Gauss-Hermite particle filter

A new particle filter based on sequential importance sampling (SIS) is proposed for the on-line estimation problem of non-Gauss nonlinear systems. In the new algorithm, a bank of Gauss-Hermite filter (GHF) is used for generating the importance density function. The density function integrates the new observations into system state transition density, so it can match the state posteriori density well. As a result, while the likelihood function is situated on the tail of state transition density or observation model has higher precise, the theoretical analysis and experimental results show that the new particle filter outperforms obviously the standard particle filter and the other filters such as the extended Kalman filter (EKF), the GHF.