论文标题
用于多个正弦的频率估计的方法低于ML阈值
A Method with Lower-than-ML Threshold for Frequency Estimation of Multiple Sinusoids
论文作者
论文摘要
在存在AWGN的情况下，估计多个正弦曲线的频率以及数据记录通常是通过基于子空间的方法（例如ESPRIT，MUSIC，MIN-NORM等）来完成的。这些方法并不假设在观察间隔之外数据为零。如果我们假设另有假设，则SNR的阈值大大降低，但所支付的价格是不可接受的偏差。在所有已知的无偏估计器中，最大样品估计器（MLE）的阈值最低，但在计算上是最昂贵的。我们提出了一种新算法，在需要时（i）零填充以及（ii）删除和重新估计。这些添加的步骤导致阈值SNR低于MLE的阈值，此处考虑的示例，即包含随机参数的正弦和最多五个组件的噪声信号。对于两丝体情况，阈值的最大改善为10 dB。估计值的偏置也等于或低于MLE。与MLE不同，所提出的方法在计算上是非常可行的。
Estimating the frequencies of multiple sinusoids in the presence of AWGN and when the data record is short is commonly accomplished by subspace-based methods such as ESPRIT, MUSIC, Min-Norm, etc. These methods do not assume that the data are zero outside the observation interval. If we assume otherwise, the threshold SNR is 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.
