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 obvious applications to non-stationary environments, have also drawn considerable interest. In this paper we present an Instrumental Variable (IV) extension of the recently developed Projection Approximation Subspace Tracking (PAST) algorithm. The IV-approach is motivated by the fact that PAST gives biased estimates when the noise vectors are not spatially white. IV-methods are well-known in the context of system identiication. The basic idea of IV-methods is that the IV-vectors decorrelate the colored noise from the signal of interest, but leave the informative signal part undestroyed. The proposed algorithm is based on a (possibly over-determined) projection like unconstrained system of equations. The resulting basic algorithm has a computational complexity of 3mn + O(n 2) where m is the dimension of the measurement vector and n is the subspace dimension. The basic IV algorithm is also extended to a second order IV version, which is demonstrated to have better tracking properties than the basic IV-algorithm. The performance of the algorithms is demonstrated with a simulation study of time-varying sinusoids in additive colored noise. Permission to publish this abstract separately is granted