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在弱条件下,利用随机鞅理论详细研究了随机梯度辨识算法的收敛性能.分析表明,只要信息向量是持续激励的(或数据乘积矩矩阵条件数有界),过程噪声是零均值不相关的,那么参数估计一致收敛于真参数.这一结论并不要求一些文献中所作的苛刻假设成立,既没有假设噪声方差和高阶矩存在,又没有假设系统是平稳和各态遍历的,也没有假设强持续激励条件成立.这一贡献放松了随机梯度算法的收敛条件.噪声方差有界和无界时的仿真例子证明了提出的收敛结论.
Under weak conditions, the stochastic martingale theory is used to study the convergence performance of stochastic gradient identification algorithm. The analysis shows that the process noise is uncorrelated with zero mean as long as the information vector is continuously excited (or the boundedness of the data product matrix is bounded) , Then the parameter estimates converge uniformly on the true parameters. This conclusion does not require that some of the harsh assumptions made in the literature hold that neither the noise variance nor the higher order moments exist, nor does it assume that the system is stationary and ergodic Suppose the strong continuous excitation condition is established, which relaxes the convergence condition of the stochastic gradient algorithm.The simulation example of the noise variance boundless and unbounded demonstrates the proposed convergence conclusion.