Scharf, Louis L., authorThorpe, Anthony J., authorIEEE, publisher2007-01-032007-01-031995Thorpe, Anthony J. and Louis L. Scharf, Data Adaptive Rank-Shaping Methods for Solving Least Squares Problems, IEEE Transactions on Signal Processing 43, no. 7 (July 1995): 1591-1601.http://hdl.handle.net/10217/750There 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.born digitalarticleseng©1995 IEEE.Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.filtering theoryadaptive signal processingadaptive filtersWiener filtersleast squares approximationsparameter estimationText