Latest-estimation Based Hierarchical Recursive Stochastic Gradient Algorithm For Output Error Model

The role played by system identification in modern industrial and non-industrial applications has been becoming increasingly important.Almost all the fields including machinery manufacturing,industrial production and the prediction of economic trends require people to grasp the mathematical model of the system.Among many traditional identification methods,the stochastic gradient identification algorithm is widely used since it can greatly reduce the computational complexity by omitting the computation of covariance matrix.However,this method could not make full use of measurable information which results in some problems such as the slow convergence speed and low identification precision.In order to solve this problem,this paper proposes a novel stochastic gradient identification algorithm based on the latest-estimation principle as well as the hierarchical identification.According to the characteristics of output error model and output error moving average model,the basic identification model is obtained via the auxiliary model.Then the hierarchical recursive stochastic gradient algorithm can be obtained by applying the hierarchical principle into identification model.For the output error moving average model,the basic idea is to combine the latest-estimation technique and the decomposition technique and to update estimation value of the noise and the output value of auxiliary model.Based on the features of the output error autoregressive model and the B-J model,the hierarchical stochastic gradient identification algorithm is proposed via the auxiliary models.After updating the estimated values of the auxiliary model output and the noise by applying the principle of the latest-estimation thought,the latest-estimation based hierarchical recursive stochastic gradient algorithm is obtained.The proposed algorithm has been simulated through MATLAB.The results demonstrate that the new algorithm in this paper can track the system parameters better compared with the traditional algorithms.The identification accuracy and convergence speed are both improved.