Nonlinear estimation techniques for impact point prediction of ballistic targets

Abstract

This paper considers three nonlinear estimation algorithms for impact point prediction (IPP) of ballistic targets. The paper assumes measurements are available from a 3D surveillance radar or phased array radar over some portion of the ballistic trajectory. The ballistic target (BT) is tracked using an extended Kalman filter (EKF), an unscented Kalman filter (UKF), and a particle filter (PF). With the track estimate as an initial condition, the equations of motion for the BT are integrated to obtain a prediction of the impact point. This paper compares the performance of the EKF, UKF, and a particular choice of PF for impact point prediction. The traditional Extended Kalman Filter equations are based on a first-order Taylor series approximation of the nonlinear transformations (expanded about the latest state estimate). Both the Unscented Kalman Filter and the Particle Filter allow nonlinear systems to be modeled without prior linearizion. The primary focus of the analysis presented in this paper is comparing the performance and accuracy of the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the chosen Particle Filter implementation for impact point prediction. The three filtering techniques are compared to the theoretical Cramer-Rao lower bounds (CRLB) of estimation error.