A Traffic Model for Velocity Data Assimilation

Abstract

This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which the observation operator is linear. This article presents a new scalar hyperbolic partial differential equation (PDE) model for traffic velocity evolution on highways, based on the seminal Lighthill-Whitham-Richards (LWR) PDE for density. Equivalence of the solution of the new velocity PDE and the solution of the LWR PDE is shown for quadratic flux functions. Because this equivalence does not hold for general flux functions, a discretized model of velocity evolution based on the Godunov scheme applied to the LWR PDE is proposed. Using an explicit instantiation of the weak boundary conditions of the PDE, the discrete velocity evolution model is generalized to a network, thus making the model applicable to arbitrary highway networks. The resulting velocity model is a nonlinear and nondifferentiable discrete time dynamical system with a linear observation operator, for which a Monte Carlo based ensemble Kalman filtering data

Travel Time and Point Speed Fusion Based on a Macroscopic Traffic Model and Non-linear Filtering

“…)in the state space model (1) is a macroscopic traffic model, the cell transmission model for velocity (CTM-v) in our case. The CTM-v model [12] is a first order model based on the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) [16] discretized using the Godunov scheme [17] and then translated from density to velocity using the hyperbolic-linear fundamental diagram [12]. Due to the nonlinearity and non-differentiability of the model and a relatively large state-vector, the method chosen for data assimilation and fusion is the ensemble Kalman filter.…”

“…Due to the nonlinearity and non-differentiability of the model and a relatively large state-vector, the method chosen for data assimilation and fusion is the ensemble Kalman filter. The EnKF and CTM-v framework is first described in [12] where details about the model as well as the filtering can be found. The adaption of the framework for the Stockholm network, which is used in this paper, is described in [18].…”

“…Given the forecasted ( ) and the analyzed ( ) estimate of the state covariance in time step n, the EnKF algorithm can be summarized as follows [12] [12], then update the ensemble mean and covariance according to:…”

“…There is a simple relationship between average speed and travel time: . In practice, we need to discretize our system, hence, with a set of discrete cells with length i s , the travel time becomes (12) where j v is the average speed in cell j and J is the set of cells traversed in the travel time observation. The travel time observation is a nonlinear function of the state, which means that we can not use this observation model directly in the filter.…”

Emerging, Collective Intelligence for Personal, Organisational and Social Use

“…There already exist a number of approaches, which use user-contributed content in order to provide useful information for various applications. For example, mobile location information and uploaded content is used to monitor online traffic and generate traffic patterns in [1], connect citizens in Boston [2], share nature experience [3], discover travel patterns and provide travel advice [4] [5], or communicate problems in a city [6]. The MIT Center for Collective Intelligence 1 is hosting a series of projects aiming at harnessing and using Collective Intelligence.…”