Instrumental variable subspace tracking using projection approximation

Subspace estimation plays an important role in, for example, sensor array signal processing. Recursive methods for subspace tracking with application to nonstationary environments have also drawn considerable interest. In this paper, instrumental variable (IV) extensions of the 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 unconstrained 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. In addition, an extension to a “second order” IV algorithm is proposed, which in certain 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