Least-Squares Adaptive Lattice and Transversal Filters: A Unified Geometric Theory

摘要

A unified theory is presented to characterize least-squares adaptive filters, in either lattice or transversal-filter form, for nonstationary processes. The derivations are based upon a geometric formulation of least-squares estimation and on the concept of displacement rank. A few basic geometric relations are shown to underlie the various algorithms. Insights into the fundamental concepts that unify lattice- and transversal-filter approaches to least-squares adaptive filters are also given. The general results are illustrated by applications to the so-called pre-windowed and growing-memory covariance formulations of the deterministic least-squares problems. (Author)