PLANE ROTATION-BASED EVD UPDATING SCHEMES FOR EFFICIENT SUBSPACE TRACKING

We present new algorithms based on plane rotations for tracking the ei genvalue decomposition (EVD) of a time-varying data covariance matrix, These algorithms directly produce eigenvectors in orthonormal form an d are well suited for the application of subspace methods to nonstatio nary data. After recasting EVD tracking as a simplified rank-one EVD u pdate problem, computationally efficient solutions are obtained in two steps, First, a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transfor m, which is represented in exponential matrix form in terms of a reduc ed set of small, unconstrained parameters. Second, two approximate dec ompositions of this exponential matrix into products of plane (or Give ns) rotations are derived, one of which being previously unknown. Thes e decompositions lead to new plane rotation-based EVD-updating schemes (PROTEUS), whose main feature is the use of plane rotations for updat ing the eigenvectors, thereby preserving orthonormality, Finally, the PROTEUS schemes are used to derive new EVD trackers whose convergence and numerical stability are investigated via simulations, One algorith m can track all the signal subspace EVD components in only O(LM) opera tions, where L and M, respectively, denote the data vector and signal subspace dimensions while achieving a performance comparable to an exa ct EVD approach and maintaining perfect orthonormality of the eigenvec tors. The new algorithms show no signs of error buildup.