MLE in presence of equality and inequality nonlinear constraints for the ballistic target problem

This paper focuses on the estimation of the impact point of a ballistic target by means of a batch processing approach which can be applied more specifically when the number of radar measurements is poor. In particular, the maximum likelihood (ML) estimator is proposed for the estimation of the ballistic target trajectory approximated to a pure parabolic curve; also the Cramer-Rao lower bound (CRLB), which gives the minimum theoretically achievable variance of the estimate, is calculated. The estimator accuracy is improved by the application of equality and inequality constraints on the trajectory characteristics such as maximum range, maximum height and trajectory plane. In the case of application of equality constraints also the CRLB can be computed and the constrained estimator improves strongly its accuracy. In real operational scenarios, a smoothed information can be expressed by means of inequality constraints. The performance of the corresponding estimator has been analyzed by means of Monte Carlo simulation, because of the unavailability of computation of the CRLB for this case.