Subspace Based Signal Analysis using Singular Value Decomposition

In this paper, we present a unified approach to the (related) problems of recovering signal parameters from noisy observations and the identification of linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques. Both known and new SVD-based identification methods are classified in a subspaceoriented scheme. The singular value decomposition of a matrix constructed from the observed signal data provides the key step to a robust discrimination between desired signals and disturbing signals in terms of signal and noise subspaces. The methods that are presented are contrasted by the way in which the subspaces are determined and how the signal or system model parameters are extracted from these subspaces. Typical examples such as the direction-of-arrival problem and system identification from input/output measurements are elaborated upon, and some extensions to time-varying systems are given.