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 fac
t that the phase is wrapped modulo 2pi 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.
The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(nlog{n})$ arithmetic operatio
ns. In this paper, we describe a new algorithm. While the complexity is still $O(nlog{n})$, it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.
