Gaussian sum filter for state estimation of Markov jump nonlinear system

This paper proposes the Gaussian sum filtering (GSF) framework for the state estimation of Markov jump nonlinear systems (MJNLSs). Through presenting the Gaussian sum approximations about the model-conditioned state posterior probability density function (PDF) and the model-conditioned measurement posterior predictive PDF, a general GSF framework in the minimum mean square error (MMSE) sense is derived. The Minor Gaussian-set design is utilized to merge the Gaussian components at the beginning, which can effectively limit the computational requirements. Simulation results demonstrate that the proposed method performs almost as well as the interacting multiple model particle filter (IMM-PF) but with much lower computational cost.