Abstract:

The Gaussian sum recursive algorithms for nonlinear non-Gaussian state space models, on the assumption that the process and measurement noises are denoted by Gaussian-sums, is firstly deduced. And then the corresponding extended Kalman sum filter (EKSF) and the Gauss-Hermite sum filter (GHSF) are proposed, which use the extended Kalman filter (EKF) and Gauss-Hermite filter (GHF) as the Gaussian sub-filter respectively. The analysis shows that the existing Gaussian sum filtering algorithms are nothing but special casesof the deduced algorithm. The simulation results show that the proposed EKSF and GHSF can deal with the state estimation of the nonlinear non-Gaussian models effectively, and only consume about 5% and 6% of the computing time required by the Gaussian sum particle filter (GSPF), while the consistent filtering performance is kept.