Conjugate continuous-discrete projection filter via sparse-Grid quadrature
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.
Cite
@article{arxiv.2504.17324,
title = {Conjugate continuous-discrete projection filter via sparse-Grid quadrature},
author = {Muhammad F. Emzir and Zaid A. Sawlan and Sami El Ferik},
journal= {arXiv preprint arXiv:2504.17324},
year = {2026}
}