Boundary Multi-Mode Observer for Aw-Rascle-Zhang Traffic Flow Model

With the development of traffic detection technology, spatially discrete traffic data (eg, cross-sectional data) have been transformed to spatially continuous data (eg, trajectory data, images, etc.). In this paper, a continuous multi-mode boundary observer based on Aw-Rascle-Zhang (ARZ) model is designed for continuous measured data and applied to actual road traffic state estimation. We consider both static and dynamic boundary controls for the observer design. By means of Lyapunov based techniques, we derive some sufficient conditions for the observer using only the information from the boundary conditions. With the multi-mode filter method, we employ the linear free-flow observers and congested observers to approach the quasi-linear ARZ model. After that, the state estimates obtained from the different models are fused according to weights, and the fused state is then used as the initial value of PDEs for the next period. A freeway link of Interstate 80 in Emeryville, California is chosen to investigate the performance of the developed observer and multi-mode filter approach.