Four State Filter with Position Measurements and also with Position and Doppler Measurements

Abstract

A one-dimensional, four state Kalman tracking filter is described for two cases: In case 1, the filter is described for position measurements only and in case 2, the filter is described for both position and Doppler measurements. The filter estimates the range, the range-rate, the rangeacceleration and the range-jerk of a moving target such as an aircraft moving with constant jerk perturbed by a plant noise of zero mean and constant variance which accounts for maneuvers and/or other random factors. In case 1, the range coordinate of the vehicle is assumed to be measured by a track-while-scan radar sensor and incase 2, the rangerate (Doppler) measurements are obtained by a trackwhile-scan radar sensor which employs pulsed Doppler processing such as a moving target detector providing unambiguous Doppler data [1,2]. The measurements are obtained at uniform sampling intervals of time T seconds and all measurements are noisy. The filter structures have been defined and the steady state results are given for both cases.