Modified gain pseudo-measurement filter for doppler radar target tracking

Abstract

This paper proposes bias-compensated pseudo-measurement filter incorporating range rate measurements in the line-of-sight Cartesian coordinate system. Radar target tracking is a nonlinear estimation problem with linear target dynamics and nonlinear measurements. Nonlinear filters such as extended Kalman filter and unscented Kalman filter are generally used. However, extended Kalman filter has limitation on the bias generated from explicit linearization and unscented Kalman filter demands large computation. The application of pseudo-linearized measurement with linear Kalman filter is suggested to resolve these issues. The pseudo-measurement filter in form of linear Kalman filter has advantages on a bias alleviation and a computation load. However, a measurement dependent Kalman gain of pseudo-measurement filter yields significant bias on an estimation. The modified gain that de-correlates Kalman gain and residual is proposed to reduce a bias. Since recent flight radar can measures range rate using Doppler effects, the conventional pseudo-measurement model in the line-of-sight Cartesian coordinates is extended to include range rate measurements. The bias of the pseudo-measurement noise is compensated and the proposed pseudo-measurement model is validated through a consistency test. The proposed model keeps its consistency up to a long range under large angular measurement noise. Then, the modification of measurement dependent Kalman gain alleviates bias of conventional pseudo-measurement filter. The theoretical analogy of modified gain approaches proposed in earlier studies is explained. The bias characteristics and asymptotic stability are also discussed. Finally, the numerical results show that the proposed de-biased pseudo-measurement filter is quite effective in processing range rate measurements.