properties of 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. |
| title | Backward Map for Filter Stability Analysis |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2405.01127 |