Hierarchical Iterative Identification For Multivariable-like Output Error Type Systems

System identification is to set up a mathematical model from the system input and output data. Recently, the identification problem of the multivariable systems has attracted widespread concern. Since there are many kinds of multivariable systems, and the identification process are much more complex than the single-variable systems. This paper focuses on "Hierarchical Iterative Identification for Multivariable-Like Output Error Type Systems" and the proposed methods are very significant and have broad applications。The paper investigates the identifi-cation problem of the output error class of multivariable systems, and the results are described as follows:1. For the multivariable system with autoregressive noise, an identification model is derived. The identification difficulty lies in that this model contains a parameter vector and a pa-rameter matrix, thus cannot be identified directly. Based on the hierarchical identification principle, a hierarchical generalized least squares algorithm and a hierarchical least square iterative algorithm are derived. The simulation results indicate that the proposed algorithm is effective.2. For the multivariable system with moving average noise, the corresponding hierarchical least squares iterative algorithm and gradient iterative parameter estimation algorithm are derived. Simulation results show that the gradient iterative algorithm has small computa-tion, but the convergence rate is slower than that of the least squares iterative algorithm.3. For the multivariable system with autoregressive moving average noise, a hierarchical least squares iterative algorithm and a gradient algorithm are proposed. The multivariable sys-tem with autoregressive noise and the multivariable system with moving average noise can be regarded as special cases of the the multivariable system with autoregressive moving av-erage noise system Thus the the multivariable system with autoregressive moving average noise system algorithm is more practical. The simulation results indicate that the proposed algorithm is quite effective.In conclusion, in this paper, we propose the identification algorithm for the class of multi-variable output error system, and further perform these algorithms by Matlab. The simulations show that the proposed algorithms are effective for the parameter identification of the multi-variable systems. At last, some difficulties and problems in the area are proposed. Such as the application of the identification in medical science, society, microeconomic or macroeconomic.