Parameter Identification of Systems with Noise in Input and Output

Abstract

In the problem of system parameters identification, most treatments made previously have assumed that the input to the system was free from noise. However, there would be many instances, where it would be more practical to assume the input to be accompanied with additive noise. Such a case is considered in the present paper, and the asymptotic unbiased estimate is obtained under certain conditions. The extended matrix approach with the ordinary least square method is used for the estimation of the parameters of the systems and the noise filter. Order identification is also discussed for this system with input noise. An application of the obtained solution to a numerical example shows that it gives a satisfactory result, both in parameter identification and in order identification.