Approximate maximum-likelihood period estimation from sparse, noisy timing data

The problem of estimating the period of a series of periodic events is considered under the condition where the measurements of the times of occurrence are noisy and sparse. The problem is common to bit synchronisation in telecommunications and pulse-train parameter estimation in electronic support, among other applications. Two new algorithms are presented which represent different compromises between computational and statistical efficiency. The first extends the separable least squares line search (SLS2) algorithms of Sidiropoulos et al., having very low computational complexity while attaining good statistical accuracy. The second is an approximate maximum-likelihood algorithm, based on a low complexity lattice search, and is found to achieve excellent accuracy.