A hybrid subspace projection method for system identification

Principal components analysis (PCA), being the most optimal linear mapper in a least-squares (LS) sense, has been predominantly used in subspace-based signal processing methods. In system identification problems, optimal subspace projections must span the joint space of the input and output of the unknown system. In this scenario, subspaces determined by the principal components of the input or the desired signal alone do not embed key information, which lies in the joint space. We first propose a hybrid subspace projection method that finds optimal projections in the joint space. The concepts behind this method are firmly rooted in statistical theory. We then derive adaptive learning algorithms to estimate the subspace projections. Finally, we show the superiority of the new framework in solving system identification problems in noisy environments.