Tracking with state dependent measurement errors

Abstract

Radar trackers give fairly large angle errors. A technique, known as Doppler beam sharpening (DBS), can be used to reduce the angle measurement errors. This analyses the Doppler returns across a stationary target to improve the accuracy. The degree of improvement depends on the angle between the tracker velocity and the line of sight to the target-the larger the angle the greater the improvement. In the system of interest, the accuracy can also be improved by increasing the stare time. This allows us to fix the ground error (not the angular error) and alter the update period. The use of DBS generates a conflict between the needs of the estimator and the needs of the guidance, which is attempting to intercept the target. This paper reports on the filtering and guidance aspects of the problem. These have been investigated using a three dimensional model with a stationary target. The tracker receives measurements of the range, range rate and azimuth and elevation angles to the target. The interval between measurements is time varying, with angle measurement errors which depend on the range to the target. The author developed a Cartesian extended Kalman filter which takes in to account the state dependence of the measurement errors, and their nonlinear nature. A simulation is used to compare the effectiveness of this filter when used with different control laws. Proportional navigation is shown to be an inappropriate law in this case, as it attempts to drive the sightline rate to zero. Alternative laws are shown to give better results. (3 pages)