The Asymptotic Method For The Identification Of Errors-in-Variables Systems

In the production process and life of mankind,a system can be considered as a collec-tion of objects which are arranged in an ordered form.Systems vary from an amplifer consisting of electronic components to the global society and economy.People always cognize and describe a system by the input-output relations.System identification is a theoretical and practical science based on the basis,and it is used as a tool to describe and cognize a system.The existed mature system identification methods assume that the process input data is noise-free,which is true in control systems as the inputs are always given by computer directly.These approaches are called common identifica-tion without input noise.However,in most applications,such as the population growth modeling,the infectious disease transmission modeling,the fault monitoring,the en-vironment modeling etc.,the measured input data is noise-corrupted.Systems where errors or measurement noises are present on both inputs and outputs are called errors-in-variables(EIV)systems.For EIV systems,the common identification methods all give biased estimation,which leads the reduction of the model accuracy.Compared to the common identification,EIV system identification is in an immature stage and basic problems still need to be resolved.EIV system identification is the research difficulty and hot spot in the field of system identification.Based on the asymptotic identification theory,this paper proposes the asymptotic esti-mation method of EIV system for both single input-single output(SISO)systems and multi-input multi-output(MIMO)systems.The detailed research work are summarized as follows.1.A method of ARX model estimation of EIV systems.The most widely used method for estimating input noise-free ARX model is the least-squares(LS)method.After analyzing the bias when applying least-squares method to EIV systems,a correlated output error(COE)criterion and a method of ARX model estimation of EIV systems(named as ARX-EIV method)are proposed.The COE criterion is used to estimate the input noise variance.Consistency of the proposed estimation is proved.Simulations are used to illustrate its performance.2.The asymptotic theory for ARX model estimation of EIV systems.The asymptot-ic theory of EIV systems is the theoretical base for model order reduction of the asymptotic method.Assuming that the model order increases as the number of estimation data increase,the asymptotic properties of the estimated ARX model are studied.The asymptotic properties of the estimated ARX model parameter-s are derived,then the asymptotic theory of the ARX model is proved and the expression for the asymptotic variance of the model is derived.3.The asymptotic method for the identification of EIV systems.The asymptotic method starts with a high-order ARX model estimation followed by a frequen-cy domain weighted model reduction.When obtaining the consistent method of ARX model estimation of EIV systems and the asymptotic theory for ARX mod-el estimation of EIV systems,an asymptotic method is developed for the EIV systems(named as EIV-ASYM method),the obtained model is consistent and a criterion for model order selection which is based on frequency domain consid-erations is proposed.Simulations and comparisons with other methods are used to illustrate the performance of the method.4.The asymptotic method for the identification of multi-input multi-output EIV sys-tems.Based on the asymptotic method for single input-single output EIV sys-tems,the EIV-ASYM method is extended to the MIMO case,which makes the applications of the EIV-ASYM method more wide.The multivariable correlated output error criterion and the power spectrum extraction method are developed for estimating the input noises variances.The MIMO version of the asymptotic theory for ARX model estimation of EIV systems is presented.The MIMO ver-sion of the asymptotic method for the identification of EIV systems is developed.Simulations are used to illustrate the performance of the method.Finally,the research work of this paper is summarized,and the perspective of the future work is presented.