DBSCAN-based particle Gaussian mixture filters

This study addresses nonlinear and non-Gaussian state estimation problems where the particle filter (PF) exhibits the impoverishment issue. This issue arises from the discretisation of the continuous posterior distribution of the state and the use of importance sampling, where the true distribution of the state is unknown. In this study, we propose density-based spatial clustering of applications with noise (DBSCAN)-based particle Gaussian mixture (PGM) filters: the PGM-DS and PGM-DU filters, where DS indicates the PGM filter with DBSCAN and DU indicates the PGM filter with DBSCAN and the unscented transform (UT). These filters assume the posterior distribution of the state to be a Gaussian mixture model (GMM) and sample particles from this GMM. At every time step, the particles are clustered into multiple Gaussian components using DBSCAN, the components are updated with the Kalman/linear minimum mean squared error (LMMSE) update, and the GMM is reconstructed with the updated means and covariances. The proposed filters are tested in three numerical simulation scenarios and compared with other state-of-the-art nonlinear filters. The results show enhanced performance and robustness across the tested simulation scenarios, with lower computational cost compared to the other filters.