A Method with Lower-than-ML Threshold for Frequency Estimation of Multiple Sinusoids

TL;DR

This paper introduces a new frequency estimation method for multiple sinusoids that achieves lower threshold SNR than traditional methods like MLE, with reduced bias and computational efficiency, especially in noisy, short data scenarios.

Contribution

The proposed algorithm combines zero-padding, removal, and re-estimation steps to surpass MLE in threshold SNR while maintaining computational feasibility.

Findings

Threshold SNR improved by up to 10 dB over MLE.

Bias of estimates is lower or equal to MLE.

Method is computationally feasible for practical use.

Abstract

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.