Effects of Gaussian perturbations on parameter estimators derived from an estimated signal subspace

The authors present theoretical analyses that are appropriate for both high and low signal-to-noise ratio (SNR) of signal subspace or SVD-based signal-processing algorithms. For the low-SNR case, the probability of obtaining an outlier is calculated and is used to determine the threshold SNR at which the variance of parameter estimation errors departs from Cramer-Rao bound behavior. At high-SNR, the perturbation of the parameter estimates from SVD-based linear prediction and Prony-Lanczos algorithms is considered using matrix approximation and Taylor series approximation