On Periodic Pulse Interval Analysis with Outliers and Missing Observations

Abstract

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.