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Adaptive Hierarchical Bayesian Kalman Filtering
about initial conditions, along with all measurement data. This information is utilized in a recursive manner to give an optimal estimate of the current system State. This optimality is in the least sÄ…uares sense.
A graphical illustration of the type of problem where the Kalman filter is useful is given in FigurÄ™ 1. Here we have a state-space model of the system that is observed through some measurement process. The measurement process delivers measurement data to the filter that contain information about the current State of the system comipted by noise from the various noise sources. The Kalman filter then processes this data to give an estimate of the current system State.
Control engineers immediately saw the Kalman filter as a practical solution to many outstanding problems. There is extensive application literaturÄ™, especially in the area of navigation. In the decade that followed the introduction of the Kalman filter, applications started appearing in the econometrics literaturÄ™, Harrison (1967) and Zellner (1971). However, it took
FigurÄ™ 1. State-Space Model and the Kalman Filter.
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