Model transformation based distributed stochastic gradient algorithm for multivariate output-error systems

Abstract

This paper is concerned with the parameter estimation problem for the multivariate system disturbed by coloured noises. Since coloured noises will reduce the estimation accuracy, the model transformation technique is employed to whiten the original system without changing the input-output relationship. In order to alleviate the heavy computational burden caused by high-dimensional variables and different types of parameters, the transformed model is divided into several sub-models according to the numbers of outputs. However, after the decomposition, all the sub-models contain a same parameter vector, resulting in many redundant estimates. A model transformation based distributed stochastic gradient (MT-DSG) algorithm is derived to cut down the redundant estimates and exchange the information among the sub-models. Compared with the centralised multivariate generalised stochastic gradient algorithm, the MT-DSG algorithm has more accurate estimates and less computational complexity. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed method.