Open AccessORDER REDUCTION OF OPTIMAL ESTIMATION PROBLEM FOR LANGEVIN EQUATION
Author(s) -
Mikhail S. Osintsev
Publication year - 2012
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2012-18-3.1-40-53
Subject(s) - riccati equation , reduction (mathematics) , mathematics , kalman filter , dimension (graph theory) , matrix (chemical analysis) , covariance matrix , order (exchange) , dimensionality reduction , model order reduction , basis (linear algebra) , algebraic riccati equation , mathematical optimization , computer science , mathematical analysis , algorithm , partial differential equation , statistics , artificial intelligence , combinatorics , geometry , projection (relational algebra) , materials science , finance , economics , composite material
The question under discussion in this paper is the optimal estimation for singular perturbed Langevin equation. On the basis of assumptions about parameters and conditions where the movement is performed, we choose three cases which have curtain peculiarities during the reduction of the optimal estimation problem. For order reduction task the theoretical method of integral manifolds is used. It allows to get the solution of Riccati equations for covariance matrix of the lter and build the corrected Kalman–Bucy lter of a lower dimension