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- Filtering_problem_(stochastic_processes) 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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- Filtering_problem_(stochastic_processes) wikiPageLength "8228".
- Filtering_problem_(stochastic_processes) wikiPageOutDegree "33".
- Filtering_problem_(stochastic_processes) wikiPageRevisionID "674667911".
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Brownian_motion.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Category:Control_theory.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Category:Estimation_theory.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Category:Signal_processing.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Category:Stochastic_differential_equations.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Category:Stochastic_processes.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Conditional_expectation.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Dimension.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Euclidean_space.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Extended_Kalman_Filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Extended_Kalman_filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Harold_J._Kushner.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Hilbert_space.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Kalman-Bucy_filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Kalman_filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Kiyoshi_Itō.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Kiyosi_Itô.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Linear-quadratic-Gaussian_control.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Linear_subspace.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Measurable_function.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Moshe_Zakai.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Nonlinear_filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Optimal_control.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Orthogonal_projection.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Probability_space.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Projection_(linear_algebra).
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Random_variable.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Ruslan_L._Stratonovich.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Ruslan_Stratonovich.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Separation_principle.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Sigma-algebra.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Sigma_algebra.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Signal_processing.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Stochastic_differential_equation.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Stochastic_process.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Stochastic_processes.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Wiener_filter.
- Filtering_problem_(stochastic_processes) wikiPageWikiLink Zakai_equation.
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "Filtering problem (stochastic processes)".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "Filtering problem".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "filtering problem".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "filtering theory".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "nonlinear filtering".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "the filtering problem".
- Filtering_problem_(stochastic_processes) wikiPageWikiLinkText "theory of stochastic processes".
- Filtering_problem_(stochastic_processes) hasPhotoCollection Filtering_problem_(stochastic_processes).
- Filtering_problem_(stochastic_processes) wikiPageUsesTemplate Template:Cite_book.
- Filtering_problem_(stochastic_processes) subject Category:Control_theory.
- Filtering_problem_(stochastic_processes) subject Category:Estimation_theory.
- Filtering_problem_(stochastic_processes) subject Category:Signal_processing.
- Filtering_problem_(stochastic_processes) subject Category:Stochastic_differential_equations.
- Filtering_problem_(stochastic_processes) subject Category:Stochastic_processes.
- Filtering_problem_(stochastic_processes) hypernym Model.
- Filtering_problem_(stochastic_processes) type Person.
- Filtering_problem_(stochastic_processes) 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.".
- Filtering_problem_(stochastic_processes) label "Filtering problem (stochastic processes)".
- Filtering_problem_(stochastic_processes) sameAs m.02w5kbv.
- Filtering_problem_(stochastic_processes) sameAs Q5449244.
- Filtering_problem_(stochastic_processes) sameAs Q5449244.
- Filtering_problem_(stochastic_processes) wasDerivedFrom Filtering_problem_(stochastic_processes)?oldid=674667911.
- Filtering_problem_(stochastic_processes) isPrimaryTopicOf Filtering_problem_(stochastic_processes).