Studies And Improvements Of Parameter Estimation Methods For System Models With Complex Heavy Tailed Noises

In many engineering practices,the stochastic noise disturbance of the system usually presents a heavy tailed distribution as the presence of outliers or the impulse interference.Research shows that the performance of the parameter estimation algorithms which based on the assumption of Gaussian noise will have a serious decline when the noise is heavy tailed.Therefore,it is of great theoretical and practical value to develop robust identification methods for heavy tailed noise.In this paper,according to the different types of stochastic system and consider the presence of heavy tailed noise,we proposed the corresponding robust identification methods for some typical models.The specific work is as follows:1.The development of system identification is reviewed,and the research status of parameter estimation problems is summarized.Moreover,the basic knowledge related to our subject such as the basic model classifications,the commonly used input signals,the typical heavy tailed noises,and so on,is introduced.2.For a class of output error moving average systems with heavy tailed noise interference,a robust identification scheme based on the iteratively reweighted correlation analysis algorithm is given,and for the imperfections of weighting function in robustness and reliability,the Tukey's m estimator is introduced,thus an improved algorithm is proposed.This algorithm can completely reject the outliers in a given region so that the robustness is improved,and the difference in the accuracy of parameter estimation between the modification in algorithm is shown by the simulation example.3.For a class of multivariable Box-Jenkins systems with heavy tailed noise interference,the submodel method is used to decompose it,and for the several multiple input single output subsystems,an iteratively reweighted generalized extended least squares algorithm is proposed.By constructing an extended parameter vector and information vector,the parameters of the system model and the noise model can be identified simultaneously.For the heavy tailed noise,this algorithm introduces the weighting function based on the Hampel's m estimator into the iterative process,by selecting the appropriate threshold parameter values,the proposed algorithm is not only robust to the heavy tailed noise but also effective in Gaussian noise.Simulation results indicate the effectiveness of the proposed algorithm.4.For a class of typical nonlinear Hammerstein systems,a robust iterative identification method is studied under the maximum likelihood framework,when the noise is heavy tailed Gaussian mixture distribution.The expectation maximization algorithm is used to solve the likelihood function with hidden variables,which can effectively weaken the influence of heavy tailed noise while guaranteeing the iterative convergence.This method can identify not only the parameters of the nonlinear model,but also the parameters of the noise distribution function.Finally,the difference between the related algorithms in parameter estimation is given by the simulation example.