Stochastic lateral noise and movement by Brownian differential models

The microscopic behavior of the vehicle can be decomposed into car following and lane changing, and can be described by the longitudinal and lateral movement. The longitudinal movement has long been studied, while the lateral counterpart, especially the stochastic lateral movement, has rarely been investigated. The lacking of an understanding of the lateral behavior makes current microscopic simulation results deviate from real-world observations. Besides, many behavior identification algorithms which rely on lateral displacement are not robust, if the lateral stochastic nature is not well studied. To fill in this gap, a stochastic differential equation approach is employed. Firstly, the lateral noise is modeled by a transformed Brownian motion. Then the noise is embedded into a differential lateral movement model. The parameters in the lateral noise and movement models all have clear physical meaning. The Fokker-Planck equation, which describes the distribution evolution of the lateral displacement, is derived. A parameters calibration procedure is derived using the Euler discretization scheme. The model is calibrated using real world data. The results show that the proposed model can well describe the lateral movement distribution.