Perturbation analysis of principal component based algorithm in frequency and DOA estimation - Li, Yongdong. (2009)
Principal component based algorithms have been extensively used in estimating the parameters of harmonics and the localization of radiating sources because of their rela-tively high resolution. In this thesis, we give the statistical performance analysis of the state-variable algorithm applied in frequency estimation. The analysis is achieved using the second-order Taylor series approximation of the principal singular vectors and val-ues of the data matrix. The first and second order perturbations of the singular vectors are first presented as vector-valued functions of the data, and the perturbations of the parameters related to the frequency estimator are derived via the functional relation-ship. Since the frequency estimator can be approximated by the second-order Taylor series expansion about the noise-free data, the bias and the variance expression of the frequency estimator are obtained without the assumption that the frequency estima-tor is unbiased. The derived theoretical expressions are verified via simulation results under different data matrix dimensions and different signal-to-noise ratios (SNR).