Conjugate continuous-discrete projection filter via sparse-grid quadrature

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.