Particle filter with multimode sampling strategy

●We deduce the standard particle filter in a new perspective.●Multimode sampling strategy for particle filter is proposed.●Adaptively sampling from hybrid importance density function is realized.●Importance density function based on updated system equation is proposed.●The new filter is more flexible to accommodate the changing system characteristics.

Particle filters provide a general numerical tool to deal with the nonlinear/non-Gaussian filtering problems. However, it is still a challenging problem to design a good proposal distribution to generate high-quality particles. In this paper, we present the concept of hybrid proposal distribution (HPD) defined by the weighted sum of multiple basic proposal distributions (BPDs), transform the adaptive particle filtering into the online weight optimization, and, as a result, propose the framework of particle filter with multimode sampling strategy. Compared with traditional sampling strategies, multimode sampling strategy is more flexible to accommodate the time-varying system characteristics. To demonstrate the efficiency of the proposed framework, a particle filter with HPD consisting of two BPDs is designed, where one BPD is the transition density and the other, first proposed in this paper, is defined by an updated system equation. The numerical simulation with two examples shows that the proposed filter outperforms the extended Kalman filter, the unscented Kalman filter, the standard particle filter and the unscented Kalman particle filter.