Optimal reduced-rank estimation and filtering

This paper provides a unified view of, and a further insight into, a class of optimal reduced-rank estimators and filters. An alternating power (AP) method for computing the optimal reduced-rank estimators and filters is derived and analyzed. The AP method is a generalization of the conventional power method for subspace computation, which is shown to be globally and exponentially convergent under weak conditions. When the rank reduction is relatively large, the AP method is computationally more efficient than the conventional methods. The AP method is useful for adaptive computation of the canonical components of a desired reduced-rank estimate, which in turn facilitates the detection of a time-varying rank. The study shown in this paper is particularly useful for applications that involve a large number of sources and a large number of receivers, where rank reduction is either inherent in the multivariate system or required to reduce the model complexity and/or the computational load.