Sinusoidal frequency estimation by signal subspace approximation

Eigenvector-based methods such as multiple signal classification (MUSIC) are currently popular in sinusoidal frequency estimation due to their high resolution. A problem with these methods is the often high cost of estimating the eigenvectors of the autocorrelation matrix spanning the signal (or noise) subspace. In this work, we propose an efficient Fourier transform-based method avoiding eigenvector computation for approximating the signal subspace. The resulting signal subspace estimate can be used directly to define a MUSIC-type frequency estimator or as a very good initial guess in context with adaptive or iterative eigenvector computation schemes. At low signal-to-noise ratios, the approximation yields better results than exact MUSIC. It is also more robust than MUSIC against overestimating the number of sinusoids. Some variations of the basic method are briefly discussed.