A geometric proof for subspace tracking theorems

Existing subspace tracking theorems play an important role in obtaining recursive subspace estimation algorithms. In this paper a novel proof to the subspace tracking theorems proposed is presented which, not only gives a new geometric interpretation to such results based on the projection theory, but also extends those theorems to a system with a more general class of system noise. In particular, we introduce a unified procedure to analyze three different systems: noise free, with spatially white noises, and with colored noises. Finally, we show that spatially white noise does not cause any bias on the subspace tracking while the colored noise may in general deteriorate the quality of such a tracking.