Filtering Theory

The focus of this book is on filtering for linear processes, and its primary goal is to design 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.

The authors employ a structural approach for several aspects of filter analysis and design, revealing an inherent freedom to incorporate other classical secondary engineering constraints in filter design. This approach requires an understanding of powerful tools that then may be used in several engineering applications besides filtering.

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-space methods as well as a first course in filtering.

Employs a structural approach to filter design, revealing an inherent freedom to incorporate other classical secondary engineering constraints into filter design Develops powerful tools that may be used in several engineering applications besides filtering Illustrates the application of filtering theory to fault detection, isolation, and estimation For a broad audience of practicing engineers, graduate students, and researchers in filtering, signal processing, and control May serve as an advanced graduate text for a course or a seminar in filtering theory in applied mathematics or engineering departments No direct competition from other texts

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.