In this paper, we present a new sensor location model that aims to maximize observability of link densities in a dynamic traffic network described using a piecewise linear system of ordinary differential equations. We develop an algebraic approach based on the eigenstructure to determine the sensor location for achieving full observability with a minimal number of sensors. Additionally, a graphical approach based on the concept of structural observability is developed. By exploiting the special property of flow conservation in traffic networks, we derive a simple analytical result that can be used to identify observable components in a partially observable system, which is the main contribution of this paper. The graphical and algebraic properties of observability are then integrated into a sensor location optimization model considering a wide range of traffic conditions. Through numerical experiments, we demonstrate the good performance of our sensor deployment strategies in terms of the average observability and estimation errors.

中文翻译：

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考虑交通动态可观察性的传感器放置：从代数和图形角度


在本文中，我们提出了一种新的传感器位置模型，旨在最大限度地提高动态交通网络中链路密度的可观测性，该模型使用常微分方程的分段线性系统进行描述。我们开发了一种基于特征结构的代数方法来确定传感器位置，从而以最少数量的传感器实现完全可观测性。此外，还开发了一种基于结构可观测性概念的图形方法。通过利用交通网络中流量守恒的特殊特性，我们得出了一个简单的分析结果，可用于识别部分可观测系统中的可观测成分，这是本文的主要贡献。然后，将可观测性的图形和代数属性集成到传感器位置优化模型中，考虑各种交通状况。通过数值实验，我们展示了传感器部署策略在平均可观测性和估计误差方面的良好性能。