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) m ethod for computing the optimal reduced-rank estimators and filters is deri ved and analyzed. The AP method is a generalization of the conventional pow er method for subspace computation, which is shown to be globally and expon entially convergent under weak conditions. When the rank reduction is relat ively large, the AP method is computationally more efficient than the conve ntional methods. The AP method is useful for adaptive computation of the ca nonical components of a desired reduced-rank estimate, which in turn facili tates the detection of a time-varying rank. The study shown in this paper i s particularly useful for applications that involve a large number of sourc es 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.