Efficient Methods for Estimating Sinusoidal Frequencies Using Line Spectral Pairs

Abstract

The maximum likelihood (ML) method of estimating the frequencies of $p$ sinusoids in the presence of AWGN is computationally very costly because of the dimensionality of the error surface; the advantage is that the ML method has the lowest threshold among all known practical estimators. We propose a low complexity method using Line Spectral Pairs (LSPs), where the LSPs are derived from an estimated $A$(z) obtained using Multiple Signal Classification (MUSIC) method. The proposed method evaluates the likelihood function at significantly fewer number of points–at most $^{5p}C_{p}$-for getting the estimates. Furthermore, no iterative finer search is required. Nevertheless, the proposed method's threshold is comparable to that of ML when tested using the well-known two-sinusoids example; similar performance was observed in the case of three sinusoids. Further improvements were observed when the beamformer function was used for detecting and removing outliers. For the two-sinusoid case, outlier removal resulted in a threshold that was lower than that of ML by as much as 9 dB (3π/2 case). We also present results for a direction of arrival (DOA) estimation example that results in the same threshold as that of ML.