Research On Identification Methods For Errors-in-Variables Linear Systems

Most of the existing identifications assume that the output of the system contains disturbance,and the input does not contain disturbance.In the actual processes,not only the output of the systems will be corrupted by noise,but the input will also be corrupted by additional measurement noise.A system in which both input and output contain disturbance noise is called errors-in-variables system.Therefore,it has important theoretical significance and application prospects to study the parameter identification methods of errors-in-variables system with disturbance in the input and output.The main contents are as follows:1.For the errors-in-variables equation-error system corrupted by white noise,the least squares estimate is biased.The bias term is related to the input noise variance.Therefore,using the statistical characteristics of the system identification model equation error,calculate the autocorrelation function of the identification model equation error,and construct an additional equation about the input noise variance to estimate the input noise variance.Then the bias compensation least squares iteration algorithm is proposed.2.For the errors-in-variables equation-error system corrupted by white noise,analyze the correlation between the system identification model equation error and the delayed noisy output.Introduce the correlation function,calculate the cross-correlation function of the information vector and the delayed noisy output,and analyze its relationship with the autocorrelation function of the noisy output.An additional equation about the input noise variance is constructed to estimate the input noise variance,and then the correlation function-based bias compensation least squares iterative algorithm is proposed.3.For the errors-in-variables output-error system corrupted by white noise,the least squares estimates are also biased.In order to eliminate the bias term,the correlation analysis method is used to derive the identification model based on the correlation function,and the correlation function-based recursive least squares algorithm is proposed.In order to directly use noisy input and output data,combing with the principle of instrument variable,the correlation function-based instrumental variable least squares algorithm is proposed.4.For the errors-in-variables output-error system corrupted by colored noise,that is,the output of the system is corrupted by the moving average model noise.Since the least squares estimate of the system is also biased,using the idea of correlation analysis,the system identification model based on correlation function is derived.Introducing the multi-innovation theory,the correlation function-based multi-innovation least squares algorithm with low identification error is proposed.For all the algorithms proposed above,this thesis gives the derivation steps,flowcharts and simulation examples.In order to illustrate the effectiveness of these algorithms,parameter estimation accuracy are compared.Finally,the thesis draws conclusions and prospects.At the end of the thesis,a summary and prospect of the current work are given.It also briefly introduces some difficulties in the identification of errors-in-variables system and the directions that are worthy of in-depth study.