Asymptotic variance expressions for identified black-box transfer function models
Asymptotic variance expressions for identified black-box transfer function models
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DOI：
10.1109/tac.1985.1104093
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发表时间：
1984-12
期刊：
影响因子：
--
通讯作者：
L. Ljung
中科院分区：
文献类型：
--
作者：
L. Ljung
黑盒传递函数模型的识别被认为是。假设传递函数模型具有一定的移位性质，例如所有多项式型模型都满足该移位性质。传递函数估计的方差的表达式推导，这是渐近的观测数据的数量和模型的订单。其结果是，输入到输出和驱动白色噪声源到加性输出扰动的传递函数的联合协方差矩阵分别正比于输入和驱动噪声的联合谱矩阵的倒数乘以加性输出噪声的谱。比例因子是模型阶数与数据数量的比率。该结果与所使用的特定模型结构无关。结果被施加到评估的性能退化，由于方差的一些典型的模型使用。最后，给出了输入设计的一些结论.
Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.