Nonlinear regression Huber-based divided difference filtering

This article derives a nonlinear regression Huber-based divided difference filtering algorithm using a nonlinear regression approach for dynamic state estimation problems with non-Gaussian noises and outliers. In this approach, the nonlinear measurement model is directly used without linear or statistically linear approximation and the Huber-based divided difference filtering problem is solved using a Gauss-Newton approach. This new proposed filter method is then applied to a benchmark problem of estimating the trajectory of an entry body from discrete-time range data measured by a radar tracking station. Simulation results demonstrate the superior performance of the proposed filter as compared to the previous filter algorithms in the presence of non-Gaussian uncertainties.