标题： 有色噪声中估计二维正弦波的强一致模型阶数选择 显示英文标题

标题： Strongly Consistent Model Order Selection for Estimating 2-D Sinusoids in Colored Noise

摘要： 我们研究了联合估计二维正弦信号的数目及其参数的问题，在存在加性色噪声场的情况下观测这些信号。 首先，我们详细阐述了当假定的正弦波数量不正确时，二维正弦信号的最小二乘估计。 在低估正弦信号数量的情况下，我们证明了最小二乘估计几乎必然收敛到主导正弦波的参数。 而在高估该数量的情况下，最小二乘估计得到的参数向量包含一个子向量，它几乎必然收敛到正弦波的真实参数。 基于这些结果，我们证明了一种新的模型阶数选择规则的强一致性。 显示英文摘要

摘要： We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2-D sinusoidal signals, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where this number is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a new model order selection rule.