Exploiting multi-vehicle interactions to improve urban vehicle tracking

The subject of traffic flow modeling began over fifty years ago when Lighthill and Whitham used flow continuity equation from fluid dynamics to describe traffic behavior. Since then, a multitude of models, broadly classified into macroscopic, mesoscopic, and microscopic models, has been developed. Macroscopic models describe the space-time evolution of aggregate quantities such as traffic flow density whereas microscopic models describe behavior of individual drivers/vehicles in the presence of other vehicles. In this paper, we consider tracking of vehicles using a specific microscopic model known as the intelligent driver model (IDM). As in other microscopic models, the IDM equations of motion of a vehicle are nonlinearly coupled to those of neighboring vehicles, with the magnitudes of coupling terms becoming larger as vehicles get closer and smaller as vehicles get farther apart. In our approach, the state of weakly coupled groups of vehicles is represented by separated probability distributions. When the vehicles move closer to each other, the state is represented by a joint probability distribution that takes into account the interaction among vehicles. We use a sum of Gaussians approach to represent the underlying interaction structure for state estimation and reduce computational complexity. In this paper we describe our approach and illustrate the approach with simulated examples.