Numerically-robust adaptive subspace tracking using Householder transformations

We develop simple principal and minor subspace tracking algorithms that exactly maintain the orthonormality of the subspace matrix estimate over time. Each of these algorithms use m identical Householder transformations to update the rows of the subspace matrix estimate at each time instant. Unlike many other approaches, ours have asymptotic complexities that scale linearly with the number of adaptive coefficients. We show that existing gradient-based and projection approximation subspace tracking (PAST) methods are first-order approximate versions of our proposed methods, and we also derive several more-accurate approximations. Simulations verify the numerical behavior of the proposed methods in subspace tracking tasks.