An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can handle an arbitrary number of dimensions and an arbitrary set of polynomial degrees along each dimension; the only requirement is that the number of observations per dimension exceeds the highest degree thereon. Embodied by a highly compact sequential algorithm, this estimator exhibits a strictly linear computational complexity in the number of observations, and is efficient at high signal-to-noise ratios (SNRs). To reinforce the performance at low and medium SNRs, where any phase estimator is bound to be hampered by the inherent ambiguity caused by phase wrappings, suitable functionalities are incorporated and shown to be highly effective.

翻译：本文提出了一种针对多项式相位信号的估计方法，即其相位在索引上呈多项式形式的复指数信号。与现有技术相比，所提出的估计器能够处理任意维数以及每个维度上任意设定的多项式阶数；唯一要求是每个维度上的观测点数超过该维度的最高阶数。该估计器体现为一种高度紧凑的序列算法，其计算复杂度在观测点数上严格呈线性，并在高信噪比条件下表现出高效性。为增强在低中信噪比下的性能——任何相位估计器在此条件下都不可避免地会受到相位卷绕引起的固有模糊性的影响——本文引入了适当的功能模块，并证明其具有显著效果。