In this paper, weighted stochastic gradient (WSG) algorithms for ARX models are proposed by modifying the standard stochastic gradient identification algorithms. In the proposed algorithms, the correction term is a weighting combination of the correction terms of the standard stochastic gradient (SG) algorithm in the current and last recursive steps. In addition, a latest estimation based WSG (LE-WSG) algorithm is also established. The convergence performance of the proposed LE-WSG algorithm is then analyzed. It is shown by a numerical example that both the WSG and LE-WSG algorithms can possess faster convergence speed and higher convergence precision compared with the standard SG algorithms if the weighting factor is appropriately chosen.
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