edited by Guanrong Chen (Univ. Houston)

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 modeling; ideal well-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. 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 recent contributions to the field, along the line of approximate Kalman filtering with emphasis on both its theoretical and practical aspects.

• Extended Kalman Filters: Continuous and Discrete Linearizations (T E Bullock & M J Moorman)
• Extended Kalman Filters: Standard, Modified and Ideal (T E Bullock & M J Moorman)
• Extended Kalman Filters: A Mathematical Analysis of Bias (M J Moorman & T E Bullock)
• Fisher Initialization in the Presence of Ill-Conditioned Measurements (D Catlin)
• Initializing the Kalman Filter with Incompletely Specified Initial Conditions (V Gómez & A Maravall)
• Robust Adaptive Kalman Filtering (A R Moghaddamjoo & R L Kirlin)
• On-Line Estimation of Signal and Noise Parameters and the Adaptive Kalman Filtering (P J Wojcik)
• Suboptimal Kalman Filtering for Linear Systems with Non-Gaussian Noises (H Wu & G Chen)
• Set-Valued Kalman Filtering (D Morrell & W C Stirling)
• Distributed Filtering Using Set Models for Systems with Non-Gaussian Noise (L Hong)
• Robust Stability Analysis of Kalman Filter Under Parametric and Noise Uncertainties (B S Chen & S C Peng)
• Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering (T H Kerr)