Optimal linear unbiased filtering with polar measurements for target tracking

In tracking applications, target dynamics is usually modeled in the Cartesian coordinates, while target measurements are directly available in the original sensor coordinates. Measurement conversion is widely used such that the Kalman filter in the Cartesian coordinates can be applied. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation, as pointed out in Li and Jilkov (2001) of a recent survey. This paper proposes a recursive filter that is theoretically optimal in the sense of minimizing the mean-square error among all linear unbiased filters in the Cartesian coordinates. The proposed filter is free of the fundamental limitations of the measurement-conversion approach. Results of an approximate implementation are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.