An eigenstructure based nonparametric algorithm to estimate the frequencies of two sinusoids in white noise

An algorithm for estimating the frequencies of two sinusoids in white noise is presented. The method uses the eigenvectors of the estimated autocorrelation matrix (ACM) to yield the signal vectors. Since the signal and the eigenvectors span the same space, one can be obtained from the other through a linear transformation. The coefficients of the linear combination are derived as the eigenvectors of a 2×2 matrix whose elements are a function of the signal power, ACM dimension, and the angle between the two signal vectors. A method for estimating the unknown angle between the signal vectors is described. Knowledge of this angle completely determines the 2×2 matrix whose eigenvectors then yield the signal vectors. A periodogram can now be used to estimate the unknown frequencies from each signal vector. The method has the attractive property of separating a two-sinusoid problem into two single-sinusoid problems. Simulation results that describe the performance of this algorithm at low signal-to-noise ratios are presented