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arXiv · 2504.17324

Conjugate continuous-discrete projection filter via sparse-Grid quadrature

Muhammad F. Emzir·Zaid A. Sawlan·Sami El Ferik
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Abstract

In this article, we study the continuous-discrete projection filter for exponential-family manifolds with conjugate likelihoods. We first derive the local projection error of the prediction step of the continuous-discrete projection filter. We then derive the exact Bayesian update algorithm for a class of discrete measurement processes with additive Gaussian noise. To control the stiffness of the natural parameters' ordinary differential equations, we introduce a regularization method via projection to the Fisher information metric's eigenspace. Lastly, we apply the proposed method to approximate the filtering density of a modified Van der Pol oscillator problem and a coupled stochastic FitzHugh--Nagumo system. The proposed projection filter shows superior performance compared to several state-of-the-art parametric continuous-discrete filtering methods.

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Muhammad F. Emzir, Zaid A. Sawlan, Sami El Ferik. 2025-04-24. Conjugate continuous-discrete projection filter via sparse-Grid quadrature. https://arxiv.org/abs/2504.17324

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