The focus of this book is on filtering for linear processes, and its primary goal is to design filters from a class of linear stable unbiased filters that yield an estimation error with the lowest root-mean-square (RMS) norm. Various hierarchical classes of filtering problems are defined based on the availability of statistical knowledge regarding noise, disturbances, and other uncertainties.

An important characteristic of the approach employed in this work for several aspects of filter analysis and design is structural in nature, revealing an inherent freedom to incorporate other classical secondary engineering constraints-such as placement of filter poles at desired locations-in filter design. Such a structural approach requires an understanding of powerful tools that then may be used in several engineering applications besides filtering.

Key features and topics covered:

• Provides an in-depth structural study of powerful tools such as Riccati equations, linear matrix inequalities, and quadratic matrix inequalities.

• Develops a general and structural theory of H2 and H-infinity optimal filtering as well as generalized H2 and H-infinity optimal filtering in a broad framework with an extensive and complete analysis and synthesis of filter design.

• Examines several hierarchically ordered layers of noise decoupled filtering problems under a single umbrella.

• Illustrates the application of filtering theory to fault detection, isolation, and estimation.

  Filtering Theory is aimed at a broad audience of practicing engineers, graduate students, and researchers in filtering, signal processing, and control. The book may serve as an advanced graduate text for a course or seminar in filtering theory in applied mathematics or engineering departments. Prerequisites for the reader are a first graduate course in state-spacemethods as well as a first course in filtering.

  Zusammenfassung
  As soon as we (AS and PS) completed writing the book on H Optimal Con- 2 trol, another task of equal magnitude was laid to our charge. This task was to work on ?ltering and related topics. This book releases us from this charge. In this endeavor, we are fortunate to have found a capable person in our friend and colleague (AAS) who helped us release our burden. The subject of ?ltering is indeed vast and immense, much more so than the subject of H Optimal Control. In this work, we have tried to present what we 2 believe to be the fundamental issues of ?ltering. The book is not intended to give a chronological development of ?ltering from a historical point of view. A vast number of books already do so. Our intent here is to develop from our perspective the complete theory of ?ltering and various design methodologies associated with it along with their practical implementations. In this respect, we present here a state-of-the-art view of exact and almost input-decoupled ?ltering, H ,and H 2 1 ?ltering and inverse ?ltering issues, and include an application of ?ltering and inverse ?ltering to fault detection, isolation, and estimation. Most of the work reported here arose out of the research conducted by one or more of us and so- times in collaboration with our students and colleagues. Supposedly, young F.

  Inhalt
  Preliminaries.- A special coordinate basis (SCB) of linear multivariable systems.- Algebraic Riccati equations and matrix inequalities.- Exact disturbance decoupling via state and full information feedback.- Almost disturbance decoupling via state and full information feedback.- Exact input-decoupling filters.- Almost input-decoupled filtering under white noise input.- Almost input-decoupled filtering without statistical assumptions on input.- Optimally (suboptimally) input-decoupling filtering under white noise inputH2 filtering.- Optimally (suboptimally) input-decoupled filtering without statistical information on the input-H? filtering.- Generalized H2 suboptimally input-decoupled filtering.- Generalized H? suboptimally input-decoupled filtering.- Fault detection, isolation, and estimationexact or almost fault estimation.- Fault detection, isolation, and estimationoptimal fault estimation.