Perturbation expansions of signal subspaces for long signals. (arXiv:1001.1051v1 [math.NA])

Singular Spectrum Analysis and many other subspace-based 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 main 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 asymptotical case when the length of the time series tends to
infinity. Results concerning conditions for convergence, rate of convergence,
and the main terms of proximity are presented.

Published by

Original source : http://arxiv.org/abs/1001.1051...