On the periodogram estimator of period from sparse, noisy timing data

The problem discussed is that of estimating the period of a sequence of periodic events when the occurrence time measurements are noisy and sparse. The problem arises in signal processing applications such as baud estimation from zero-crossings in telecommunications and in pulse repetition interval estimation in electronic support measures. Estimation techniques have been based on periodogram maximisation [1][2], Euclidean algorithms [3][4][5], least squares line search [6], lattice line search [7], Gaussian maximum likelihood [8] and least squares [9]. Aside from [9], there has been no rigorous statistical analysis. In this paper, we show that the periodogram maximiser has excellent (theoretical) asymptotic statistical properties, illustrating them via simulation.