Multi-Innovation Stochastic Gradient Type Identification Methods

Regular identification,for example least squares,Kalman filtering and least mean square algorithm are the parameter estimation methods using the single-innovation modification technology. The multi-innovation identification method extends the single-innovation identification, has good convergence property and strong robustnesand and can overcome the effect of bad data on parameter estimation.Therefore,this thesis is not only significant in theory,but also potentially valuable in applications and multi-innovation stochastic gradient type identification methods is made of the research title of the thesis,which is based on the project "Study of Modelling and Identification of a Class of Nonlinear Systems(The National Nature Science Foundation of China 60574051)".This thesis is a kind of basal research and has meaning both in thearoy and applications.After correlative references are refered by the author,the multi-innovation identification problems of systems with colored noise and the nonlinear input are studied and convergence properties of some parameter estimation methods propesed are analyzed.And results are presented as follows.Multi-innovation stochastic gradient type identification methods for linear models:1.Some methods have been studied to identify the parameters of linear models with colored noise in academia,such as least squares,stochastic gradient,identification and so on.But the computation of the least squares is too large,and the convergengce rate of the stochastic gradient identification is too slow.In order to improve convergence rate,the thesis first makes the stochastic gradient type identification method based on the multi-innovation for the linear controlled AR models(CAR models).Then the thesis derivates the multi-innovation stochastic gradient parameter eatimation for the controlled ARMA models(CARMA models) based on the extended stochastic gradient identification. With stochastic process theory and martingale theory the convergence properties of multi-innovation extended stochastic gradient identification method are proved.Some examples are given to testify multi-innovation stochastic gradient identification methods have faster convergence rate than the regular stochastic gradient identification methods in the end.2.Based on the studies of CAR models,the thesis applies multi-innovation identification methods to more complicated linear models,just as dynamic adjustment models(CARAR models) and general stochastic system models(CARARMA models).And multi-innovation generalized stochastic gradient identification and multi-innovation generalized extended stochastic gradient identification are researched to estimate and compute parameters of these models.Then simulation examples are given to demonstrate the methods for these models are proposed.Multi-innovation stochastic gradient type identification methods of the nonlinear input models: 3.Based on the studies of multi-innovation(extended) stochastic gradient identification for the linear CAR and CARMA models,with this method the thesis identifies the nonlinear input CAR models and gives the detailed steps to estimate parameters.And then the parameter estimation errors under the persistent,excitation condition is studied.The following digital examples illustrate the properties of the methods are good.4.To aim at the nonlinear input models with colored noise,the thesis researches on multi-innovation extended stochastic gradient identification for the nonlinear input CARMA models, multi-innovation generalized stochastic gradient identification for the nonlinear input dynamic adjustment models(CARAR models) and multi-innovation generalized extended stochastic gradient identification for the nonlinear input CARARMA models.And digital examples is concluded.The digital simulation shows that multi-innovation generalized stochastic type gradient identification may improve the convergence rate and identification precision a lot.Finally,a simple conclusion of this thesis is given.The difficulties and further objectives of stochastic gradient type identification methods based on the multi-innovation theory are also simply outlined in the end.