{"ID":2864361,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23920","arxiv_id":"2509.23920","title":"Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.23920","url_pdf":"https://arxiv.org/pdf/2509.23920v1","authors":"[\"Masahiro Kurisaki\"]","published":"2025-09-28T14:50:45Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"math.PR\",\"stat.ME\",\"stat.ML\"]","methods":"[]","has_code":false}