Bias Compensation Based Least Squaresestimation With A Forgetting Factor For Errors-in-variables Models

Errors-In-Variables(EIV) models are a class of systems with noises in the input and output. When the standard least-squares(LS) identification algorithms are applied to this kind of models, the parameter estimation is biased. In or der to overcome this shortcoming, a feasible method is to estimate the bias term from the standard LS algorithm, and then obtain the consistent estimation by compensating the bias. This idea is the so-called bias compensation. Furthermore, in order to estimate time-varying parameters, a forgetting factor can be introduced to reduce the impact of the old data. In this dissertation, based on the idea of bias compensation, unbiased LS algorithms with a forgetting factor for EIV models are developed. The proposed algorithms can be applied for the parameter identification of parameter time-varying systems. The main content of this dissertation is as follows.First, the recursive least-squares(RLS) algorithms for EIV models with a forgetting factor are analyzed, and then the expression of the bias term in the standard LS identification algorithms is given.For EIV models with white noises in both input and output, a known augmented parameter is introduced to obtain the bias term, and then two equations related to the weighted variances of the two noises are formulated. With the estimated weighted variances, the estimate of the bias term is derived. Based on the aforementioned preliminaries, the bias compensation based RLS algorithms with a forgetting factor(FFBCRLS) are proposed in this dissertation for the EIV models.For EIV models with white noises in input and colored noises in output, a pre-filter with known zeros is introduced to derive the bias term, and then a set of equations related to weighted variances of the input noises and weighted co-variances of output noises are obtained. With these, the FFBCRLS algorithms are proposed for this kind of EIV models.Finally, simulations are conducted to check the performance of the proposed identification algorithms. The EIV models with different time-varying parameters are under tests. It is illustrated that the two proposed algorithms in this dissertation have better performance compared with some existing identification algorithms.