TY - JOUR
T1 - Optimal estimation of parameters and states in stochastic time-varying systems with time delay
AU - Torkamani, Shahab
AU - Butcher, Eric A.
N1 - Funding Information:
Financial support from the National Science Foundation , under the Grant No. CMMI-0900289 is gratefully appreciated.
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
KW - Extended Kalman-Bucy filter
KW - Nonlinear filtering
KW - Parameter estimation
KW - Stochastic delay differential equations
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U2 - 10.1016/j.cnsns.2012.12.017
DO - 10.1016/j.cnsns.2012.12.017
M3 - Article
AN - SCOPUS:84875242312
VL - 18
SP - 2188
EP - 2201
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 8
ER -