Comparison of RNLS, EKF and SDDRE Filters of Nonlinear Dynamic System

Abstract

This work focuses on filters for nonlinear dynamic systems with nonlinear measurements. The Recursive Nonlinear Least Square Error (RNLS) filter has been recently derived for the state estimation of nonlinear dynamic systems. The RNLS is optimal under the LMSE criterion. Performances of RNLS, EKF and SDDRE-based filters are compared on a common basis. The Pareto formalism is used as a tool for such comparison on a common basis. The comparison is performed for a $6^{\mathrm {t}\mathrm {h}}$ order nonlinear system. This system models a tracking target that performs a coordinated turn/barrel-roll maneuver with unknown turning rate, measured by radar in polar coordinates. It is demonstrated by simulations that the RNLS filter is the optimal filter with respect to the quadratic criterion it is designed for. This places the RNLS filter as a vital candidate estimator of nonlinear systems.