Instrumental Variable Subspace Tracking

Subspace estimation plays an important role in, for example, sensor array signal processing. Recursive methods for subspace tracking with application to non-stationary environments , have also drawn considerable interest. In this paper, Instrumental Variable (IV) extensions of the recently developed Projection Approximation Subspace Tracking (PAST) algorithm are presented. The IV-approach is motivated by the fact that PAST gives biased estimates when the noise is not spatially white. The proposed algorithms are based on a projection like uncon-strained criterion, with a resulting computational complexity of 3ml + O(mn) where m is the dimension of the measurement vector, l is the dimension of the IV vector, and n is the subspace dimension. Also an extension to a \second order" IV algorithm is proposed, which in certain 1 scenarios is demonstrated to have better tracking properties than the basic IV-PAST algorithms. The performance of the algorithms is demonstrated with a simulation study of a time-varying array processing scenario.