Continuous Nonlinear State Prediction by Finite Volume Method on Logically Rectangular Grids

This paper deals with the state estimation of the nonlinear stochastic models with continuous dynamics and discrete measurement. Namely, the numerical solution to the Fokker-Planck equation, representing the estimator time update, is explored. Unlike the classical approaches, which use the finite difference method and operate on a standard rectangular grid, this paper utilizes finite volume method on the logically rectangular grid. In particular, the circular grid is chosen, which better approximates an estimated conditional probability density function support and improves time update accuracy without any impact on the its computational complexity. The benefits of the solution are illustrated in a numerical example. Keywords: State estimation, Bayesian inference, Nonlinear systems.