Approximate nonlinear filtering for a two-dimensional diffusion with one-dimensional observations in a low noise channel

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Paula Milheiro de Oliveira (Author) FEUP; Jean Picard (Author) Other

Journal

Title: SIAM Journal on Control and Optimization

Vol. 41 No. 6

Pages: 1801-1819

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 0 Citations

ISI Web of Science

Scopus - 1 Citation

COMPENDEX

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

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

Other information

Authenticus ID: P-000-RZV

DOI: 10.1137/s0363012902363920

Abstract (EN): The asymptotic behavior of a nonlinear continuous time filtering problem is studied when the variance of the observation noise tends to 0. We suppose that the signal is a two-dimensional process from which only one of the components is noisy and that a one-dimensional function of this signal, depending only on the unnoisy component, is observed in a low noise channel. An approximate filter is considered in order to solve this problem. Under some detectability assumptions, we prove that the filtering error converges to 0, and an upper bound for the convergence rate is given. The efficiency of the approximate filter is compared with the efficiency of the optimal filter, and the order of magnitude of the error between the two filters, as the observation noise vanishes, is obtained.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19