On Tracking a Stochastically Time-Varying Subspace

Abstract

Subspace tracking has a long and still growing list of applications with recent interest stimulated by the advent of ’streaming’ data. Despite the considerable literature, all of it motivated by the desire to track time varying subspaces, there seems to be almost no analysis of that time varying problem. Rather existing analyses assume the subspace is fixed. Here, for the first time we develop a true subspace tracking analysis in continuous time. It turns out to be a very hard problem and so we tackle the problem of a rank 1 subspace.