Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime

Masahiro Kurisaki

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arXiv · 2509.23920

Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime

Masahiro Kurisaki

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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.

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Masahiro Kurisaki. 2025-09-28. Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime. https://arxiv.org/abs/2509.23920

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