Sinusoidal frequency estimation via sparse zero crossings

We consider estimation of the period of a sinusoid in additive Gaussian noi se, based on observations of the zero-crossing (ZC) times, The problem is t reated in a continuous-time framework,It is assumed that the signal-to-nois e ratio is sufficient (approximately greater than or equal to 8 dB) such th at the noise may be approximated as additive in the phase, An exact mean-sq uare error analysis is provided for this approximation, We apply modified E uclidean algorithms (MEAs) and their least-squares refinements in this fram ework, to estimate the period of the sinusoid, with low complexity. Unlike linear regression methods based on phase samples, the proposed approach wor ks with very sparse ZC measurements, and is resistant to outliers. The MEA- based approach is motivated by the fact that, in the noise-free case, the g reatest common divisor (gcd) of a sparse set of the first differences of th e zero crossing times is very highly likely to be the half-period of the si nusoid. The MEA acts to robustly estimate the gcd of the observed noisy dat a. The MEA period estimate may be refined via a least-squares approach, tha t asymptotically achieves the appropriate Cramer-Rao bound. Simulation resu lts illustrate the algorithms with as few as 10 zero-crossing times. The al gorithm behavior is also studied using Bernoulli and random burst models fo r the missing ZC times, and good performance is demonstrated with very spar se observations, Published by Elsevier Science Ltd.