Designing orthonormal subspace tracking algorithms

Subspace tracking is important for many communications and signal processing tasks. Many of the simplest subspace tracking methods, however, only approximately maintain the orthonormality of the subspace matrix estimate. In this paper, we describe a generalized procedure for designing principal subspace tracking algorithms that maintains the orthonormality of the subspace matrix estimate in a numerically-robust fashion. Our generalized algorithm families include two orthonormal update principal subspace tracking algorithms as special cases, and all but one of the new algorithms are computationally-simpler than these existing approaches. Moreover, we show how to modify these algorithms to perform minor subspace tracking in a numerically-stable fashion. Simulations verify the numerically-robust performances of the algorithms in principal and minor subspace tracking tasks, respectively.