Hierarchical extended parameter identification methods and convergence for finite impulse response moving average models based on the hierarchical identification principle

Hierarchical least squares is the extension of recursive least squares and the hierarchical least squares algorithm has higher computational efficiency than the recursive least squares algorithm. On the basis of reviewing and surveying some important contributions in the literature of system identification, this article explores some hierarchical extended identification methods for finite impulse response moving average models from observation data, including the hierarchical extended stochastic gradient algorithm, the hierarchical multi-innovation extended stochastic gradient algorithm, the hierarchical extended gradient algorithm, the hierarchical multi-innovation extended gradient algorithm, the hierarchical extended least squares algorithm and the hierarchical multi-innovation extended least squares algorithm. The proposed extended hierarchical methods for the finite impulse response moving systems can be extended to equation-error autoregressive moving average systems and output-error autoregressive moving average systems.