Chen G. (ed.) Approximate Kalman Filtering

World Scientific, 1993. — 233 p.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 Filtering for Nonlinear Systems
Extended Kalman Filters 1: Continuous and Discrete Linearizations
Extended Kalman Filters 2: Standard, Modified and Ideal
Extended Kalman Filters 3: A Mathematical Analysis of Bias
Initialization of Kalman Filtering
Fisher Initialization in the Presence of Ill-Conditioned Measurements
Initializing the Kalman Filter with Incompletely Specified Initial Conditions
Adaptive Kalman Filtering in Irregular Environments
Robust Adaptive Kalman Filtering
On-line Estimation of Signal and Noise Parameters and the Adaptive Kalman Filtering
Suboptimal Kalman Filtering for Linear Systems with Non-Gaussian Noise
Set-valued and Distributed Kalman Filtering
Set-valued Kalman Filtering
Distributed Filtering Using Set Models for Systems with Non-Gaussian Noise
Stability Analysis and Numerical Approximation of Kalman Filtering
Robust Stability Analysis of Kalman Filter under Parametric and Noise Uncertainties
Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering