Theoretically, a Kalman filter is an estimator for what is called the linear quadratic Gaussian (LQG) problem, which is the problem of estimating the instantaneous “state” of a linear dynamic system perturbed by Gaussian white noise, by using measurements linearly related to the state, but corrupted by Gaussian white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error. R. E. Kalman introduced the “filter” in 1960 (Kalman 1960).
Practically, the Kalman filter is certainly one of the greater discoveries in the history of statistical estimation theory, and one of the greatest discoveries in the twentieth century. It has enabled humankind to do many things that could not have been done without it, and it has become as indispensable as silicon in the makeup of many electronic systems. The Kalman filter’s most immediate applications have been for the control of complex dynamic systems, such as continuous manufacturing processes,...
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References and Further Reading
Gelb A et al (1974) Applied optimal estimation. MIT Press, Cambridge
Grewal MS, Andrews AP (2008) Kalman filtering theory and practice using MATLAB, 3rd edn. Wiley, New York
Grewal MS, Kain J (September 2010) Kalman filter implementation with improved numerical properties, Transactions on automatic control, vol 55(9)
Grewal MS, Weill LR, Andrews AP (2007) Global positioning systems, inertial navigation, & integration, 2nd edn. Wiley, New York
Kalman RE (1960) A new approach to linear filtering and prediction problems. ASME J Basic Eng 82:34–45
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Grewal, M.S. (2011). Kalman Filtering. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_321
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