Efficient, high performance, subspace tracking for time-domain data

• Published in: IEEE transactions on signal processing Vol. 48; no. 12; pp. 3307 - 3315
• Main Author: Davila, C.E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; Algorithms; Applied sciences; Complexity; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Eigenvectors; Exact sciences and technology; Filtering algorithms; Information, signal and communications theory; Matrices; Reduction; Sampling methods; Services and terminals of telecommunications; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; Speech enhancement; Subspaces; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Telemetry: remote control, remote sensing; radar; Time domain analysis; Tracking; Performance evaluation; Time domain method; Invariant subspace; Algorithm performance; Eigenvector; Correlation matrix; Time series; Theoretical study; Adaptive filtering; Tracking(movable target); Covariance matrix
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.886994

This paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time-domain (i.e., time series) data. The algorithms track the d principal N-dimensional eigenvectors of the data covariance matrix with a complexity of O(Nd/sup 2/), yet they have performance comparable with algorithms having O(N/sup 2/d) complexity. The computation reduction is achieved by exploiting the shift-invariance property of temporal data covariance matrices. Experiments are used to compare our algorithms with other well-known approaches of similar and/or lower complexity. Our new algorithms are shown to outperform the subset of the general approaches having the same complexity. The new algorithms are useful for applications such as subspace-based speech enhancement and low-rank adaptive filtering.