Perturbation expansions of signal subspaces for long signals

Singular Spectrum Analysis and many other subspacebased methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of special “signal” and “perturbed signal” matrices. In this paper, the analysis of the largest principal angle between these subspaces is performed in terms of the perturbation expansions of the corresponding orthogonal projectors. Applicable upper bounds are derived. The main attention is paid to the asymptotic case when the length of the time series tends to infinity. Results concerning conditions for convergence, the rate of convergence, and the main terms of proximity are presented.

Keywords

signal subspace methods, perturbation expansion, asymptotic analysis, singular spectrum analysis

2010 Mathematics Subject Classification

Primary 65F30, 65Gxx. Secondary 65F15.

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Published 1 January 2010