Accession Number : ADA187436

Title :   Nonlinear Filtering and Large Deviations: A PDE-Control Theoretic Approach,

Corporate Author : MARYLAND UNIV COLLEGE PARK

Personal Author(s) : James, M R ; Baras, J S

PDF Url : ADA187436

Report Date : 26 Feb 1987

Pagination or Media Count : 22

Abstract : We consider the asymptotic nonlinear filtering problem dx = f(x) dt + sq. rt. epsilon, dy = h(x) dt + sq. rt. epsilon, and obtain the limit as epsilon approaches 0 of epsilon log (q(xt) to the epsilon power) = - W(x, t) for unnormalised conditional densities (q(x,t)) to the epsilon power, using PDE methods. Here, W(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi- Bellman equation. Hijab has also studied this filtering problem, and we extend his large deviation result for certain unnormalised conditional measures. The resulting variational problem corresponds to the above control problem.

Descriptors :   *CONTROL THEORY, *NONLINEAR SYSTEMS, DETERMINANTS(MATHEMATICS), ESTIMATES, ELECTRONS, FILTERS, SOLUTIONS(GENERAL), VISCOSITY, CYCLOTRON RESONANCE, CONTROL, DETERMINATION, OPTIMIZATION, EQUATIONS, ELECTRON GAS, TWO DIMENSIONAL, PROBABILITY DENSITY FUNCTIONS, VARIATIONAL METHODS, ASYMPTOTIC SERIES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE