Data adaptive rank-shaping methods for solving least squares problems

Data adaptive rank-shaping methods for solving least squares problems Thorpe, Anthony J. ; Scharf, Louis L. "Supported by the Office of Naval Research, Mathematics Division, under contract No. N00014-89-J-1070 and by Bonneville Power Administration under Contract #DEBI7990BPO7346." 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. Colorado State University. Libraries 1995 text ; image application/pdf ECElls00019.pdf FACFECEN100408ARTI eng c1995 IEEE

Data adaptive rank-shaping methods for solving least squares problems

Thorpe, Anthony J. ; Scharf, Louis L.

"Supported by the Office of Naval Research, Mathematics Division, under contract No. N00014-89-J-1070 and by Bonneville Power Administration under Contract #DEBI7990BPO7346."

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.

Colorado State University. Libraries

1995

text ; image

application/pdf

ECElls00019.pdf

FACFECEN100408ARTI

eng

c1995 IEEE