Instrumental-variable methods for identification of Hammerstein systems
Instrumental-variable methods for identification of Hammerstein systems
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DOI：
10.1080/00207178208922632
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发表时间：
1982-03
影响因子：
2.1
通讯作者：
P. Stoica;T. Söderström
中科院分区：
文献类型：
--
作者：
P. Stoica;T. Söderström
摘要推导并分析了Hammerstein模型中工具变量方法的相容性条件。有必要有一个没有过度参数化的模型和一个“强烈持续激励”的输入，即输入和它们的功率共同持续激励。一些具体的工具的选择被证明是一致的。这些工具被形成为经滤波的输入和输入的幂。如果输入是白色噪声或者某个传递函数是正实数，则可以保证一致性。一般来说，仪器向量的维数大于参数向量。它表明，然后，一个非奇异的线性变换的工具给出了一个新的和仍然一致的估计。还包括一些使用本文提出的IV变体的模拟。
Abstract Consistency conditions for instrumental-variable methods applied to Hammerstein models are derived and analysed. It is necessary to have a model that is not over-parametrized and an input that is ‘ strongly persistently exciting ’, i.e. the inputs and their powers are jointly persistently exciting. Some specific choices of the instruments are proved to give consistency. Those instruments are formed as filtered inputs and powers of the input. Consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive-real. The vector of instruments is, in general, of larger dimension than the parameter vector. It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate. Some simulations using the IV variants proposed in this paper are also included.