Frequency estimation via sparse zero crossings

We consider estimation of the frequency of a single sinusoid in Gaussian noise at high SNR using zero crossing times with (perhaps very many) missing observations. A period estimator is developed based on a modified Euclidean algorithm (MEA). The MEA is a computationally simple method for estimating the greatest common divisor (GCD) of a noisy contaminated data set. The approach is motivated by the fact that in the noise-free case the GCD of a set of the first differences of the zero crossing times is, with high probability, the half-period of the sinusoid. Simulation results demonstrate period estimation with 75% of the zero crossing times missing, and the data set contaminated with outliers.