Estimating the frequencies of multiple, closely-spaced noisy sinusoids when the data record is short is commonly accomplished by subspace-based methods such as ESPRIT, MUSIC, etc. These methods do not assume that the data are zero outside the observation interval. If we assume otherwise, the threshold SNR lowered significantly, but the price paid is unacceptable bias. Among all known unbiased estimators, the maximum-likelihood estimator (MLE) has the lowest threshold, but is computationally the most expensive. We propose a new algorithm that carries out, when needed, (i) zero-padding, and (ii) removal and re-estimation. These added steps result in a threshold SNR that is lower than that of the MLE for the examples considered herein, viz., noisy signals containing sinusoids with random parameters and up to five components. The maximum improvement in threshold was 10 dB for the two-sinusoid case. The bias of the estimates is also either equal to or lower than MLE’s. Unlike the MLE, the proposed method is very much computationally feasible.

通常，通过基于子空间的方法（例如ESPRIT，MUSIC等）可以估算出数据记录较短时多个紧密排列的嘈杂正弦波的频率。这些方法不假定观察间隔之外的数据为零。如果我们以其他方式假设，则阈值SNR显着降低，但是付出的代价是不可接受的偏差。在所有已知的无偏估计器中，最大似然估计器（MLE）具有最低阈值，但在计算上最昂贵。我们提出了一种新算法，该算法在需要时执行（i）零填充，以及（ii）删除和重新估计。这些增加的步骤导致阈值SNR低于MLE的阈值SNR对于本文中考虑的示例，即，噪声信号包含具有随机参数和最多五个分量的正弦波。对于两个正弦曲线的情况，阈值的最大改善为10 dB。估计的偏差也等于或小于MLE的偏差。与MLE不同，该方法在计算上非常可行。