Parameter estimation for periodic discrete event processes

Methods for estimating the pulse repetition interval and the pulse time-of-arrival jitter variance of a periodic pulse train (PT) are given. The estimators operate on data comprising a set of pulse time-of-arrival measurements which are corrupted by additive noise (timing jitter). Parameter estimators are formulated using two jitter models common to PT applications. The estimators include a closed-form maximum likelihood approach, recursive least squares estimation, and a Kalman filter approach that incorporates both jitter models. Comparison with Cramer-Rao lower bounds shows the estimators to be statistically efficient for a correct choice of jitter model. The estimator performance penalty for using the incorrect jitter model is also presented. Finally, the utility of the estimators is demonstrated using PT measurements from an operational radar