An accurate estimation of the noise power from noisy data leads to better estimation of signal-to-noise ratio (SNR) and is useful in detection, estimation, and prediction. The major contributions of this paper are to estimate the polynomial degree and the noise power from data coming from an underlying polynomial with additive Gaussian noise, using an AR model. The two proposed methods have been inspired by the recent results that all finite degree polynomials have equivalent representation in finite order autoregressive (AR) models, with known AR coefficients and different constant terms. Preliminary experiments in a variety of scenarios provide estimations of the constant term and the standard deviation of these estimations, which are then used as a guide to developing theoretically the probability density functions. In the first stage, the degree of a polynomial is selected by minimizing the variance of the estimations of the constant term in the equivalent AR model. In the second stage, the noise variance is estimated using the estimated degree of a polynomial, a combination of the variance of the estimations of the constant term, and another known parameter. Further computer experiments have been carried out for evaluating the proposed methods for degree and noise power estimations. Four well-known and well-regarded maximum likelihood-based approaches have been used for comparisons.

从噪声数据准确估计噪声功率可导致更好的信噪比（SNR）估计，并在检测，估计和预测中很有用。本文的主要贡献是使用AR模型，根据来自具有加性高斯噪声的基础多项式的数据来估计多项式度和噪声功率。最近提出的结果启发了这两种提议的方法，即所有有限度多项式在有限阶自回归（AR）模型中具有等效表示，且具有已知的AR系数和不同的常数项。在各种情况下的初步实验提供了常数项的估计以及这些估计的标准偏差，然后将其用作理论上开发概率密度函数的指南。在第一阶段 通过最小化等效AR模型中常数项的估计方差来选择多项式的次数。在第二阶段，使用多项式的估计次数，常数项的估计值的方差和另一个已知参数的组合来估计噪声方差。已经进行了进一步的计算机实验，以评估提出的度和噪声功率估计方法。比较中使用了四种众所周知且备受推崇的基于最大似然的方法。和另一个已知的参数。已经进行了进一步的计算机实验，以评估提出的度和噪声功率估计方法。比较中使用了四种众所周知且备受推崇的基于最大似然的方法。和另一个已知的参数。已经进行了进一步的计算机实验，以评估提出的度和噪声功率估计方法。比较中使用了四种众所周知且备受推崇的基于最大似然的方法。