The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes.

中文翻译：

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具有相关噪声的动态网络中模块识别的局部直接方法

具有已知拓扑结构的动态网络中局部模块的识别最近已经通过制定条件来实现模块动态的一致估计，假设具有在不同节点上不相关的干扰。这些条件通常反映了一组节点信号的选择，这些节点信号在 MISO 识别设置中被用作预测器输入。在本文中，对不同节点信号上的过程噪声可以相互关联的情况进行了扩展以达到识别设置。在这种情况下，本地模块可能需要嵌入到 MIMO 识别设置中，以达到具有最大似然特性的一致估计。这需要正确处理混杂变量。结果是一组算法，根据给定的网络拓扑和干扰相关结构，选择一组合适的节点信号作为 MISO 或 MIMO 识别设置中的预测器输入和输出。提出了三种算法，它们在选择测量节点信号的方法上有所不同。可以考虑最大或最小数量的测量节点信号，以及预先选择的一组测量节点。