Optimal estimation of parameters and states in stochastic time-varying systems with time delay

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• 作者：Shahab Torkamani ; ^{shahab@nmsu.edu} ; Eric A. Butcher
• 关键词：Stochastic delay differential equations ; Parameter estimation ; Nonlinear filtering ; Extended Kalman&ndash ; Bucy filter
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：18
• 期：8
• 页码：2188-2201
• 全文大小：858 K

文摘

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.