Parametric subspace fitting methods for array signal processing.

摘要

Many signal processing problems are concerned with estimating signal parameters from sensor array measurements. In radar and underwater applications, large arrays are often employed to accurately determine source locations. Information regarding geologic structures is often obtained in seismic exploration by estimating signal parameters from array data. In radio and microwave communications, arrays are used to achieve directional sensitivity, separating desired signals from jammers and interferences. Array signal processing has drawn much attention and many methods for parameter estimation from array data have appeared in the literature.;In this thesis, a subspace fitting framework is presented in which several existing algorithms appear as special cases. The asymptotic distribution of the parameter estimation error is derived for the general subspace fitting problem. The asymptotic distributions for different algorithms are then obtained as special cases of these results. This common framework sheds light on the algebraic and asymptotic relations between the various methods.;Within the class of subspace fitting methods, a novel minimum variance estimator termed Weighted Subspace Fitting (WSF) is derived. WSF is a nonlinear, multidimensional estimation procedure and a Gauss-Newton type algorithm is suggested for determining the estimates. Based on the asymptotic distribution of the WSF cost function, a strongly consistent detection procedure is developed.;Under the assumption of Gaussian distributed emitter signals, the so-called stochastic Maximum Likelihood (ML) technique is known to provide statistically efficient estimates, i.e., it achieves the Cramer-Rao bound. It is shown that the WSF and ML estimates are asymptotically identical. As a consequence, the WSF method is also asymptotically efficient. The asymptotic analysis of the ML and subspace fitting methods is extended to non-Gaussian emitter signals and the asymptotic properties of the resulting estimates are shown to be independent of the distribution of the signal waveforms. Implications of this for the modeling aspects of the array problem are discussed. Numerical examples of the theoretical results as well as simulations are also presented.