A Cartesian coordinate conversion algorithm for radar tracking with range rate measurement

Abstract

Using the target location and the target range rate as radar observation data, a tracking filter based on the extended Kalman filter is discussed. For this tracking filter, the Cartesian coordinate will be used, with the north as one axis, the one with the object position vector as one axis, or the one with the target velocity vector as one axis. However, it has not been reported if the computed variables (estimate values of the motion parameters of the object, such as location and velocity, and the error covariance matrix as the evaluation value of the estimation error) in a tracking filter using a specific Cartesian coordinate can be converted to the parameters in the tracking filter using another Cartesian coordinate. Because it remains to discover whether conversion is possible, research still continues to find a Cartesian coordinate that has good tracking performance. It is proven here, using a mathematical induction method in regard to the sampling time, that no matter which Cartesian coordinate is used in the forementioned tracking filter, its computational parameters can be converted to those of the tracking filter using an arbitrary Cartesian coordinate. As a result, comparison and evaluation of the tracking filter performance are unnecessary when different Cartesian coordinates are used. In addition, the equations are derived for conversion of the target motion parameters, covariance matrix, and gain matrix between these tracking filters. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80 (4): 51–61, 1996