Perturbation analysis of an SVD-based linear prediction method for estimating the frequencies of multiple sinusoids

A linear prediction approach is studied for estimating the frequencies of sinusoids in white noise. It is shown that in the first step, the continuity of the generalized inverse and the concept of angle between subspaces play an important role. The continuity concept helps explain the need for a low rank approximation, and the quality of the approximation is appraised by using the notion of angle between subspaces. For the second step, the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined. It is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity