A particle filter for freeway traffic estimation

Abstract

Abstract-This paper considers the traffic flow estimation problem for the purposes of on-line traffic prediction, mode detection and ramp-metering control. The solution to the estimation problem is given within the Bayesian recursive framework. A particle filter (PF) is developed based on a freeway traffic model with aggregated states and an observation model with aggregated variables. The freeway is considered as a network of components, each component representing a different section of the traffic network. The freeway traffic is modelled as a stochastic hybrid system, i. [12].In the present paper we develop a particle filter for freeway traffic flow estimation. Particle filters (PFs) are appropriate for traffic state estimation because they can cope with large, and highly nonlinear models as well as non-Gaussian signals. The structure of the particle filter corresponds closely to compositional modelling, and it allows a parallelization for different sections of the road, thus allowing a reduction in the computational time.In [21] a solution to highway traffic estimation is proposed using a sequential Monte Carlo algorithm, based on first-order traffic models (only dynamics of the traffic density is modelled), distinguishing between the free-flow mode and the congestion mode. The traffic mode is estimated via a Monte Carlo technique, the so called mixture Kalman filter [5] which is applied for recursively estimating the traffic density. In contrast to [21], the traffic in the present paper is described by a second-order model, and we develop a filter that estimates both traffic density and speed.The particle filter presented in Section IV uses aggregated traffic and observation models. The state model is a recently developed compositional model [4] for freeway traffic. Sending and receiving functions describe respectively the downstream and upstream propagation of perturbations. The freeway is considered as a network of components (Fig. 1), each component representing a different section of the traffic network. Several sections form a link. Sensors are available only at some boundaries between sections. Measurements are averaged over regular or irregular time intervals before being transmitted to the estimation agent. Within the estimation agent an update of the conditional distribution of the traffic density and speed estimate is performed using Monte Carlo simulation (for all sections concurrently and possibly via parallel processing). Whenever a new measurement is received a Bayesian update of this conditional distribution is evaluated via the PF. The PF can easily be extended to models where for the very important sections a detailed model is used, while for other sections a more aggregate, coarse model is employed. 43rd IEEE Conference on Decision and Control

Applicable filtering framework for online multiclass freeway network estimation

“…These are undesirable because in traffic flow these errors may act as perturbations that are propagated through the traffic model and end up with unrealistic traffic jam when they grow large enough. To overcome these disadvantages of the EKF method to highly non-linear traffic models, improved filtering techniques have been introduced for freeway traffic estimation, ranging from Unscented Kalman Filter method [13] to Particle Filter method [14,15]. However, a generic filtering framework applicable to multiclass freeway networks has not been well-established.…”

An Unscented Kalman Filter for Freeway Traffic Estimation

“…The UKF performance is evaluated versus the PF developed in (Mihaylova and Boel 2004) over of freeway stretch of 4 [km] consisting of eight segments with data, having periods of congestion. The data are generated by the compositional model (Boel and Mihaylova 2006) with independent measurement noises for different runs and with different initial state conditions.…”

“…The traffic is described by the recently developed model (Boel and Mihaylova 2006) that is an extension to the cell-transmission model (Daganzo 1994). We compare the UKF to the PF from (Mihaylova and Boel 2004). The freeway network is modelled as a sequence of segments (Fig.…”

“…In (Sun et al 2003) a solution to highway traffic estimation is proposed by a sequential Monte Carlo algorithm, the so-called mixture Kalman filtering, and in (Mihaylova and Boel 2004) a particle filter (PF) is developed. The mixture Kalman filter (MKF) (Chen and Liu 2000) is essentially a bank of Kalman filters run with the Monte Carlo sampling approach.…”

Distributed Particle Filter for Urban Traffic Networks Using a Platoon-Based Model

“…It is a standard algorithm for recursive estimation problems where a full Bayesian update of the estimated quantity's probability distribution is computationally infeasible. The PF has been already used for motorway traffic estimation [2], [8], [13]; we have recently proposed to adapt it for urban traffic as well [10]. In [16], recursive traffic state estimation is achieved via a Kalman filter (KF) combining sensor data with conservation equations of vehicles.…”