Quasi-ML period estimation from incomplete timing data

Given a noisy sequence of (possibly shifted) integer multiples of a certain period, it is often of interest to accurately estimate the period. With known integer regressors, the problem is classical linear regression. In many applications, however, the regressors are unknown integers, and only loose bounds on the period are available. Examples include hop period and timing estimation, wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band; Pulse Repetition Interval (PRI) analysis; and passive rotating-beam radio scanning. We study several pertinent period estimators. Our emphasis is on a Quasi-Maximum Likelihood approach developed herein and an earlier method based on the Fourier Transform of a Dirac delta train representation of the data. Surprisingly, both are capable of attaining the clairvoyant Cramér-Rao Bound at moderate signal-to-noise ratios (SNRs), even for short (e.g., 10) samples. We carefully address parameter identifiability issues and corroborate our findings with extensive simulations.