Iterative Identification Algorithms for Continuous-Time Systems with Unknown Time Delay in the Presence of Measurement Noise

This paper considers the identification problem of continuous-time systems with unknown time delay from sampled input-output data. By using a digital pre-filter, an approximated discrete-time estimation model is first derived, in which the system parameters remain in their original form and the time delay need not be an integral multiple of the sampling period. Then an unseparable nonlinear least-squares (UNSEPNLS) method and a separable nonlinear least-squares (SEPNLS) method for identification of transfer function parameters and time delay are derived. Furthermore, an unseparable nonlinear instrumental variable (UNSEPNIV) method and a separable nonlinear instrumental variable (SEPNIV) method are proposed, to eliminate estimate bias due to measurement noise. Simulational results show that the UNSEPNIV and SEPNIV methods yield consistent estimates in the presence of measurement noise.