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A of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this 'variance equation' completely specif… - Rudolf E. Kálmán
" "A of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this 'variance equation' completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or non-stationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The duality principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of s. Some aspects of this are considered briefly.
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About Rudolf E. Kálmán
Rudolf Emil Kálmán (May 19, 1930 - July 2, 2016) was a Hungarian-American electrical engineer, mathematical system theorist, and college professor, noted for his co-invention and development of the , a mathematical algorithm that is widely used in signal processing, control systems, and Guidance, navigation and control.
Also Known As
Alternative Names:
Kálmán Rudolf Emil
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Rudy Emil Kálmán
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Rudolf E. Kalman
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Kalman Rudolf Emil
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Rudy Emil Kalman
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R. E. Kalman
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Additional quotes by Rudolf E. Kálmán
:(2) The computational aspect. The classical (more accurately, old-fashioned) view is that a mathematical problem is solved if the solution is expressed by a formula. It is not a trivial matter, however, to substitute numbers in a formula. The current literature on the Wiener problem is full of semi-rigorously derived formulas which turn out to be unusable for practical computation when the order of the system becomes even moderately large...
I would like to comment briefly on Professor Zadeh's presentation. His proposals could be severely, ferociously, even brutally criticized from a technical point of view. This would be out of place here. But a blunt question remains: Is professor Zadeh presenting important ideas or is he indulging in wishful thinking? No doubt Professor Zadeh's enthusiasm for fuzziness has been reinforced by the prevailing climate in the U.S.-one of unprecedented permissiveness. 'Fuzzification, is a kind of scientific permissiveness; it tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work and patient observation.
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