Sadler, Brian M.Casey, Stephen D.Analysis of periodic pulse trains based on time of arrival is considered, with perhaps very many missing observations and contaminated data. A period estimator is developed based on a modified Euclidean algorithm. This algorithm is a computationally simple, robust method for estimating the greatest common divisor of a noisy contaminated data set. The resulting estimate, while not maximum likelihood, is used as initialization in a three-step algorithm that achieves the Cramer-Rao bound for moderate noise levels, as shown by comparing Monte Carlo results with the Cramer-Rao bounds. An extension using multiple independent data records is also developed that overcomes high levels of contamination.en-USdigital communicationsestimationfilteringrobust information processingsignal processingparameter estimation of pulse trainsnumber theoryharmonic analysisIntelligent Control SystemsTechnical Report