Stochastic filtering with moment representation

2023/03/24 by Zhao, Zheng, Sarmavuori, Juha · 1 citation
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR)

paper · doi:10.48550/arxiv.2303.13895

Abstract

Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the filtering distributions by their moments. The key enablement is a quadrature method that uses orthonormal polynomials spanned by the moments. We prove that this moment-based filter is asymptotically exact in the order of moments, and show that the filter is also computationally efficient and is in line with the state of the art.

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• Diffusion differentiable resampling

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