Bias compensation-based recursive least-squares estimation with forgetting factors for output error moving average systems

The bias compensation technique combined with the least-squares estimation algorithm with forgetting factors is applied to the parameter estimation of output error models with moving average noise. It is shown that the bias term induced by the noise is determined by the weighted average variance of the white noise and the parameters of the unknown noise model. Therefore, in order to give a recursive estimation of the bias term, an interactive estimation of the weighted average variance and noise parameters is constructed by using the principle of hierarchical identification. In addition, a recursive form is also established to estimate the so-called weighted average variance of the white noise. The estimation algorithm is finally established by combining the interactive estimation and the recursive estimation of weighted average variance. A simulation example is employed to show the effectiveness of the proposed bias compensation based least-squares estimation algorithm with two forgetting factors.