A constrained optimization approach for an adaptive generalized subspace tracking algorithm

Abstract

In this paper, we present a new algorithm for tracking the generalized signal subspace recursively. It is based on an interpretation of the generalized signal subspace as the solution of a constrained minimization task. This algorithm, referred to as the CGST algorithm, guarantees the C x -orthonormality of the estimated generalized signal subspace basis at each iteration which C x denotes the correlation matrix of the sequence x(t). Thus, the proposed algorithm avoids C xorthonormalization process after each update for postprocessing algorithms which need C x -orthonormal basis for the generalized signal subspace. An efficient implementation of the proposed algorithm enhances applicability of it in real time applications. Various simulation results show outstanding performance of the proposed algorithm.

Online Dominant Generalized Eigenvectors Extraction Via A Randomized Method

“…The generalized Hermitian eigenvalue problem (GHEP) [1] is of great interest in signal processing, machine learning and data analysis applications. The GHEP algorithms provide powerful tools to treat problems in blind source separation [2,3], feature extraction [4,5], noise filtering [6], fault detection [7], antenna array processing [8], classification [9], and speech enhancement [10]. Traditional methods for solving the GHEP include power and inverse iteration based methods, Lanczos method and Jacobi-Davidson method [1,11].…”

“…The generalized eigenvalues and eigenvectors are extracted from a matrix pencil (A, B). In online applications [2,4,[6][7][8][9][10], however, this pair is unknown, and the rank-1 update strategy [14-16, 18, 19] uses the observed streaming stochastic signals to estimate it. Also, in many cases, the signal subspace spanned by the dominant generalized eigenvectors, lies in a low-dimensional space [10].…”