A fast hybrid DSC-GS-MLE approach for multiple sinusoids estimation

In this paper, we develop a novel hybrid method for estimation of frequencies of complex multiple sinusoids buried in noise. The algorithm applies two concepts of estimation statistics − data-supported optimization (DSO) and contracting grid search (CGS) to grid-search maximum likelihood estimator (GS-MLE), which is an optimal estimator in terms of accuracy, compared to any other reported method. This hybrid data-supported contracting GS-MLE (DSC-GS-MLE) technique is observed to reduce the time complexity of computationally burdensome GS-MLE. The proposed algorithm has two variants − two-stage variant (DSC-GS-MLE-2) and three-stage variant (DSC-GS-MLE-3). Extensive Monte Carlo simulations show that DSC-GS-MLE-2 retains the optimality of GS-MLE for two and three sinusoids cases. On the other hand, DSC-GS-MLE-3 is suboptimal when compared to GS-MLE but proves to be even faster than DSC-GS-MLE-2 for two sinusoids case, although it does not produce reliable estimates for three sinusoids case. Moreover, they are verified to achieve the Cramér–Rao lower bound (CRLB) as GS-MLE does, even for the closely spaced sinusoids (comparative tables are being reported in Sect. 4 of this manuscript).