Best Linear Unbiased Filtering for Target Tracking with Spherical Measurements

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 can be applied in the Cartesian coordinates. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation. In this paper, we present explicitly the best linear unbiased filter for nonlinear measurement, which is optimal in the sense of minimizing the mean-square error among all linear unbiased filters and is free of the fundamental limitations of the measurementconversion method. Results of an approximate implementation for spherical measurements are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.