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
Simple examples and problems that require only paper and pen to
solve lead to an intuitive understanding of how theory works in
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
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.
"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)
Dan Simon is a contributing author for Digital Photography All-in-One Desk Reference For Dummies, he is also a regular contributor to the Growing Edge and Pennsylvania magazines. Dan has more than 25 years experience as a journalist and photographer. He began his career as a Navy journalist with assignments aboard several ships, and in Norfolk, VA, Dededo, Guam, and McMurdo Station, Antarctica. After leaving the service in 1990, Dan worked as a river guide and photographer on Pennsylvania's Lehigh River. During the past 10 years, he's worked as a writer and photographer for several Pennsylvania and New Jersey newspapers, including the Wilkes-Barre Times Leader and Allentown Morning Call. His writing and photography have appeared in numerous books, magazines, web sites, and newspapers, including: The New York Times; ESPN; National Geographic Reference Atlas of North American Birds, Fifth Edition; Mid-Atlantic Real Estate Journal; Baltimore Daily Record; Tri-State Real Estate Journal; Corridor Real Estate Journal; All Hands magazine; Army Times; Gloucester County Times; White Haven Journal Herald; Butler Eagle; www.greenworks.tv; and www.drexel.edu/doj/gallery.asp. Dan is currently working on a master's degree in communications from Drexel University (Philadelphia, PA). Dan holds a bachelor's degree in general studies (design arts) from Drexel and an associate's in computer graphic arts from Gloucester County College (Sewell, NJ). He is also a graduate of the military's Defense Information School (Information Specialist Journalist and Broadcaster and Intermediate Photojournalism).
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. 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.