Design of Efficient Point-Mass Filter with Application in Terrain Aided Navigation

TL;DR

This paper addresses state estimation for linear stochastic dynamics within terrain-aided navigation by introducing an Efficient Point-Mass Filter (ePMF) that unifies continuous and discrete dynamics. The key innovation is transforming the time-update into a convolution, enabling FFT-based and sine-transform-based predictions that dramatically reduce computational complexity to $O(N \log(N))$ while maintaining accuracy. The authors develop grid-movement compensation, non-diagonal noise handling via diffusion-diagonalization, and accommodate time-varying dynamics, demonstrated on TAN scenarios where 2D and 4D models achieve substantial speedups with competitive performance. MATLAB implementations are released to facilitate practical adoption. Overall, the work offers a robust, fast alternative to particle filtering for high-dimensional grid-based state estimation in navigation contexts.

Abstract

This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based point-mass filter (PMF), which is the most computationally demanding part of the PMF algorithm. A novel efficient PMF (ePMF) estimator, unifying continuous and discrete, approaches is proposed, designed, and discussed. By numerical illustrations, it is shown, that the proposed ePMF can lead to a time complexity reduction that exceeds 99.9% without compromising accuracy. The MATLAB code of the ePMF is released with this paper.

Figures (2)

• Figure 1: Computational to physical space re-shaping for 2D space and Gaussian noise
• Figure 2: Scheme of the grid re-design