Gaussian particle filtering

Sequential Bayesian estimation for dynamic state space models involves recursive estimation of hidden states based on noisy observations. The update of filtering and predictive densities for nonlinear models with non-Gaussian noise using Monte Carlo particle filtering methods is considered. The Gaussian particle filter (GPF) is introduced, where densities are approximated as a single Gaussian, an assumption which is also made in the extended Kalman filter (EKF). It is analytically shown that, if the Gaussian approximations hold true, the GPF minimizes the mean square error of the estimates asymptotically. The simulations results indicate that the filter has improved performance compared to the EKF, especially for highly nonlinear models where the EKF can diverge.