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

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 accuracy. The MATLAB code of the ePMF is released with this paper.