Parameter estimation for censored exponential random variables

Estimating the parameter of a Swerling target's radar cross section (RCS) is of interest as it may provide a discriminating feature to aid measurement-to-track association in multi-target tracking problems. Proper estimation of this statistic requires the appropriate characterization of the probability distribution function of the target's signal to noise ratio (SNR) and, in particular, compensating for censoring due to detection thresholding and saturation. In this paper, the maximum likelihood estimator for the upper and lower censored pdf of an exponential random variable is derived, and a method for solving the resulting equation is given. Two computationally simpler approximations are also proposed, and the performance of the standard exponential estimator is compared to the derived estimator and approximations.