The asymptotic properties of polynomial phase estimation by least squares phase unwrapping

Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation 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 therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.