Likelihood function modeling of particle filter in presence of non-stationary non-gaussian measurement noise

A generalized likelihood function model of a sampling importance resampling (SIR) particle filter (PF) has been derived for state estimation of a nonlinear system in the presence of non-stationary, non-Gaussian white measurement noise. The measurement noise is modeled by Gaussian mixture probability density function and the noise parameters are estimated by maximizing the log likelihood function of the noise model. This model is then included in the likelihood function of the SIR particle filter (PF) at each time step for online state estimation of the system. The performance of the proposed algorithm has been evaluated by estimating the states of (i) a non-linear system in the presence of non-stationary Rayleigh distributed noise and (ii) a radar tracking system in the presence of glint noise. The simulation results show that the proposed modified SIR PF offers best performance among the considered algorithms for these examples.