A Robust Nonlinear Filter for Doppler Radar Target Tracking

Abstract

The smooth variable structure filter (SVSF) offers robust state estimation in the presence 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 tangential velocity, leading to a nonlinear and underdetermined measurement model in Cartesian coordinates and thus precluding the use of the standard SVSF. In this paper, a novel robust estimator, referred to as the sequential smooth variable structure filter (SSVSF), is proposed for Doppler radar target tracking. The Doppler radar measurement vector is partitioned into two parts, i.e., the position (containing range, azimuth, and elevation) and the range rate, and is used for a two-stage sequential processor. In the first stage, the target position measurement is transformed into Cartesian coordinates via the unbiased converted measurement (UCM) strategy, so that a generalized SVSF is implemented for robust target state estimation with a linear measurement model. In the second stage, a pseudo measurement is constructed from the product of range and range rate, and accordingly, an approximate linear minimum mean square error (LMMSE) estimator is developed to update the first-stage estimation. Simulation results validate the effectiveness of the proposed algorithm in Doppler radar tracking, and superior robustness to the conventional nonlinear Bayesian filter in the case of target motion uncertainty.