'Institute of Electrical and Electronics Engineers (IEEE)'
Abstract
Includes bibliographical references.There are two types of problems in the theory of least squares signal processing: parameter estimation and signal extraction. Parameter estimation is called "inversion" and signal extraction is called "filtering." In this paper, we present a unified theory of rank shaping for solving overdetermined and underdetermined versions of these problems. We develop several data-dependent rank-shaping methods and evaluate their performance. Our key result is a data-adaptive Wiener filter that automatically adjusts its gains to accommodate realizations that are a priori unlikely. The adaptive filter dramatically outperforms the Wiener filter on atypical realizations and just slightly underperforms it on typical realizations. This is the most one can hope for in a data-adaptive filter.Supported by the Office of Naval Research, Mathematics Division, under contract No. N00014-89-J-1070 and by Bonneville Power Administration under Contract #DEBI7990BPO7346
