Estimating period from sparse, noisy timing data

The problem discussed in this paper is that of estimating the period of a sequence of periodic events when the measurements of the occurrence times are noisy and sparse. The problem is common to many signal processing applications, such as baud estimation from zero-crossings in telecommunications and in pulse repetition interval estimation in electronic support measures. Previous algorithms have been based on periodogram maximisation [1, 2], Euclidean algorithms [3-5], least-squares line search [6], lattice line search [7] and Gaussian maximum likelihood [8]. Until now, very little has been known about the asymptotic statistical properties of any such algorithm. In this paper, a new algorithm is proposed, based on a modified least-squares approach. Under very general properties, the estimators of the system parameters are shown to have excellent (theoretical) asymptotic statistical properties. These properties are illustrated using a number of simulations.