<title>Subspace tracking with quasi-rectangular data windows</title>

Abstract

In signal processing, it is often necessary to decompose sampled data into its principal components. In adaptive sensor array processing, for example, Singular Value Decomposition (SVD) and/or Eigenvalue Decomposition (EVD) can be used to separate sensor data into “signal” and “noise” subspaces. Such decompositions are central to a number of techniques, such as MUSIC, ESPIRIT, and the Eigencanceller. Unfortunately, SVD and EVD algorithms are computationally intensive. When the underlying signals are nonstationary, “fast subspace tracking” methods provide a far less complex alternative to standard SVD methods. This paper addresses a class of subspace tracking methods known as “QR-Jacobi methods.” These methods can track the <i>r</i> principal eigenvectors of a correlation matrix in <i>O(Nr) </i>operations, where <i>N</i> is the dimensionality of the correlation matrix. Previously, QR-Jacobi methods have been formulated to track the principal eigenvectors of an “exponentially windowed” data correlation matrix. Finite duration data windowing strategies were not addressed. This paper extends the prior QR-Jacobi methods so as to implement rectangular sliding data windows, as well as other windows. Illustrated examples are provided.