Grewal M.S., Andrews A.P. Kalman Filtering: Theory and Practice Using MatLAB

3rd edition. — John Wiley, 2008. — 589 p.This book is designed to provide familiarity with both the theoretical and practical aspects of Kalman filtering by including real-world problems in practice as illustrative examples. The material includes the essential technical background for Kalman filtering and the more practical aspects of implementation: how to represent the problem in a mathematical model, analyze the performance of the estimator as a function of system design parameters, implement the mechanization equations in numerically stable algorithms, assess its computational requirements, test the validity of results, and monitor the filter performance in operation. These are important attributes of the subject that are often overlooked in theoretical treatments but are necessary for application of the theory to real-world problems.
In this third edition, we have included important developments in the implementation and application of Kalman filtering over the past several years, including adaptations for nonlinear filtering, more robust smoothing methods, and developing applications in navigation.
We have also incorporated many helpful corrections and suggestions from our readers, reviewers, colleagues, and students over the past several years for the overall improvement of the textbook.
All software has been provided in MATLAB1 so that users can take advantage of its excellent graphing capabilities and a programming interface that is very close to the mathematical equations used for defining Kalman filtering and its applications. See Appendix A for more information on MatLAB software.
The inclusion of the software is practically a matter of necessity, because Kalman filtering would not be very useful without computers to implement it. It provides a better learning experience for the student to discover how the Kalman filter works by observing it in action.
The implementation of Kalman filtering on computers also illuminates some of the practical considerations of finite-wordlength arithmetic and the need for alternative algorithms to preserve the accuracy of the results. If the student wishes to apply what she or he learns, then it is essential that she or he experience its workings and failings — and learn to recognize the difference.General Information
Linear Dynamic Systems
Random Processes and Stochastic Systems
Linear Optimal Filters and Predictors
Optimal Smoothers
Implementation Methods
Nonlinear Filtering
Practical Considerations
Applications to Navigation
MatLAB Software
A Matrix Refresher