A Projection Filter Algorithm for Stochastic Systems with Correlated Noise and State-Dependent Measurement Covariance

The solution of the optimal filtering problem for nonlinear stochastic systems can be efficiently approximated by using a projection filter. A recent work by Emzir et al. [1] proposed a novel framework that employs automatic differentiation to implement the projection filter for exponential family manifolds. This approach can effectively overcome the curse of dimensionality in the optimal filtering problem by exploiting the sparse-grid scheme. In this paper, we extend this framework to a class of stochastic differential equations where both state and measurement noises are correlated and the measurement processes have state-dependent covariances. We derive the projection filter equation for this class of systems on exponential family manifolds and present a numerical example to demonstrate its performance in solving a challenging nonlinear filtering problem.