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Kalman Filter Recent Advances and Applications

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The discussion about the manned spacecraft program was initiated at NASA in 1959. Only one year later, Dr. Kalman and Dr. Schmidt linked the linear Kalman filter and the perturbation theory in order to obtain the Kalman-Schmidt filter, currently known as the extended Kalman filter. This approach would be implemented in 1961 using an IBM 704 computer (running at approximately 4000 operations per second) for simulation purposes, and subsequently, in July 1969, for making the descent of the Apollo 11 lunar module to the Moon possible.

The seminal Kalman filter paper, entitled A new approach to linear filtering and prediction problems, and published in 1960, reformulated the Wiener problem and proposed a new solution based on state transition, avoiding the stationary limitations of the Wiener filter and giving a more suitable algorithm to be implemented in computers. This paper concludes with a prophetic sentence: “… The Wiener problem is shown to be closely connected to other problems in the theory of control. Much remains to be done to exploit these connections.”

The aim of this book is to provide an overview of recent developments in Kalman filter theory and their applications in engineering and scientific fields. The book is divided into 24 chapters and organized in five blocks corresponding to recent advances in Kalman filtering theory, applications in medical and biological sciences, tracking and positioning systems, electrical engineering and, finally, industrial processes and communication networks. Various Kalman filtering techniques applied to non-linear and/or non-gaussian systems are discussed in chapters 1-5 of this book. Unscented and robust Kalman filters are introduced and their adaptive versions proposed. Fuzzy sets are also employed in order to improve the filtering performance. Kalman filters, as described in chapters 6-9, can also be employed in medical and biological sciences allowing medical diagnosis and monitoring techniques, such as Electroencephalograms (EEGs), to be improved. Classical applications of Kalman filters, those relating to tracking and positioning systems, are also included in this book (chapters 10-15). New applications in cellular and wireless networks and personal navigation systems are shown. Kalman filters have also been applied to evaluation of the power quality in electrical grids and estimation of variables in electrical motors. These applications are shown in chapters 16-19 of this book. Chapters 20-24 propose Kalman Filtering applications in industrial processes, such as fault detection diagnosis and measurements during manufacturing processes. Communication systems are also treated, such as the case of video coding and channel tracking.
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