Mathematics of Kalman-Bucy Filtering
Mathematics of Kalman-Bucy Filtering

Author: P.A. Ruymgaart

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 181

ISBN-13: 3642968422

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Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but also in the social sciences, biological sciences, medical sciences, as well as all other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without them fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters. The material is meant to be a theoretical complement to courses dealing with applications and is designed for students who are well versed in the techniques of Kalman-Bucy filtering but who are also interested in the mathematics on which these may be based. The main topic addressed in this book is continuous-time Kalman-Bucy filtering. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously, which are hence more appropriately mod eled by differential equations than by difference equations. On the other hand, observations from the former can be obtained in a discrete fashion.

Estimation, Control, and the Discrete Kalman Filter
Estimation, Control, and the Discrete Kalman Filter

Author: Donald E. Catlin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 286

ISBN-13: 1461245281

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In 1960, R. E. Kalman published his celebrated paper on recursive min imum variance estimation in dynamical systems [14]. This paper, which introduced an algorithm that has since been known as the discrete Kalman filter, produced a virtual revolution in the field of systems engineering. Today, Kalman filters are used in such diverse areas as navigation, guid ance, oil drilling, water and air quality, and geodetic surveys. In addition, Kalman's work led to a multitude of books and papers on minimum vari ance estimation in dynamical systems, including one by Kalman and Bucy on continuous time systems [15]. Most of this work was done outside of the mathematics and statistics communities and, in the spirit of true academic parochialism, was, with a few notable exceptions, ignored by them. This text is my effort toward closing that chasm. For mathematics students, the Kalman filtering theorem is a beautiful illustration of functional analysis in action; Hilbert spaces being used to solve an extremely important problem in applied mathematics. For statistics students, the Kalman filter is a vivid example of Bayesian statistics in action. The present text grew out of a series of graduate courses given by me in the past decade. Most of these courses were given at the University of Mas sachusetts at Amherst.

Optimal and Robust Estimation
Optimal and Robust Estimation

Author: Frank L. Lewis

Publisher: CRC Press

Published: 2017-12-19

Total Pages: 546

ISBN-13: 1420008293

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More than a decade ago, world-renowned control systems authority Frank L. Lewis introduced what would become a standard textbook on estimation, under the title Optimal Estimation, used in top universities throughout the world. The time has come for a new edition of this classic text, and Lewis enlisted the aid of two accomplished experts to bring the book completely up to date with the estimation methods driving today's high-performance systems. A Classic Revisited Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition reflects new developments in estimation theory and design techniques. As the title suggests, the major feature of this edition is the inclusion of robust methods. Three new chapters cover the robust Kalman filter, H-infinity filtering, and H-infinity filtering of discrete-time systems. Modern Tools for Tomorrow's Engineers This text overflows with examples that highlight practical applications of the theory and concepts. Design algorithms appear conveniently in tables, allowing students quick reference, easy implementation into software, and intuitive comparisons for selecting the best algorithm for a given application. In addition, downloadable MATLAB® code allows students to gain hands-on experience with industry-standard software tools for a wide variety of applications. This cutting-edge and highly interactive text makes teaching, and learning, estimation methods easier and more modern than ever.

Kalman Filtering
Kalman Filtering

Author: Mohinder S. Grewal

Publisher: John Wiley & Sons

Published: 2015-02-02

Total Pages: 639

ISBN-13: 111898496X

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The definitive textbook and professional reference on Kalman Filtering – fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.

Fault Diagnosis and Reconfiguration in Flight Control Systems
Fault Diagnosis and Reconfiguration in Flight Control Systems

Author: Chingiz Hajiyev

Publisher: Springer Science & Business Media

Published: 2003-10-31

Total Pages: 394

ISBN-13: 9781402076053

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The problem of fault diagnosis and reconfigurable control is a new and actually developing field of science and engineering. The subject becomes more interesting since there is an increasing demand for the navigation and control systems of aerospace vehicles, automated actuators etc. to be more safe and reliable. Nowadays, the problems of fault detection and isolation and reconfigurable control attract the attention the scientists in the world. The subject is emphasized in the recent international congresses such as IF AC World Congresses (San Francisco-1996, Beijing-1999, and Barcelona-2002) and lMEKO World Congresses (Tampere-1997, Osaka-1999, Vienna-2000), and also in the international conferences on fault diagnosis such as SAFEPROCESS Conferences (Hull-1997, Budapest-2000). The presented methods in the book are based on linear and nonlinear dynamic mathematical models of the systems. Technical objects and systems stated by these models are very large, and include various control systems, actuators, sensors, computer systems, communication systems, and mechanical, hydraulic, pneumatic, electrical and electronic devices. The analytical fault diagnosis techniques of these objects have been developed for several decades. Many of those techniques are based on the use of the results of modem control theory. This is natural, because it is known that fault diagnosis process in control systems is considered as a part of general control process. xxii In organization of fault diagnosis of control systems, the use of the concepts and methods of modem control theory including concepts of state space, modeling, controllability, observability, estimation, identification, and filtering is very efficient.

Bayesian Filtering and Smoothing
Bayesian Filtering and Smoothing

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2013-09-05

Total Pages: 255

ISBN-13: 110703065X

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A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Optimal Filtering
Optimal Filtering

Author: Brian D. O. Anderson

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 370

ISBN-13: 0486136892

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Graduate-level text extends studies of signal processing, particularly regarding communication systems and digital filtering theory. Topics include filtering, linear systems, and estimation; discrete-time Kalman filter; time-invariant filters; more. 1979 edition.

Kalman Filtering Techniques for Radar Tracking
Kalman Filtering Techniques for Radar Tracking

Author: K.V. Ramachandra

Publisher: CRC Press

Published: 2000-01-03

Total Pages: 258

ISBN-13: 9780824793227

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A review of effective radar tracking filter methods and their associated digital filtering algorithms. It examines newly developed systems for eliminating the real-time execution of complete recursive Kalman filtering matrix equations that reduce tracking and update time. It also focuses on the role of tracking filters in operations of radar data processors for satellites, missiles, aircraft, ships, submarines and RPVs.

Beyond the Kalman Filter: Particle Filters for Tracking Applications
Beyond the Kalman Filter: Particle Filters for Tracking Applications

Author: Branko Ristic

Publisher: Artech House

Published: 2003-12-01

Total Pages: 328

ISBN-13: 9781580538510

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For most tracking applications the Kalman filter is reliable and efficient, but it is limited to a relatively restricted class of linear Gaussian problems. To solve problems beyond this restricted class, particle filters are proving to be dependable methods for stochastic dynamic estimation. Packed with 867 equations, this cutting-edge book introduces the latest advances in particle filter theory, discusses their relevance to defense surveillance systems, and examines defense-related applications of particle filters to nonlinear and non-Gaussian problems. With this hands-on guide, you can develop more accurate and reliable nonlinear filter designs and more precisely predict the performance of these designs. You can also apply particle filters to tracking a ballistic object, detection and tracking of stealthy targets, tracking through the blind Doppler zone, bi-static radar tracking, passive ranging (bearings-only tracking) of maneuvering targets, range-only tracking, terrain-aided tracking of ground vehicles, and group and extended object tracking.

Fundamentals of Stochastic Filtering
Fundamentals of Stochastic Filtering

Author: Alan Bain

Publisher: Springer Science & Business Media

Published: 2008-10-08

Total Pages: 395

ISBN-13: 0387768963

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This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.