Stable Subspace Tracking Algorithm Based on a Signed URV Decomposition

摘要

Subspace estimation and tracking are of fundamental importance in many signal processing algorithms. The class of “Schur subspace estimators” provides a complete parametrization of all “principal subspace estimates,” defined as the column spans of corresponding low-rank matrix approximants that lie within a specified 2-norm distance of a given matrix. The parametrization is found in terms of a two-sided hyperbolic decomposition (Hyperbolic URV, or HURV), which can be computed using hyperbolic rotations. Unfortunately, such rotations are commonly associated with numerical instabilities.