Statically Fused Smooth Variable Structure Filter for Robust Tracking with Doppler Radar

Abstract

The smooth variable structure filter (SVSF) provides robust state estimation in case of model uncertainty but requires a linear measurement model and a full-rank measurement matrix. Doppler radar reports target position and range rate in the polar or spherical coordinates without the tangential velocity, leading to a nonlinear and underdetermined measurement model, which does not satisfy the requirements of the standard SVSF. In this paper, we propose a robust nonlinear estimator, named as the statically fused smooth variable structure filter (SFSVSF), for robust target state estimation with Doppler radar. First, the converted position measurement (CPM) is calculated in Cartesian coordinates and a converted Doppler measurement (CDM) is constructed from the product of the range and range rate measurements. Accordingly, the nonlinear Doppler radar measurement model is decomposed into a Cartesian-measurement model and a pseudo-measurement model. Both are linear time-invariant and underdetermined, and can be handled by the generalized SVSF. Thus, two generalized SVSFs, referred to as the CPM-SVSF and the CDM-SVSF, are implemented based on these two sub-models for robust estimations of the Cartesian state and the pseudo state, respectively. The Cartesian-state estimation and the pseudo-state estimation are statically fused by an approximate linear minimum mean square error (LMMSE) estimator for the final estimation of target state. Simulation results show the effectiveness of the SFSVSF algorithm in nonlinear estimation and the advantage in robustness over the EKF in case of target motion uncertainty.