Gaussian Mixture-Based Point Mass Filtering
Felipe Giraldo-Grueso, Andrey A. Popov, Renato Zanetti · 2024
The accuracy of the point mass filter (PMF) relies on the precise placement of grid points. Since the approximated probability distributions are evaluated only at these points, suboptimal choices in grid placement can result in an inaccurate representation of the posterior distribution. This work addresses this issue by representing the propagated grid points as a Gaussian mixture, enabling a Gaussian sum filter (GSF) update before grid construction. The use of the GSF update enhances the accuracy of the mean and covariance estimates, from which a new grid can be constructed. This approach leads to improved grid placement and reduces the number of points required to achieve satisfactory results. A comparative analysis is conducted between this new approach, the traditional PMF, and a PMF variant that uses an unscented Kalman filter update before grid construction. Using a simple bivariate example, the new variant is shown to approximate the posterior distribution better than the other filters. Furthermore, the new approach is evaluated in two sequential filtering problems: the first involves the Ikeda map, and the second focuses on terrain-relative navigation for Martian exploration. The results show a more accurate, and more consistent filter compared to the other two PMF variants considered.