Optimal State Estimation
Kalman, H Infinity, and Nonlinear Approaches
1. Auflage Juli 2006
552 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
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. The examples are presented to accomplish two distinct goals-first, to help the reader gain an intuitive understanding, and second, to help the reader see how the theory can be applied to real-world problems. The author's 14 years of industrial experience, along with his theoretical contributions to the field, make him uniquely qualified to present this subject in a way that is both mathematically rigorous and practical. In addition to the basic theory of state estimation, this book presents recent research results in a way that can be easily understood by readers with a background in linear systems. The Matlab source code for the numerous examples in the book is available on the Internet. This allows the student to recreate the example results presented in the book and experiment with other simulation setups and parameters.
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. 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.
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.
PART IV NONLINEAR FILTERS.
13 Nonlinear Kalman filtering.
13.1 The linearized Kalman filter.
13.2 The extended Kalman filter.
13.3 Higher-order approaches.
13.4 Parameter estimation.
13.5 Summary.
Problems.
14 The unscented Kalman filter.
14.1 Means and covariances of nonlinear transformations.
14.2 Unscented transformations.
14.3 Unscented Kalman filtering.
14.4 Other unscented transformations.
14.5 Summary.
Problems.
15 The particle filter.
15.1 Bayesian state estimation.
15.2 Particle filtering.
15.3 Implementation issues.
15.4 Summary.
Problems.
Appendix A: Historical perspectives.
Appendix B: Other books on Kalman filtering.
Appendix C: State estimation and the meaning of life.
References.
Index.
