A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: * Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation * Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice * MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.

Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation. Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals received are used to determine highly sensitive processes such as the flight path of a plane, the orbit of a space vehicle, or the control of a machine. The authors use dynamic models from mechanical and aerospace engineering to provide immediate results of estimation concepts with a minimal reliance on mathematical skills. The book documents the development of the central concepts and methods of optimal estimation theory in a manner accessible to engineering students, applied mathematicians, and practicing engineers. It includes rigorous theoretial derivations and a significant amount of qualitiative discussion and judgements. It also presents prototype algorithms, giving detail and discussion to stimulate development of efficient computer programs and intelligent use of them. This book illustrates the application of optimal estimation methods to problems with varying degrees of analytical and numercial difficulty. It compares various approaches to help develop a feel for the absolute and relative utility of different methods, and provides many applications in the fields of aerospace, mechanical, and electrical engineering.

This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation. Even so, theoretical and mathematical concepts are introduced and developed sufficiently to make the book a self-contained source of instruction for readers without prior knowledge of the basic principles of the field. The work is the product of the technical staff of The Analytic Sciences Corporation (TASC), an organization whose success has resulted largely from its applications of optimal estimation techniques to a wide variety of real situations involving large-scale systems. Arthur Gelb writes in the Foreword that "It is our intent throughout to provide a simple and interesting picture of the central issues underlying modern estimation theory and practice. Heuristic, rather than theoretically elegant, arguments are used extensively, with emphasis on physical insights and key questions of practical importance." Numerous illustrative examples, many based on actual applications, have been interspersed throughout the text to lead the student to a concrete understanding of the theoretical material. The inclusion of problems with "built-in" answers at the end of each of the nine chapters further enhances the self-study potential of the text. After a brief historical prelude, the book introduces the mathematics underlying random process theory and state-space characterization of linear dynamic systems. The theory and practice of optimal estimation is them presented, including filtering, smoothing, and prediction. Both linear and non-linear systems, and continuous- and discrete-time cases, are covered in considerable detail. New results are described concerning the application of covariance analysis to non-linear systems and the connection between observers and optimal estimators. The final chapters treat such practical and often pivotal issues as suboptimal structure, and computer loading considerations. This book is an outgrowth of a course given by TASC at a number of US Government facilities. Virtually all of the members of the TASC technical staff have, at one time and in one way or another, contributed to the material contained in the work.

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems

Classification, Parameter Estimation and State Estimation is a practical guide for data analysts and designers of measurement systems and postgraduates students that are interested in advanced measurement systems using MATLAB. 'Prtools' is a powerful MATLAB toolbox for pattern recognition and is written and owned by one of the co-authors, B. Duin of the Delft University of Technology. After an introductory chapter, the book provides the theoretical construction for classification, estimation and state estimation. The book also deals with the skills required to bring the theoretical concepts to practical systems, and how to evaluate these systems. Together with the many examples in the chapters, the book is accompanied by a MATLAB toolbox for pattern recognition and classification. The appendix provides the necessary documentation for this toolbox as well as an overview of the most useful functions from these toolboxes. With its integrated and unified approach to classification, parameter estimation and state estimation, this book is a suitable practical supplement in existing university courses in pattern classification, optimal estimation and data analysis. Covers all contemporary main methods for classification and estimation. Integrated approach to classification, parameter estimation and state estimation Highlights the practical deployment of theoretical issues. Provides a concise and practical approach supported by MATLAB toolbox. Offers exercises at the end of each chapter and numerous worked out examples. PRtools toolbox (MATLAB) and code of worked out examples available from the internet Many examples showing implementations in MATLAB Enables students to practice their skills using a MATLAB environment

The papers in this volume were presented at an International Symposium on Optimal Estimation in Approximation Theory which was held in Freudenstadt, Federal Republic of Germany, September 27-29, 1976. The symposium was sponsored by the IBM World Trade Europe/Middle East/Africa Corporation, Paris, and IBM Germany. On behalf of all the participants we wish to express our appreciation to the spon sors for their generous support. In the past few years the quantification of the notion of com plexity for various important computational procedures (e. g. multi plication of numbers or matrices) has been widely studied. Some such concepts are necessary ingredients in the quest for optimal, or nearly optimal, algorithms. The purpose of this symposium was to present recent results of similar character in the field or ap proximation theory, as well as to describe the algorithms currently being used in important areas of application of approximation theory such as: crystallography, data transmission systems, cartography, reconstruction from x-rays, planning of radiation treatment, optical perception, analysis of decay processes and inertial navigation system control. It was the hope of the organizers that this con frontation of theory and practice would be of benefit to both groups. Whatever success th•~ symposium had is due, in no small part, to the generous and wise scientific counsel of Professor Helmut Werner, to whom the organizers are most grateful. Dr. T. J. Rivlin Dr. P. Schweitzer IBM T. J. Watson Research Center IBM Germany Scientific and Education Programs Yorktown Heights, N. Y.

This text 1s designed to introduce the fundamentals of esti mation to engineers, scientists, and applied mathematicians. The level of the presentation should be accessible to senior under graduates and should prove especially well-suited as a self study guide for practicing professionals. My primary motivation for writing this book 1s to make a significant contribution toward minimizing the painful process most newcomers must go through in digesting and applying the theory. Thus the treatment 1s intro ductory and essence-oriented rather than comprehensive. While some original material 1s included, the justification for this text lies not in the contribution of dramatic new theoretical re sults, but rather in the degree of success I believe that I have achieved in providing a source from which this material may be learned more efficiently than through study of an existing text or the rather diffuse literature. This work is the outgrowth of the author's mid-1960's en counter with the subject while motivated by practical problems aSSociated with space vehicle orbit determination and estimation of powered rocket trajectories. The text has evolved as lecture notes for short courses and seminars given to professionals at Pr>efaae various private laboratories and government agencies, and during the past six years, in conjunction with engineering courses taught at the University of Virginia. To motivate the reader's thinking, the structure of a typical estimation problem often assumes the following form: • Given a dynamical system, a mathematical model is hypothesized based upon the experience of the investigator.

A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.

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.

This book discusses state estimation and control procedures for a low-cost unmanned aerial vehicle (UAV). The authors consider the use of robust adaptive Kalman filter algorithms and demonstrate their advantages over the optimal Kalman filter in the context of the difficult and varied environments in which UAVs may be employed. Fault detection and isolation (FDI) and data fusion for UAV air-data systems are also investigated, and control algorithms, including the classical, optimal, and fuzzy controllers, are given for the UAV. The performance of different control methods is investigated and the results compared. State Estimation and Control of Low-Cost Unmanned Aerial Vehicles covers all the important issues for designing a guidance, navigation and control (GNC) system of a low-cost UAV. It proposes significant new approaches that can be exploited by GNC system designers in the future and also reviews the current literature. The state estimation, control and FDI methods are illustrated by examples and MATLAB® simulations. State Estimation and Control of Low-Cost Unmanned Aerial Vehicles will be of interest to both researchers in academia and professional engineers in the aerospace industry. Graduate students may also find it useful, and some sections are suitable for an undergraduate readership.