Hierarchical multi-innovation generalised extended stochastic gradient methods for multivariable equation-error autoregressive moving average systems

This study presents the modelling technology of multivariable equation-error autoregressive moving average (EEARMA) systems through observational data of systems. Aiming to develop a simplified identification algorithm, the original multivariable EEARMA model to be identified is separated into two sub-identification models. After the model decomposition, a two-stage generalised extended stochastic gradient (GESG) algorithm is presented in accordance with these two separated submodels. By adding more observations to the recursive computation, the corresponding two-stage multi-innovation GESG (MI-GESG) algorithm, namely, hierarchical multi-innovation generalised extended stochastic gradient algorithm, is derived for the multivariable EEARMA systems through expanding the innovation vector to the innovation matrices. The simulation example verifies that the performance about the computational accuracy of the two-stage MI-GESG algorithm is improved compared with the two-stage GESG algorithm.