Bias-compensation-based least-squares estimation with a forgetting factor for output error models with white noise

In this paper, the bias-compensation-based recursive least-squares (LS) estimation algorithm with a forgetting factor is proposed for output error models. First, for the unknown white noise, the so-called weighted average variance is introduced. With this weighted average variance, a bias-compensation term is first formulated to achieve the bias-eliminated estimates of the system parameters. Then, the weighted average variance is estimated. Finally, the final estimation algorithm is obtained by combining the estimation of the weighted average variance and the recursive LS estimation algorithm with a forgetting factor. The effectiveness of the proposed identification algorithm is verified by a numerical example.