APPROXIMATE KALMAN FILTERING

Editor:  Guanrong Chen, University of Houston, Texas, USA

Publisher:   World Scientific Pub., ISBN 981-02-1359-X, $58, Summer 1993.

Abstract:

The standard Kalman filtering algorithm gives optimal (linear, unbiased and 
minimum error-variance) estimates of the unknown state vectors of a linear 
dynamic-observation system, under regular conditions such as perfect data 
information, complete noise statistics, exact linear modeling, etc. In practice,
however, some of these conditions may not be satisfied, so that ``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 various irregular cases. It has been realized that
approximate Kalman filtering is even more important and useful in applications.

This book is a collection of several tutorial and survey articles summarizing 
the state-of-the-art development and recent contributions to the field, along 
the line of approximate Kalman filtering with emphasis on both its theoretical 
and practical aspects.

Table of Contents

Foreword
Preface

I. Extended Kalman Filtering for Nonlinear Systems                       1

   T. E. Bullock and M. J. Moorman
   Extended Kalman Filters 1: Continuous and Discrete Linearizations     3

   T. E. Bullock and M. J. Moorman
   Extended Kalman Filters 2: Standard, Modified and Ideal               9

   M. J. Moorman and T. E. Bullock
   Extended Kalman Filters 3: A Mathematical Analysis of Bias           15

II. Initialization of Kalman Filtering                                  21

   D. Catlin   Fisher Initialization in the Presence of Ill-Conditioned 
   Measurements

                                                         23
   V. Gomez and A. Maravall
   Initializing the Kalman Filter with Incompletely Specified 
   Initial Conditions                                                   39

III. Adaptive Kalman Filtering in Irregular Environments                63

   A. R. Moghaddamjoo and R. L. Kirlin
   Robust Adaptive Kalman Filtering                                     65

   P. J. Wojcik
   On-line Estimation of Signal and Noise Parameters and Adaptive 
   Kalman Filtering

                                                    87
   H. Wu and G. Chen
   Suboptimal Kalman Filtering for Linear Systems with Non-Gaussian 
   Noise                                                               113

IV. Set-valued and Distributed Kalman Filtering                        137

   D. Morrell and W. C. Stirling
   Set-valued Kalman Filtering                                         139

   L. Hong
   Distributed Filtering Using Set Models for Systems with 
   Non-Gaussian Noise                                                  161

V. Stability Analysis and Numerical Approximations of Kalman Filtering 177

   B. S. Chen and S. C. Peng
   Robust Stability Analysis of the Kalman Filter under Parametric 
   and Noise Uncertainties                                             179

   T. H. Kerr
   Numerical Approximations and Other Structural Issues in Practical
   Implementations of Kalman Filtering                                 193

Further Reading 221
Notation 223
Subject Index 225