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The fundamental role of general orthonormal bases in system identification

机译:一般正交基在系统识别中的基本作用

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The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well-known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalized Fourier series and the asymptotic properties of Toeplitz-like matrices in such a way that the new variance expressions presented here encompass pre-existing ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them.
机译:本文的目的是三方面的。首先,要确定与预期相反的是,众所周知且经常使用的渐近方差结果的准确性可能取决于模型结构中固定极点或零点的选择。其次,要导出新的方差表达式,该表达式可以提供大大提高的准确性,同时还可以明确显示任何固定极点或零点的影响。这是通过在广义傅里叶级数和Toeplitz-like矩阵的渐近性质上采用某些新结果而实现的,这种方式使得此处介绍的新方差表达式包含已存在的特殊情况作为特殊情况。通过后面的分析,有关在系统识别中使用正交基础结构的最新工作出现了新的观点。即,正交基不只是提供改进的数值属性的实现选项。实际上,它们是估计的一个内在部分,因为如此处所示,正交基数量化了估计的渐近变异性,无论它们是否实际用于计算它们。

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