Comparison of four methods for the identification of linear systems with a time delay

Four methods for identification of the parameters and time delay in a linear time-invariant system are compared. The four techniques are (1) least squares, (2) "Extended" Kalman Filter, (3) filtered maximum likelihood, and (4) Fast Fourier Transform. The input and output data are obtained by simulating a second order system, and noise is added to the output data. Five parameters in the system transfer function are identified: the gain constant, two pole locations, one zero location, and the time delay. The results show that the filtered maximum likelihood technique is superior with noisy measurements. All the methods identified the parameters and time delay with noiseless measurements.