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Data adaptive rank-shaping methods for solving least squares problems




Scharf, Louis L., author
Thorpe, Anthony J., author
IEEE, publisher

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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.


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filtering theory
adaptive signal processing
adaptive filters
Wiener filters
least squares approximations
parameter estimation


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