Kalman filtering algorithm gives optimal (linear, unbiased and minimum error-variance) estimates of the unknown state vectors of a linear dynamic-observation system, under the regular conditions such as perfect data information; complete noise statistics; exact linear modelling; ideal will-conditioned matrices in computation and strictly centralized filtering. In practice, however, one or more of the aforementioned conditions may not be satisfied, so that the standard Kalman filtering algorithm cannot be directly used, and hence "approximate Kalman filtering" becomes necessary. In the last decade, a great deal of attention has been focused on modifying and/or extending the standard Kalman filtering technique to handle such irregular cases. This book is a collection of several survey articles summarizing recent contributions to the field, along the line of approximate Kalman filtering with emphasis on its practical aspects.
During the past decade, Approximation Theory has reached out to encompass the
approximation-theoretic and computational aspects of several exciting areas in applied
mathematics such as wavelets, fractals, neural networks, and computer-aidedgeometric
design, as well as the modern mathematical development in science and
technology. The objective of this book series is to capture this exciting development
in the form of monographs, lecture notes, reprint volumes, text books, edited review
volumes, and conference proceedings.
Approximate Kaiman Filtering, the second volume of this series, represents
one of the engineering aspects of Approximation Theory. This is an important
subject devoted to the study of efficient algorithms for solving many of the realworld
problems when the classical Kaiman filter does not directly apply. The series
editor would like to congratulate Professor Guanrong Chen for his excellent job in
editing this volume and is grateful to the authors for their fine contributions.