Identification of dynamic noisy input-output system

Identification of linear dynamic systems from noisy input and output measurements is studied. In order to deal with this task, a modified bias compensation least square (BCLS) method is proposed. In the proposed method, the backward output predictor (BOP) is introduced. With the help of analyzing the properties of auto-function of least square (LS) error and cross-function of the BOP error and the LS error, the estimate of the asymptotic bias is obtained. Then based on the principle of bias compensation, the consistent parameter estimate of the noisy input-output system can be obtained. Simulation results are given to illustrate the effectiveness of the proposed algorithm.