An approach of the order identification for the transfer function of systems with superimposed noise

Conventional methods for estimating the transfer function models based on deterministic perturbations of the input such as step, pulse and sinusoidal changes have not always been successful because the response of the system may be masked by uncontrollable disturbances, collectively referred to as noise. Particularly in multisensor-integrated systems, the effect of noise from the sensors is not negligible and so the information on the system model and noise model is important for the accurate control of the integrated systems. In this paper, a statistical method for estimating the transfer function models with superimposed noise is presented. Similarity between the auto-correlation function of linear filter system driven by white noise and the impulse response function of dynamic system enables us to develop a method of identifying the order of dynamic systems. In order to identify the systems with superimposed noise, this paper derives R-, S-, and GPAC array which provide us with pretty clear information on the identification of dynamic systems with noise. From the derived arrays, we can obtain the order of transfer function model and also the order of noise model represented by an ARMA process. Finally, an example of order identification of transfer function model and noise model is presented to show effectiveness of the proposed algorithm.