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.