Affine Projection Subspace Tracking
Marc Vilà, Carlos Alejandro López, Jaume Riba
Abstract
In this paper, we consider the problem of estimating and tracking an R-dimensional subspace with relevant information embedded in an N-dimensional ambient space, given that N>>R. We focus on a formulation of the signal subspace that interprets the problem as a least squares optimization. The approach we present relies on the geometrical concepts behind the Affine Projection Algorithms (APA) family to obtain the Affine Projection Subspace Tracking (APST) algorithm. This on-line solution possesses various desirable tracking capabilities, in addition to a high degree of configurability, making it suitable for a large range of applications with different convergence speed and computational complexity requirements. The APST provides a unified framework that generalises other well-known techniques, such as Oja’s rule and stochastic gradient based methods for subspace tracking. This algorithm is finally tested in a few synthetic scenarios against other classical adaptive methods.
BibTeX
@inproceedings{icassp2021_affineprojection,
title = {Affine Projection Subspace Tracking},
author = {Marc Vilà and Carlos Alejandro López and Jaume Riba},
booktitle = {ICASSP 2021},
year = {2021}
}