The problem of estimating the period of a periodic point process is considered when the observations are sparse and noisy. There is a class of estimators that operate by maximizing an objective function over an interval of possible periods, notably the periodogram estimator of Fogel & Gavish [1] and the line-search algorithms of Sidiropoulos et al. [2] and Clarkson [3]. For numerical calculation, the interval is sampled. However, it is not known how fine the sampling must be in order to ensure statistically accurate results. In this paper, a new estimator is proposed which eliminates the need for sampling. For the proposed statistical model, it calculates a maximumlikelihood estimate. It is shown that the expected arithmetic complexity of the algorithm is O(n 3 log n) where n is the number of observations. Numerical simulations demonstrate the superior statistical performance of the new estimator.

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Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. One approach attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and must be unwrapped before regression can be performed. In this paper we consider an estimator that performs phase unwrapping in a least squares manner. We describe the asymptotic properties of this estimator, showing that it is strongly consistent and asymptotically normally distributed.

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