Bias Compensation Based Least Squares Estimation With A Forgetting Factor For Output Error Models

System identification is to determinate a mathematic model from the observedinput-output data by minimizing some error criterion function. In this domain, theleast squares (LS) method has been widely used. However, a biased parameterestimate may be obtained if this identification method is directly applied to outputerror models. In order to obtain unbiased parameter estimations, the biascompensation technique has been proposed in1970’s. On the other hand, the datasaturation phenomenon is inevitable along with the increase of the observed data ifthe new data has the same influence with the old one. Thus, by introducing aforgetting factor, the influence of the old data can be weakened such that the datasaturation phenomenon is restrained. In addition, most of the practical systemparameters are time-varying. It has been shown that the parameters of time-varyingsystem can be estimated by the LS with a forgetting factor. In this dissertation, withthe combination of bias compensation techniques and the forgetting factor, unbiasedestimation algorithms are derived for output error models. The main researchcontents in the domain are listed as follows.First, a bias compensation with a forgetting factor based least squaresestimation is proposed for output error models, which is perturbed by random whitenoises. In this algorithm, a term of bias compensation is firstly formulated, which isto eliminate the bias. Then a weighted average variance of unknown white noise isestimated, and the unbiased estimates are eventually obtained.For output error models perturbed by colored noises, a bias compensation witha forgetting factor based least squares estimation is also derived, in which apre-filter technique is introduced. By using the known zeros of the filter, the biasterm is compensated and consequently the unbiased estimates are obtained.Finally, the proposed algorithms are tested for their effectiveness. The outputerror models with time-varying parameters which change according to step, linear,square and sine curves are considered. Besides, for comparison, the algorithmswithout a forgetting factor are also considered. The simulation results reveal that theproposed algorithms have advantage for the identification of time-varying systemsover some existing algorithms.