Bias-compensation based method for errors-in-variables model identification

It is well known that least-squares (LS) method gives biased parameter estimates when the input and output measurements are corrupted by noise. One possible approach for solving this bias problem is the bias-compensation based method such as the bias-compensated least-squares (BCLS) method. In this paper, a new bias-compnesation based method is proposed for identification of noisy input-output system. The proposed method is based on compensation of asymptotic bias on the instrumental variables type (IV-type) estimates by making use of noise covariances estimates. In order to obtain the noise covariances estimates, an overdetermined system of equations is introduced, and the noise covariances estimation algorithm is derived by solving this overdetermined system of equations. From the combination of the parameter estimation algorithm and the noise covariances estimation algorithm, the proposed biascompensated instrumental variables type (BCIV-type) method can be established. The results of a simulated example indicate that the proposed algorithm provides good estimates.