Best linear unbiased estimation algorithm with Doppler measurements in spherical coordinates

In an active radar-tracking system, the target-motion model is usually modeled in the Cartesian coordinates, while the radar measurement usually is obtained in polar/spherical coordinates. Therefore the target-tracking problem in the Cartesian coordinates becomes a nonlinear state estimation problem. A number of measurement-conversion techniques, which are based on position measurements, are widely used such that the Kalman filter can be used in the Cartesian coordinates. However, they have fundamental limitations to result in filtering performance degradation. In fact, in addition to position measurements, the Doppler measurement or range rate, containing information of target velocity, has the potential capability to improve the tracking performance. A filter is proposed that can use converted Doppler measurements (i.e. the product of the range measurements and Doppler measurements) in the Cartesian coordinates. The novel filter is theoretically optimal in the rule of the best linear unbiased estimation among all linear unbiased filters in the Cartesian coordinates, and is free of the fundamental limitations of the measurement-conversion approach. Based on simulation experiments, an approximate, recursive implementation of the novel filter is compared with those obtained by four state-of-the-art conversion techniques recently. Simulation results demonstrate the effectiveness of the proposed filter.