Rapid accurate frequency estimation of multiple resolved exponentials in noise

The estimation of the frequencies of the sum of multiple resolved exponentials in noise is an important problem due to its application in diverse areas from engineering to chemistry. Yet to date, no low cost Fourier-based algorithm has been successful at obtaining unbiased estimates that achieve the Cramér-Rao lower bound (CRLB) over a wide range of signal-to-noise ratios. In this work, we achieve precisely this goal, proposing a fast yet accurate estimator that combines an iterative frequency-domain interpolation step with a leakage subtraction scheme. By analysing the asymptotic performance and the convergence behaviour of the estimator, we show that the estimate of each frequency converges to the asymptotic fixed point. Thus, the estimator is asymptotically unbiased and the variance is extremely close to the CRLB. We verify the theoretical analysis by extensive simulations, and demonstrate that the proposed algorithm is capable of obtaining more accurate estimates than state-of-the-art high resolution methods while requiring significantly less computational effort.