Extension of SGMF using Gaussian sum approximation for nonlinear/non-Gaussian model and its application in multipath estimation

The multipath estimation of global navigation satellite system (GNSS) signal is actually the state estimation of nonlinear/non-Gaussian systems. The extension of sliced Gaussian mixture filter (ESGMF) based on Gaussian sum approximation is proposed for the state estimation of nonlinear/non-Gaussian state space, and the probability density function (PDF) expression of states is derived recursively for a time varying system. Resampling is applied to the prediction PDF to reduce the complexity of Bayesian inference. The simulation result of multipath estimation with ESGMF shows that the ESGMF algorithm performs better in accuracy than the algorithms based on particle filter (PF) and extended Kalman filter (EKF).