Suggested Citation:
Hu, Xinyue (2024)

Sensor Placement Considering the Observability of Traffic Dynamics: on the Algebraic and Graphical Perspectives

. Institute of Transportation Studies, University of California, Davis, Dissertation UCD-ITS-RR-24-87

Abstract:

Traffic data is crucial for traffic operation and management. Traffic sensors serve as one of themost important sources for such data. One important mission of the traffic sensor is to provide an accurate and reliable general picture of the traffic system.

In this dissertation, a new sensor location model is developed to maximize the observability of link densities in a dynamic traffic network described using a piecewise linear ordinary differential equation system. We develop an algebraic approach based on the eigenstructure to determine the sensor location for achieving full observability with a minimal number of sensors. The proposed Algebraic Approach is efficient and generic and it can be applied to any dynamical system with direct state observation. 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.

 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.