Identification of noisy input-output models using the least-squares based methods

This paper addresses the problem of parameter estimation of noisy input-output models, where the measurements of both the input and the output of the system are corrupted by noise. Motivated by the fact that the Koopmans-Levin method and the maximum likelihood estimation type methods assume the known ratio of the variances of the input noise and the output noise, some key equations are derived by using correlation analysis and the knowledge of the noise variance ratio. An objective function is introduced for the purpose of solely finding the input noise variance. An estimate of the system parameters can then be easily obtained without involving any iteration procedure. This leads to the establishment of an efficient identification algorithm. Performance comparisons with other existing identification methods are made via computer simulations.