Point-mass Filter with Functional Decomposition of Transient Density and Two-level Convolution

Abstract

The paper deals with Bayesian state estimation using the point-mass filter with a particular focus on the prediction step involving the convolution of two grids of points. To reduce the computational costs of the step, a functional decomposition-based convolution was proposed by Tichavský et al. (2022), which approximates the transient probability density function over an approximation region. This paper addresses the problem of having spacious grids of points due to state uncertainty while the approximation region is kept small to preserve low computational complexity. A two-level convolution is proposed based on splitting the grids into subgrids and processing the convolution in the upper level for the subgrids and in the lower level for their points. An example demonstrates the proposed technique efficiency.