Approximate filters for a nonlinear discrete time filtering problem with small observation noise

• Type: Article in International Scientific Journal
• Date: 1994

Authors

Paula Milheiro de Oliveira (Author) FEUP

Journal

The Journal is awaiting validation by the Administrative Services.

Title: Stochastics and Stochastic Reports

Vol. 46

Pages: 1-24

ISSN: 1045-1129

Scientific classification

CORDIS: Technological sciences > Engineering ; Physical sciences > Mathematics > Probability theory ; Physical sciences > Mathematics > Applied mathematics > Engineering mathematics ; Physical sciences > Mathematics > Applied mathematics

Other information

Authenticus ID: P-00P-RZN

DOI: 10.1080/17442509408833866

Resumo (PT): We study the asymptotic behavior of a nonlinear one-dimensional filtering discrete time problem, as some parameter e tends to 0. Our model can be viewed as a discretization of a nonlinear continuous time problem with smell observation noise. Finite dimensional approximate filters arc proposed and results concerning estimations of their performance are stated and proved. We consider specially the case of both white noises with variance of order 0(r). The proof the result that we give about the error between the approximate filter and the optimal one will make use of probability changes and differentiation with respect to the initial condition. Then we give the main ideas of how to treat other cases, the same kind of proofs allowing us to get to the desired results. For more details on those cases see Milheiro.

Abstract (EN): We study the asymptotic behavior of a nonlinear one-dimensional filtering discrete time problem, as some parameter e tends to 0. Our model can be viewed as a discretization of a nonlinear continuous time problem with smell observation noise. Finite dimensional approximate filters arc proposed and results concerning estimations of their performance are stated and proved. We consider specially the case of both white noises with variance of order 0(r). The proof the result that we give about the error between the approximate filter and the optimal one will make use of probability changes and differentiation with respect to the initial condition. Then we give the main ideas of how to treat other cases, the same kind of proofs allowing us to get to the desired results. For more details on those cases see Milheiro.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24