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

We propose a continuous-time prediction error identification method to iden tify combined deterministic-stochastic continuous-time processes with time delay. It minimizes the prediction error using the Levenberg-Marquardt opti mization method with exact derivatives of the objective function with respe ct 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 p roposed method can incorporate directly both small and large sampling times as well as irregular sampling time. It can determine the time delay system atically; meanwhile, previous methods use ad hoe approaches. We derive the error covariance matrix and justify the small sampling problem of discrete- time identification methods.