Optimal State Estimation - Kalman, H Infinity, and Nonlinear Approaches

Informationen zum Autor DAN SIMON , PhD, is an Associate Professor at Cleveland State University. Prior to this appointment, Dr. Simon spent fourteen years working for such firms as Boeing, TRW, and several smaller companies. Klappentext 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®-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. A solutions manual is available for instructors. 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. Zusammenfassung This is a book that is clear and lucid in its presentation of the technically difficult area of state estimation. The bottom-up approach taken in this text lays the foundation one block at a time until the reader has a firm grasp of optimal filtering. Inhaltsverzeichnis Acknowledgments. Acronyms. List of algorithms. Introduction. PART I INTRODUCTORY MATERIAL. 1 Linear systems theory. 1.1 Matrix algebra and matrix calculus. 1.1.1 Matrix algebra. 1.1.2 The matrix inversion lemma. 1.1.3 Matrix calculus. 1.1.4 The history of matrices. 1.2 Linear systems. 1.3 Nonlinear systems. 1.4 Discretization. 1.5 Simulation. 1.5.1 Rectangular integration. 1.5.2 Trapezoidal integration. 1.5.3 RungeKutta integration. 1.6 Stability. 1.6.1 Continuous-time systems. 1.6.2 Discretetime systems. 1.7 Controllability and observability. 1.7.1 Controllability. 1.7.2 Observability. 1.7.3 Stabilizability and detectability. 1.8 Summary. Problems. 2 Probability theory. 2.1 Probability. 2.2 Random variables. 2.3 Transformations of random variables. 2.4 Multiple random variables. 2.4.1 Statistical independence. 2.4.2 Multivariate statistics. 2.5 Stochastic Processes. 2.6 White noise and colored noise. 2.7 Simulating correlated noise...

List of contents

Acknowledgments.
 
Acronyms.
 
List of algorithms.
 
Introduction.
 
PART I INTRODUCTORY MATERIAL.
 
1 Linear systems theory.
 
1.1 Matrix algebra and matrix calculus.
 
1.2 Linear systems.
 
1.3 Nonlinear systems.
 
1.4 Discretization.
 
1.5 Simulation.
 
1.6 Stability.
 
1.7 Controllability and observability.
 
1.8 Summary.
 
Problems.
 
Probability theory.
 
2.1 Probability.
 
2.2 Random variables.
 
2.3 Transformations of random variables.
 
2.4 Multiple random variables.
 
2.5 Stochastic Processes.
 
2.6 White noise and colored noise.
 
2.7 Simulating correlated noise.
 
2.8 Summary.
 
Problems.
 
3 Least squares estimation.
 
3.1 Estimation of a constant.
 
3.2 Weighted least squares estimation.
 
3.3 Recursive least squares estimation.
 
3.4 Wiener filtering.
 
3.5 Summary.
 
Problems.
 
4 Propagation of states and covariances.
 
4.1 Discretetime systems.
 
4.2 Sampled-data systems.
 
4.3 Continuous-time systems.
 
4.4 Summary.
 
Problems.
 
PART II THE KALMAN FILTER.
 
5 The discrete-time Kalman filter.
 
5.1 Derivation of the discrete-time Kalman filter.
 
5.2 Kalman filter properties.
 
5.3 One-step Kalman filter equations.
 
5.4 Alternate propagation of covariance.
 
5.5 Divergence issues.
 
5.6 Summary.
 
Problems.
 
6 Alternate Kalman filter formulations.
 
6.1 Sequential Kalman filtering.
 
6.2 Information filtering.
 
6.3 Square root filtering.
 
6.4 U-D filtering.
 
6.5 Summary.
 
Problems.
 
7 Kalman filter generalizations.
 
7.1 Correlated process and measurement noise.
 
7.2 Colored process and measurement noise.
 
7.3 Steady-state filtering.
 
7.4 Kalman filtering with fading memory.
 
7.5 Constrained Kalman filtering.
 
7.6 Summary.
 
Problems.
 
8 The continuous-time Kalman filter.
 
8.1 Discrete-time and continuous-time white noise.
 
8.2 Derivation of the continuous-time Kalman filter.
 
8.3 Alternate solutions to the Riccati equation.
 
8.4 Generalizations of the continuous-time filter.
 
8.5 The steady-state continuous-time Kalman filter
 
8.6 Summary.
 
Problems.
 
9 Optimal smoothing.
 
9.1 An alternate form for the Kalman filter.
 
9.2 Fixed-point smoothing.
 
9.3 Fixed-lag smoothing.
 
9.4 Fixed-interval smoothing.
 
9.5 Summary.
 
Problems.
 
10 Additional topics in Kalman filtering.
 
10.1 Verifying Kalman filter performance.
 
10.2 Multiple-model estimation.
 
10.3 Reduced-order Kalman filtering.
 
10.4 Robust Kalman filtering.
 
10.5 Delayed measurements and synchronization errors.
 
10.6 Summary.
 
Problems.
 
PART I l l THE H, FILTER.
 
11 The H, filter.
 
11.1 Introduction.
 
11.2 Constrained optimization.
 
11.3 A game theory approach to H, filtering.
 
11.4 The continuous-time H, filter.
 
11.5 Transfer function approaches.
 
11.6 Summary.
 
Problems.
 
12 Additional topics in H, filtering.
 
12.1 Mixed KalmanIH, filtering.
 
12.2 Robust Kalman/H, filtering.
 
12.3 Constrained H, filtering.
 
12.4 Summary.
 
Problems.

Report

"This book is obviously written with care and reads very easily. A very valuable resource for students, teachers, and practitioners...highly recommended." ( CHOICE , February 2007)
"The dozens of helpful step-by-step examples, visual illustrations, and lists of exercises proposed at the end of each chapter significantly facilitate a reader s understanding of the book s content." ( Computing Reviews.com , December 4, 2006)

Product details

• Authors: Simon, D Simon, Dan Simon, Dan (Cleveland State University) Simon, Simon Dan
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 21.07.2006
• EAN: 9780471708582
• ISBN: 978-0-471-70858-2
• No. of pages: 552
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Regelungstechnik, Probability and statistics, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Control Systems Technology, Electronics and communications engineering, Zustandsschätzung