GENERALIZED GAUSSIAN CUBATURE FOR NONLINEAR FILTERING

A novel method for nonlinear filtering based on a generalized Gaussian cubature approach is shown. Specifically, a new point-based nonlinear filter is developed which is not based on one-dimensional quadrature rules, but rather uses multi-dimensional cubature rules for Gaussian distributions. The new generalized Gaussian cubature filter is not in general limited to odd-order degrees of accuracy, and provides a wider range of order of accuracy. The method requires the solution of a set of nonlinear equations for finding optimal cubature points, but these equations are only required to be solved once for each state dimensional and order of accuracy. This rule is also extended to anisotropic cases where the order of accuracy is not isotropic in dimension. This method allows for tuning of the cubature rules to develop problem-specific rules that are optimal for the given problem. The generalized Gaussian cubature filter is applied to benchmark problems in astrodynamics, and it is compared against existing nonlinear filtering methods.