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

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.

► A method for parameter and state estimation in stochastic delay systems is proposed.
► All the states are estimated from noise-corrupted, possibly incomplete measurements.
► The proposed technique is capable of estimating all parameters of the system at once.
► The approach is successfully implemented on various linear and nonlinear systems.