On periodic pulse interval analysis with outliers and missing observations

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, although it is not maximum likelihood, is used as initialization in a three-step algorithm that achieves the Cramer-Rao bound (CRB) for moderate noise levels, as shown by comparing Monte Carlo results with the CRBs. This approach solves linear regression problems with missing observations and outliers. Comparisons with a periodogram approach based on a point process model are shown. An extension using multiple independent data records is also developed that overcomes high levels of contamination