Refined Nonlinear Gaussian Quadrature Filter
Bin Jia, Ming Xin · 2019
Gaussian filters have been widely used in various applications due to their simplicity and effectiveness. For nonlinear estimation problems, Gaussian filters are usually developed from numerical quadrature rules to approximate the Gaussian weighted integrals in nonlinear filtering algorithms. However, the Gaussian assumption may not be viable after propagation of quadrature through nonlinear dynamics, which leads to degraded quadrature and inaccurate update of mean and covariance. In this paper, we propose a new refined nonlinear Gaussian quadrature filter in which the predicted probability density function (PDF) is not assumed Gaussian. A set of Monte Carlo samples are first propagated through nonlinear dynamics. The statistic moments can be directly obtained from the propagated Monte Carlo samples. The refined quadrature points and weights are generated from the moments' information using the arbitrary polynomial chaos method. Since the refined quadrature points contain higher order statistic information of the propagated PDF, they have the potential to better represent the uncertainty and provide a more accurate estimate. Numerical examples show the effectiveness of the proposed filter.