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Recursive Identification of Hammerstein With Noisy Observations *

机译：具有嘈杂观察结果的Hammerstein递归识别 *

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The paper considers the recursive identification of Hammerstein systems with noisy output, while its input may or may not be corrupted by noise. The system in the latter case is usually called as EIV system. The conditions required in this paper are considerably weaker than those used in previous works, e.g., the orders of the linear subsystem are allowed to be unknown and no additional conditions are imposed on its moving average part. The nonlinearity is general in the sense that a certain class of functions is out of consideration in some previous papers. In the paper, the almost sure convergence together with convergence rate are established for the estimates for coefficients of the linear part, and then the almost sure convergence for the estimates for the nonlinearity at any given points are derived by using kernel functions. The convergence rate for the nonlinearity is also obtained for the case where the system input is available without noise. A numerical example is provided, and the simulation results are consistent with the theoretical analysis.
机译：本文考虑了具有噪声输出的Hammerstein系统的递归识别，而其输入可能会或可能不会被噪声破坏。在后一种情况下，该系统通常称为EIV系统。本文要求的条件比以前的工作要弱得多，例如，允许线性子系统的阶数未知，并且对其移动平均数部分不施加其他条件。在某些先前的论文中没有考虑某种功能的意义上说，非线性是普遍的。在本文中，建立线性部分系数估计的几乎确定的收敛性和收敛速度，然后使用核函数推导任意给定点的非线性估计的几乎确定的收敛性。在系统输入可用而无噪声的情况下，也可以获得非线性的收敛速度。给出了算例，仿真结果与理论分析吻合。

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