Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918149988810752 |
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| author | Kurisaki, Masahiro |
| author_facet | Kurisaki, Masahiro |
| contents | We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a system of ordinary differential equations. This approach mitigates the trade-off between computational efficiency and accuracy inherent in existing methods such as Gaussian approximations and particle filters. Moreover, by incorporating an Edgeworth-type expansion, our method captures complex features of the conditional distribution, such as multimodality, with significantly lower computational cost than conventional filtering algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime Kurisaki, Masahiro Signal Processing Probability Methodology Machine Learning We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a system of ordinary differential equations. This approach mitigates the trade-off between computational efficiency and accuracy inherent in existing methods such as Gaussian approximations and particle filters. Moreover, by incorporating an Edgeworth-type expansion, our method captures complex features of the conditional distribution, such as multimodality, with significantly lower computational cost than conventional filtering algorithms. |
| title | Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime |
| topic | Signal Processing Probability Methodology Machine Learning |
| url | https://arxiv.org/abs/2509.23920 |