This text presents a thorough discussion of the mathematical theory of Kalman filtering. The filtering equations are derived in a series of elementary steps enabling the optimality of the process to be understood. The book provides a comprehensive treatment of various major topics in Kalman-filtering theory, including uncorrelated and correlated noise, coloured noise, steady-state theory, nonlinear systems, systems identification, numerical algorithms and real-time applications. A series of problems for the student, together with a complete set of solutions, are also included. The style of the book is informal, and the mathematics elementary but rigorous, making it accessible to all those with a minimal knowledge of linear algebra and systems theory. In this second edition, in addition to some minor corrections and up-dating, the section on real-time system identification has been expanded and a brief introduction to wavelet analysis has been included. This textbook on applied mathematics, electrical engineering and aerospace engineering is intended for graduate and senior undergraduate students and university and industrial researchers.
From the reviews:
“To summarize, the authors have succeeded in bringing together the mathematical theory and the needs of practitioners. The newly added chapters, in particular the one on wavelets, give the book a proper finish. For a book of this size, it leaves little to be desired. It presents a wealth of details while at the same time avoiding unnecessary abstraction.” (Andreas Ruppin, Berlin, Germany (SSN Stat. Software News, 2000, 34,3-4)
"A rigorous and concise introduction to Kalman filtering is presented in this well-written book. It is suitable for graduate studies, as well as refresher courses and self-study. ... One of the strong features of the book is that Kalman filtering is presented from a few different viewpoints. ... The many end-of-chapters exercises--and the section at the end of the book with solutions and hints to several of them--are another strong feature of the book." (Vladimir Botchev, ACM Computing Reviews, July, 2009)
From the reviews of the third edition:
“The proofs and derivations in the third edition of Kalman Filtering with Real-Time Applications lead to a deep understanding of the linear Kalman filter algorithm as an optimal estimator for the state sequence in a system with stochastic dynamics and measurements. It is a good book for researchers with a strong mathematical background who will be building Kalman filters and smoothers. It is also a good text for teaching a course on linear Kalman filtering and some of its extensions.” (Bradley M. Bell, SIAM Review, Vol. 52 (2), 2010)
From the reviews of the fourth edition:
“It is written not only for self-study but also for use in a one-quarter or one-semester introductory course on Kalman filtering theory for upper-division undergraduate or first-year graduate to applied mathematics or engineering students. In addition, it is hoped that it will become a valuable reference to any industrial or government engineer.” (George S. Stavrakakis, Zentralblatt MATH, Vol. 1206, 2011)
