Weighted Multi-innovation Stochastic Gradient Identification Algorithms For Output Error Models

Parameter identification is the premise and foundation for the analysis and designing of controlled systems.The stochastic gradient identification algorithm is a type of common that differs from the least square identification algorithm.Because it uses less of the system information at each step of the recursive process,the stochastic gradient algorithm has a smaller computational load,but its identification precision is also simultaneously reduced.There are many kinds of system models for parameter identification.The output error model is a common identification model,which include the output error model,the output error auto regression model,output error moving average model and output error auto regressive moving average model.This dissertation focuses on the output error identification model and the stochastic gradient identification algorithm,through a series of improved ideas such as weighted,multi-innovation and the latest estimation,the basic stochastic gradient algorithm is improved,and the improved identification algorithms based on output error model have higher precision and faster convergence speed,and they also have a smaller computational load.The specific research contents are as follows:In order to improve the problem of low utilization ratio of the system information,this dissertation uses the weighted and the multi-innovation ideas to improve the basic stochastic gradient identification algorithm,and also introduces a weighted value to combine the correction term at the current time and the last time at each step of the recursive process,and then deduces the weighted multi-innovation stochastic gradient algorithm based on the four types of output error models.In order to improve the identification precision of the weighted multi-innovation stochastic gradient identification algorithm,this dissertation uses the latest estimation identification ideas to improve the weighted multi-innovation stochastic gradient identification algorithm.Particular way is,using the parameter estimation at the latest time to instead of it at the previous time,and then obtains the weighted multiinnovation stochastic gradient algorithm based on latest estimation for the four types of output error models.In order to validate the effectiveness of the proposed identification algorithm,this dissertation does some MATLAB simulations of the basic stochastic gradient identification algorithm and the improved algorithms proposed in this paper for each of the four specific output error models.The simulation results verify the effectiveness of the improved algorithms.If we choose an appropriate weighted value,the improved algorithms can have greater precision than the basic stochastic gradient algorithm.This dissertation lists the calculation form of the improved algorithms and the basic stochastic gradient algorithm,through the computational load and the simulation experiment results,it can be found that the proposed algorithms can have the same identification precision as the basic stochastic gradient or better identification precision than the basic stochastic gradient algorithm under the condition of the smaller computational load.The complete proof process of the convergence of weighted stochastic gradient identification algorithm and the weighted stochastic gradient identification algorithm based on latest estimation are given in this dissertation.The verification also demonstrate the effectiveness of the improved identification algorithms proposed in this dissertation.