Stochasic Properties of a Tracking Filter with Pseudo-Measurements in Line-of-Sight coordinate System

This paper presents a tracking filter using pseudo-measurements in an estimated line-of-sight Cartesian coordinate system(ELCCS) whose x-axis is on the line-of-sight to an estimated target position. A target dynamics model and a measurement equation in the ELCCS are derived first and then a tracking filter in the ELCCS named moving coordinate tracking filter(MCIF) is proposed. It is shown that this MCTF is equivalent to a Kalman filter in the inertial Cartesian coordinate system which is widely used in the target tracking system. By approximating the MCTF for a pseudo-measurement noise and an error covariance matrix in the ELCCS, decoupling of three axes can be achieved. In this case, named decoupled moving coordinate tracking filter(DMCTF), computation time can be drastically reduced by utilizing its parallel structure. Finally, the stochastic properties of the MCTF and DMCTF are presented. Especially, a sufficient condition of nondestabilizing deviation for the DMCTF is proposed. The performance of the MCTF and DMCTF are compared with a conventional Kalman tracking filter.