This paper proposes a subspace identification method for closed-loop EIV (errors-in-variables) problems based on instrumental variables . First, a unified framework is derived, and then the reason is discussed why some existing subspace methods based on instrumental variables could be biased under closed-loop conditions. Afterwards a remedy is given to eliminate the bias by simply replacing the instrumental variable. Using orthogonal projection, the resulting instrumental variable method is very simple and easy to extend. In addition, simulation studies illustrate the effects of different instrumental variables.

中文翻译：

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正交投影基于工具变量的闭环EIV系统子空间识别

本文提出了一种基于工具变量的闭环EIV问题的子空间识别方法。首先，导出一个统一的框架，然后讨论在闭环条件下为什么一些基于工具变量的现有子空间方法可能存在偏差的原因。之后，给出了一种补救措施，只需替换工具变量即可消除偏差。使用正交投影，所得的仪器变量方法非常简单且易于扩展。此外，仿真研究还说明了不同工具变量的影响。