On the high resolution and unbiased frequency estimates of sinusoids in white noise--A new adaptive approach

A new adaptive algorithm is proposed to give an unbiased and high resolution frequency estimate of sinusoids in white noise. Base on the normalized Least-Squares (LS) lattice algorithm and the inverse power iteration method, the eigenvector associated with the minimum eigenvalue of the signal covariance matrix is estimated in the algorithm. The zeros of the "eigenvector polynomial" thus obtained are all on the unit circle and at the angles of the sinusoid frequencies. It is an adaptive realization of the Pisarneko\´s "harmonic retrieval" method. But differing from the adaptive method proposed by Thompson where the eigenvector is obtained through a gradient search in a constrained optimization formulation, in the new method the eigenvector is computed by an inverse power iteration. It enjoys all the advantages of the normalized LS lattice such as fast computations, low round-off noise and an easy stability check, etc. as well as fast convergence rate of the inverse power iteration method. Computer simulation results are shown.