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 - standard, modified and ideal, M.J. Moorman and T.E. Bullock; bias in extended Kalman filters - a mathematical analysis, T.E. Bullock and M.J. Moorman; robust adaptive Kalman filtering, A.R. Moghaddamjoo and R.L. Kirlin; on-line estimation of signal and noise parameters and adaptive Kalman filtering, P.J. Wojcik; adaptive Kalman filtering under irregular environment, G. Chen; fisher initialization in the presence of ill-conditioned measurements, D. Catlin; initializing the Kalman filter with incompletely specified initial conditions, A. Maravall and V. Gomez; set-valued Kalman filtering, D. Morrell and W.C. Stirling; distributed filtering using set models for systems with non-Gaussian noise, L. Hong; suboptimal Kalman filtering for linear systems with non-Gaussian noises, H.Y. Wu and G. Chen; robust stability analysis of Kalman filter under parametric and noise uncertainties, B.S. Chen; numerical approximations and other structural issues in practical implementations of Kalman filtering, T.H. Kerr.