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Kalman filtering is an optimal state estimation process applied to a dynamic system
that involves random perturbations. More precisely, the Kalman filter gives a linear,
unbiased, and minimum error variance recursive algorithm to optimally estimate the
unknown state of a dynamic system from noisy data taken at discrete real-time. It
has been widely used in many areas of industrial and government applications such
as video and laser tracking systems, satellite navigation, ballistic missile trajectory
estimation, radar, and fire control. With the recent development of high-speed
computers, the Kalman filter has become more useful even for very complicated
real-time applications.
In spite of its importance, the mathematical theory of Kalman filtering and its
implications are not well understood even among many applied mathematicians and
engineers. In fact, most practitioners are just told what the filtering algorithms are
without knowing why they work so well. One of the main objectives of this text is
to disclose this mystery by presenting a fairly thorough discussion of its mathe-
matical theory and applications to various elementary real-time problems
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