  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.
