Weighted hierarchical stochastic gradient identification algorithms for ARX models

In this paper, a weighted hierarchical stochastic gradient algorithm and a latest estimation-based weighted hierarchical stochastic gradient algorithm for ARX models are proposed. Different from some existing stochastic gradient algorithms, the correction term of the developed algorithms is in a weighted form of the correction terms in the current and last recursive steps of the hierarchical stochastic gradient algorithm. Further, the convergence property of the presented latest estimation-based weighted hierarchical stochastic gradient algorithm is analysed. It is illustrated by a numerical example that both the weighted hierarchical stochastic gradient and the latest estimation-based weighted hierarchical stochastic gradient algorithms possess higher convergence accuracy compared with some existing hierarchical stochastic gradient algorithms if the weighting factor is appropriately chosen.