This paper derives an identification algorithm for Hammerstein nonlinear systems with dynamic disturbances and measurement noise. The dynamic disturbance is viewed as a time-varying sequence to be estimated and its model structure and excitation signal are not considered. By extending the parameter and information vector, an extended recursive least squares algorithm is proposed first time to identify recursively both the system parameters and dynamic disturbance of a Hammerstein output error model. By constructing matrix forgetting factor, the dot product operation is used to update covariance matrix, which improves the estimation accuracy of time-invariant system parameters and the tracking performance of dynamic disturbance. The auxiliary model technique ensures that consistent estimation of model parameters can be obtained. The adaptive forgetting factor improves the convergence rate of the algorithm under finite sampling data. Numerical example with Monte-Carlo simulation test is used to verify the superiority of the proposed algorithm.

本文推导了具有动态扰动和测量噪声的Hammerstein非线性系统的辨识算法。动态扰动被视为一个时变序列进行估计，并且不考虑其模型结构和激励信号。通过扩展参数和信息向量，首次提出了一种扩展的递推最小二乘算法，以递归地识别系统参数和Hammerstein输出误差模型的动态扰动。通过构造矩阵遗忘因子，使用点积运算来更新协方差矩阵，从而提高了时不变系统参数的估计精度和动态扰动的跟踪性能。辅助模型技术可确保获得对模型参数的一致估计。自适应遗忘因子提高了有限采样数据下算法的收敛速度。数值算例与蒙特卡洛仿真实验一起验证了所提算法的优越性。