Sensor placement considering the observability of traffic dynamics: On the algebraic and graphical perspectives

In this paper, the authors 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. They 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, the authors 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, the authors demonstrate the good performance of our sensor deployment strategies in terms of the average observability and estimation errors.