Abstract
As method of parameter estimation for linear discrete-time systems in the presence of noise, the linear least-squares method based on the equation error is commonly used since the processing involved in the implementation is straightforward. As is known the method has a very serious drawback that the estimate is principally biased. In order to overcome this problem, recently, the generalized least-squares method and the instrumental variable method have been suggested. However, in these methods, it is not yet proved analytically that the estimates converge to the true parameter values. Also, in the generalized least-squares method, the noise parameters, which are not necessary if only the system is to be identified, have to be estimated in conjunction with the required system parameters.
This paper proposes a new linear parameter estimation method which is established with introducing the “Complex Equation Error.” The complex equation error corresponds to the Fourier transformation of the ordinary equation error. By applying this method, the consistent estimate of system parameters can be obtained through a simple linear procedure.
