Fast Tracking of Time-Variant Systems Using Local Affine Subspaces

Various audio and speech processing applications require the identification and tracking of linear acoustic systems. Previous analyses have demonstrated that in many scenarios the set of possible impulse responses forms a low dimensional manifold. Existing approaches have used this fact to improve the convergence properties of an identification algorithm, e.g., by projecting the estimated impulse response vector onto a set of lower dimensional affine subspaces that are learned from data that is known a priori. In this paper, we present a novel variant of the Kalman filter that only tracks a low dimensional system representation in a linear subspace. Experimental results show that the proposed approach is robust in adverse signal-to-noise ratios and reduces the relative system distance compared to state-of-art approaches when tracking time-variant systems.