Reliable Time Propagation Algorithms for PMF and RBPMF

This paper addresses the reliable time propagation algorithms for Point Mass Filter (PMF) and Rao–Blackwellized PMF (RBPMF) for the nonlinear estimaton problem. The conventional PMF and RBPMF process the probability diffusion for the time propagation with the direct sampled-values of the process noise. However, if the grid interval is not dense enough, it fails to represent the statistical characteristics of the noise accurately so the performance might deteriorate. To overcome that problem, we propose time propagation convolution algorithms adopting Moment Matched Gaussian Kernel (MMGK) on regular grids through mass linear interpolation. To extend the dimension of the MMGK that can accurately describe the noise moments up to the kernel length, we propose the extended MMGK based on the outer tensor product. The proposed time propagation algorithms using one common kernel through the mass linear interpolation not only improve the performance of the filter but also significantly reduce the computational load. The performance improvement and the computational load reduction of the proposed algorithms are verified through numerical simulations for various nonlinear models.