Prediction error identification method for continuous-time processes with time delay

We propose a continuous-time prediction error identification method to identify combined deterministic-stochastic continuous-time processes with time delay. It minimizes the prediction error using the Levenberg-Marquardt optimization method with exact derivatives of the objective function with respect to the adjustable parameters that include the time delay. Compared with previous discrete-time identification methods, the proposed method does not suffer from a small sampling time problem. Also, while previous continuous-time approaches using transforms cannot treat a large sampling time, the proposed method can incorporate directly both small and large sampling times as well as irregular sampling time. It can determine the time delay systematically; meanwhile, previous methods use ad hoc approaches. We derive the error covariance matrix and justify the small sampling problem of discrete-time identification methods.