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首页> 外文期刊>IEEE Transactions on Automatic Control >The Weighted Nearest Neighbor Estimate for Hammerstein System Identification
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The Weighted Nearest Neighbor Estimate for Hammerstein System Identification

机译：Hammerstein系统识别的加权最近邻估计

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This paper concerns the nonparametric identification problem for a class of nonlinear discrete-time dynamical systems that is characterized by its cascade structure. This is a Hammerstein system being a series connection of a nonlinear memoryless element followed by a linear dynamic system. The input-output training data generated from the system are dependent and they do not reveal the strong mixing property. The nonlinear part of the system is recovered with the weighted k-nearest neighbor regression estimate. The a priori information is nonparametric, both the nonlinear characteristic and the impulse response of the linear part are completely unknown and can be of any form. Local and global properties of the estimate are examined. Whatever the probability density of the input signal, the estimate converges at every continuity point of the characteristic as well as in the global sense. We derive the formulas for asymptotic bias and the variance and evaluate the corresponding rate of convergence. The convergence rate is independent of the shape of the input density and is proved to be optimal. These results allow us to find a set of optimal nonnegative weights that further improve the accuracy of our estimation algorithm. Our findings are supported by simulation experiments.
机译：本文涉及一类非线性离散时间动态系统的非参数识别问题，其特征在于其级联结构。这是Hammerstein系统，是非线性记忆元件的串联连接，后跟线性动态系统。从系统产生的输入输出培训数据取决于，它们没有透露强大的混合性。系统的非线性部分用加权k最近邻回归估计恢复。先验信息是非参数，线性部分的非线性特性和脉冲响应都是完全未知的并且可以是任何形式。审查了估计的本地和全球性质。无论输入信号的概率密度如何，估计会聚在特征的每个连续点以及全局意义上。我们推导出渐近偏差的公式和方差，评价相应的收敛速率。收敛速度与输入密度的形状无关，并且被证明是最佳的。这些结果允许我们找到一组最佳的非负重量，从而进一步提高了我们估计算法的准确性。我们的研究结果得到了模拟实验支持。

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