Conditional Density Driven Grid Design in Point-Mass Filter

Abstract

The paper is devoted to the state estimation of nonlinear stochastic dynamic systems. The stress is laid on a grid-based numerical solution to the Bayesian recursive relations using the point-mass filter (PMF). In the paper, a novel conditional density driven grid (CDDG) design is proposed. The CDDG design takes advantage of non-equidistant grid points by combination of two grids; dense and sparse. The dense grid is designed to cover the state space region, where the significant mass of one or both conditional (i.e., predictive and filtering) densities is anticipated. The sparse grid covers the support of the conditional distribution tails only. As a consequence, the CDDG design improves the point-mass approximation of the conditional densities and offers better estimation performance compared to the standard equidistant grid with the same number of points and, thus, with the same computational complexity. Performance of the CDDG-based PMF is illustrated in a terrain-aided navigation scenario.