A consideration on identification of time varying parameter system with unknown parameter variation

Frequently, we have to deal with the systems whose parameters vary randomly around the unknown trend as the variaiotn of the circumference. It is important to consider the identification problem of such time varying parameter systems. Generally speaking, as the measurements of the system output which are used for the system identification are noisy, the noise influence upon the estimates decreases by time average. But the more measurement data are used to identify the time varying parameter system, the more estimates have the time lag, as the noise ininfluence may be smaller. Therefore, it is natural that the adequate number of the mesurement data to be used exists. Especially, in the case of the rapidly varying parameter and the low S/N ratio, it is difficult to identify the system exactly. Under these circumference, there may be the model whose structure is simpler than the one of the system. In this paper, we investigate the number of to be used and the structure of the model to identify the time varying parameter systems.