Standard and Gaussian Particle Filters for Nonlinear System with Missing Measurements

In this paper, we propose three particle filters which are standard particle filter and two Gaussian particle filters for nonlinear system with missing measurements. For standard particle filter, we derive an explicit expression for the importance weights when the possible occurrence of measurement loss is taken into account. Based on this importance weights, a modified standard particle filtering algorithm with missing measurements is proposed. To improve sampling efficiency, we also propose two Gaussian particle filters for nonlinear system with missing measurements. For Gaussian particle filter, we derive the formulas for the importance density function when take the missing measurements into account. To fulfill the numerical computation of these formulas, we give two approximated methods based on local linearization and unscented transform. Based on these two approximated methods, the two Gaussian particle filtering algorithms with missing measurements are proposed. The effectiveness of the proposed methods are illustrated through a nonlinear simulation example.