Performance Analysis of Subspace-Based Parameter Estimation Algorithms

摘要

We have developed new perturbation formulas for signal and orthogonal subspaceswhich are estimated from a noisy data matrix. These formulas are: (1) based on a finite amount of data; (2) derived under the assumption of high signal-to-noise ratio; and (3) applicable to arrays of arbitrary geometry, and they provide a common foundation for all our analyses. We have analyzed a number of array processing algorithms which we classify as follows: (1) Signal subspace algorithms: ESPRIT, State-space realization (including TAM), and Matrix Pencil, (2) Orthogonal subspace algorithms: MUSIC and Min-Norm. We have developed analytical variance formulas for the case in which estimates are obtained by searching for the extrema of a function (used with arbitrary array geometry), as well as the case in which estimates are obtained by rooting a polynomial or finding the eigenvalues of a matrix (used with a uniform line array geometry). In addition, we have developed improvements to a state-space algorithm for frequency-wavenumber (2-D) estimation. We give a procedure to pair individual frequency and wavenumber estimates, and we also show how a 2-D forward-backward data matrix can be used to improve the performance of the state-space approach. Keywords: Abstracts, Electrical engineering.