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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) hasPhotoCollection Filtering_problem_(stochastic_processes).
- 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) type Abstraction100002137.
- Filtering_problem_(stochastic_processes) type Cognition100023271.
- Filtering_problem_(stochastic_processes) type Communication100033020.
- Filtering_problem_(stochastic_processes) type Concept105835747.
- Filtering_problem_(stochastic_processes) type Content105809192.
- Filtering_problem_(stochastic_processes) type DifferentialEquation106670521.
- Filtering_problem_(stochastic_processes) type Equation106669864.
- Filtering_problem_(stochastic_processes) type Hypothesis105888929.
- Filtering_problem_(stochastic_processes) type Idea105833840.
- Filtering_problem_(stochastic_processes) type MathematicalStatement106732169.
- Filtering_problem_(stochastic_processes) type Message106598915.
- Filtering_problem_(stochastic_processes) type Model105890249.
- Filtering_problem_(stochastic_processes) type PsychologicalFeature100023100.
- Filtering_problem_(stochastic_processes) type Statement106722453.
- Filtering_problem_(stochastic_processes) type StochasticDifferentialEquations.
- Filtering_problem_(stochastic_processes) type StochasticProcess113561896.
- Filtering_problem_(stochastic_processes) type StochasticProcesses.
- 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)".
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- Filtering_problem_(stochastic_processes) sameAs Q5449244.
- Filtering_problem_(stochastic_processes) sameAs Filtering_problem_(stochastic_processes).
- Filtering_problem_(stochastic_processes) wasDerivedFrom Filtering_problem_(stochastic_processes)?oldid=602210488.
- Filtering_problem_(stochastic_processes) isPrimaryTopicOf Filtering_problem_(stochastic_processes).