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 to do linearization 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, as pointed out in Part III of a recent survey conducted by the authors. 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 for measurements in the spherical coordinates are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.