algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It
is an algorithm which makes optimal use of imprecise
data on a linear (or nearly linear) system with Gaussian errors to continuously update
the best estimate of the system's current state.
See also Wiener Filter
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References Casti, J. L. "The Kalman Filter." Ch. 1 in New York: Wiley, pp. 101-154, 2000. Five
More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th-Century
Mathematics. Chui, C. K.
and Chen, G. Berlin: Springer-Verlag,
Filtering: With Real-Time Applications, 2nd ed. Grewal, M. S. Englewood Cliffs, NJ: Prentice-Hall, 1993. Kalman
Filtering: Theory & Practice. Kalman,
R. E. "A New Approach to Linear Filtering and Prediction Problems."
Trans. ASME Ser. D. J. Basic Eng. 82, 35-45, 1960. Kalman,
R. E. and Bucy, R. S. "New Results in Linear Filtering and Prediction
Theory." Trans. ASME Ser. D. J. Basic Eng. 83, 95-108, 1961. Simon,
D. New York:
Wiley, 2006. Optimal
State Estimation: Kalman, Hinfty, and Nonlinear Approaches. Referenced on Wolfram|Alpha Kalman Filter
Cite this as:
Weisstein, Eric W. "Kalman Filter." From
--A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/KalmanFilter.html