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- Q5449244 subject Q5881968.
- Q5449244 subject Q7013146.
- Q5449244 subject Q7035969.
- Q5449244 subject Q8806217.
- Q5449244 subject Q8818223.
- Q5449244 abstract "In the theory of stochastic processes, the filtering problem is a mathematical model for a number of filtering problems in signal processing and the like. The general idea is to form some kind of "best estimate" for the true value of some system, given only some (potentially noisy) observations of that system. The problem of optimal non-linear filtering (even for the non-stationary case) was solved by Ruslan L. Stratonovich (1959, 1960), see also Harold J. Kushner's work and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filter known as Zakai equation. The solution, however, is infinite-dimensional in the general case. Certain approximations and special cases are well-understood: for example, the linear filters are optimal for Gaussian random variables, and are known as the Wiener filter and the Kalman-Bucy filter. More generally, as the solution is infinite dimensional, it requires finite dimensional approximations to be implemented in a computer with finite memory. A finite dimensional approximated nonlinear filter may be more based on heuristics, such as the Extended Kalman Filter or the Assumed Density Filters, or more methodologically oriented such as for example the Projection Filters, some sub-families of which are shown to coincide with the Assumed Density Filters.In general, if the separation principle applies, then filtering also arises as part of the solution of an optimal control problem. For example, the Kalman filter is the estimation part of the optimal control solution to the Linear-quadratic-Gaussian control problem.".
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- Q5449244 wikiPageWikiLink Q5881968.
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- Q5449244 wikiPageWikiLink Q6916189.
- Q5449244 wikiPageWikiLink Q7013146.
- Q5449244 wikiPageWikiLink Q7035969.
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- Q5449244 wikiPageWikiLink Q8806217.
- Q5449244 wikiPageWikiLink Q8818223.
- Q5449244 comment "In the theory of stochastic processes, the filtering problem is a mathematical model for a number of filtering problems in signal processing and the like. The general idea is to form some kind of "best estimate" for the true value of some system, given only some (potentially noisy) observations of that system. The problem of optimal non-linear filtering (even for the non-stationary case) was solved by Ruslan L. Stratonovich (1959, 1960), see also Harold J.".
- Q5449244 label "Filtering problem (stochastic processes)".