On A Class of Perturbation Based Subspace Tracking Algorithms

In this paper a class of subspace tracking algorithms applicable to, for example, sensor array signal processing is presented. The basic idea of the algorithm is to reduce the amount of computations required for an exact SVD/EVD update, using a certain perturbation strategy. Perhaps the most remarkable property of the proposed algorithms is that the same class of algorithm can be applied to the signal subspace tracking of both auto-and cross-covariance matrices. The problem of tracking the signal subspace of cross-covariance matrices arises for example when so-called Instrumental Variable (IV) methods are applied to DOA estimation in colored noise. Actually, the proposed algorithms do not just track the signal subspace; the dominant part of the SVD/EVD is tracked. Another interesting feature of the proposed class of algorithms is its close relationship with Karasalo's classical subspace averaging algorithm. In fact, the proposed class of algorithms may be seen as a generalized version of subspace averaging, applicable also to the IV scenario. Although we mainly consider subspace tracking in a sensor array processing scenario, other interesting applications are brieey described: a) recursive multivariable system identiication, b) adaptive ltering, c) updating of rank deecient least squares problems.