A perturbation theory for the analysis of SVD-based algorithms

The problem of statistically analyzing the performance of signal processing algorithms which use the singular value decomposition is adressed in this paper. Such decomposition, which is widely used in system identification and parameter estimation, is a non-linear operation. Consequently, when applied to random data, statistical results are extremely difficult to obtain. The first-order Taylor series expansion is generally used in computing the statistics but the derivative term makes the staistical analysis very difficult. In this paper, a power-like method which results in a simple expression is proposed. The singular vector perturbation using both approaches for the case of low rank approximation is examined.