Fixed-point iteration Gaussian sum filtering estimator with unknown time-varying non-Gaussian measurement noise

This paper addresses the state estimation problem in the presence of unknown time-varying non-Gaussian measurement noise (NGMN) modeled by Gaussian mixture distribution(GMD). Recently, the variational Bayesian (VB)-based estimators have been successfully used in the state estimation problem in the presence of unknown measurement noise. However, we reveal that when the state-space model is non-Gaussian, exploiting the traditional VB method, the joint posterior probability density function of the state and parameters of non-Gaussian measurement noise has no analytical result. To fill this gap, a fixed-point iteration Gaussian sum filtering (FPI-GSF) estimator is proposed to jointly estimate the state and the unknown time-varying NGMN online. The proposed estimator utilizes a fixed-point iteration scheme to iteratively calculate the state posterior distribution through the GSF and noise parameters posterior distribution via the VB method, thus it avoids calculating the joint posterior distribution. Simulation results demonstrate the effectiveness of the proposed estimator.