Transfer function estimation from noisy input and output data

Two new types of bias-eliminated least-squares (BELS) based algorithms are proposed for consistent identification of linear systems with noisy input and output measurements. It is shown that estimation of the noise variances can be implemented through one-dimension over-parametrization of the system transfer function. The two modified BELS algorithms are attractive and meaningful in that noisy data are used directly in identification with no prefiltering and a direct estimate of system parameters is given without any parameter transformation. Simulation examples are included to demonstrate the effectiveness of the two proposed algorithms.