This article focuses on the parameter estimation for a class of nonlinear systems, that is, multi‐input single‐output or two‐input single‐output Hammerstein finite impulse response systems with autoregressive moving average noise. The key is to investigate new estimation methods for on‐line parameter estimation of the considered system. By using the gradient search and introducing the forgetting factor, the forgetting factor stochastic gradient estimation method is developed. For the purpose of improving the parameter estimation accuracy, the system is decomposed into three subsystems with fewer variables applying the key term separation technique: the first two subsystems contain the unknown parameters related to the input and the third subsystem contains the unknown parameters related to the noise. Then a three‐stage forgetting factor stochastic gradient algorithm is proposed based on the hierarchical identification principle for interactively identifying each subsystem. The simulation results show the effectiveness of the presented algorithm.

中文翻译：

---

一类非线性系统的三阶段遗忘因子随机梯度参数估计方法

本文重点研究一类非线性系统的参数估计，即具有自回归移动平均噪声的多输入单输出或双输入单输出Hammerstein有限脉冲响应系统。关键是研究所考虑系统的在线参数估计的新估计方法。通过使用梯度搜索并引入遗忘因子，发展了遗忘因子随机梯度估计方法。为了提高参数估计的准确性，应用关键术语分离技术将系统分解为三个具有较少变量的子系统：前两个子系统包含与输入有关的未知参数，第三个子系统包含与输入有关的未知参数。噪声。在此基础上，提出了一种基于层次识别原理的三阶段遗忘因子随机梯度算法，用于交互式识别各个子系统。仿真结果表明了该算法的有效性。