Filter design based on multiple model estimation

We show that famous filtering algorithms such as Gaussian sum filter (GSF) and particle filter (PF) are derived from the multiple model estimation (MME). Based on the MME, we propose a new filter called particle Gaussian sum filter (PGSF) to overcome the problems of GSF and PF. To realize the algorithm of PGSF, we also show that ensemble Kalman filter (EnKF) asymptotically approaches Gaussian filter (GF) when using sufficiently large ensemble number. The PGSF employing the EnKF achieves higher estimation accuracy than that using the extended Kalman filter (EKF), while the latter approach is much faster in terms of processing time. We compare the proposed filter with several existing filters and demonstrate its effectiveness through a numerical simulation.