Accurate frequency estimation using SVD method and Steiglitz-McBride algorithm

In many applications it is desired to estimate frequencies of sinusoids from a signal which is contaminated by a white noise. The Steiglitz-McBride algorithm (S-MA) works well for one sinusoid or when frequencies are seperated widely. However, when frequencies are close, the S-MA does not work. In the S-MA the initial estimate of the characteristic equation coefficients is based on Prony's method which is biased. The singular value decomposition (SVD) method works much better than Prony's method. The SVD method is used for initial estimate of frequencies and then the S-MA is used to estimate a single frequency at a time while all other frequencies are held fixed in each iteration. The iteration continues until the solution converges. It is shown that the new method improves the performance greatly.