Linear estimation and detection in Krylov subspaces

One major area in the theory of statistical signal processing is reduced-rank - timation where optimal linear estimators are approximated in low-dimensional subspaces, e. g., in order to reduce the noise in overmodeled problems, - hance the performance in case of estimated statistics, and/or save compu- tional complexity in the design of the estimator which requires the solution of linear equation systems. This book provides a comprehensive overview over reduced-rank ? lters where the main emphasis is put on matrix-valued ? lters whose design requires the solution of linear systems with multiple right-hand sides. In particular, the multistage matrix Wiener ? lter, i. e., a reduced-rank Wiener ? lter based on the multistage decomposition, is derived in its most general form. In numerical mathematics, iterative block Krylov methods are very po- lar techniques for solving systems of linear equations with multiple right-hand sides, especially if the systems are large and sparse. Besides presenting a - tailed overview of the most important block Krylov methods in Chapter 3, which may also serve as an introduction to the topic, their connection to the multistage matrix Wiener ? lter is revealed in this book. Especially, the reader will learn the restrictions of the multistage matrix Wiener ? lter which are necessary in order to end up in a block Krylov method. This relationship is of great theoretical importance because it connects two di? erent ? elds of mathematics, viz., statistical signal processing and numerical linear algebra.