Quality of Traffic Observability on Highways With Lagrangian Sensors

Abstract

Observability is essential to estimate the states of a system from sensor measurements. Observability indicates the sufficiency of the sensors for state estimation. In a highway traffic setting, using global positioning system-enabled smartphones as sensors sets this observability problem in the Lagrangian dynamics framework, in which the moving vehicle that follows the microscopic dynamics of the system senses its own current state. This paper addresses the question of how different numbers of sensor vehicles in the traffic stream affect the observability of the system. This was accomplished by performing spatiotemporal discretization of the traffic hydrodynamics to obtain a system on which the rank observability condition was applied. Then, the observability problem for a generic system was studied in terms of the average penetration of these mobile devices in the traffic stream. Simulation results are provided to support the developments in this paper. Note to Practitioners —This paper is motivated by the problem of observing the state of traffic in a highway setting from Lagrangian sensors. These are sensors that travel with individual vehicles rather than the traditional sensors that remain at fixed positions. There is much literature written on traditional sensors, but currently, there is development on what additional value Lagrangian sensors can provide. Lagrangian sensors recently became plausible, and readily available with the growth of smartphones. The problem that is studied is how much of the traffic behavior can be inferred from different numbers of the Lagrangian sensors. A traditional mathematical model for traffic flow is studied in the Lagrangian coordinates. The concept of observability and condition number is used to analyze how much and how well the sensors can capture traffic information. This problem is studied with idealized vehicle behavior, but this paper will be extended to cope with more realistic driving behaviors in the future.