Convergence Analysis of Weighted Stochastic Gradient Identification Algorithms Based on Latest-Estimation for ARX Models

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.