Resampling Algorithms for Particle Filters: A Computational Complexity Perspective
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10-11 November 2011, Melbourne, Australia
Particle filter state estimator for large urban networks Nicolae Marinic˘a and Ren´e Boel Abstract— This paper applies a particle filter (PF) state estimator to urban traffic networks. The traffic network consists of signalized intersections, the roads that link these intersections, and sensors that detect the passage time of vehicles. The traffic state X(t) specifies at each time time t the state of the traffic lights, the queue sizes at the intersections, and the location and size of all the platoons of vehicles inside the system. The basic entity of our model is a platoon of vehicles that travel close together at approximately the same speed. This leads to a discrete event simulation model that is much faster than microscopic models representing individual vehicles. Hence it is possible to execute many random simulation runs in parallel. A particle filter (PF) assigns weights to each of these simulation runs, according to how well they explain the observed sensor signals. The PF thus generates estimates at each time t of the location of the platoons, and more importantly the queue size at each intersection. These estimates can be used for controlling the optimal switching times of the traffic light. Index Terms— Bayesian estimation, particle filtering, urban traffic, platoon based model, stochastic systems.
I. I NTRODUCTION Estimation and prediction of the traffic state in an urban network is an important component of the feedback loop used in on-line road traffic management. Both PF and the distributed model predictive controllers (MPC) that we use for adapting the switching times, require a fast and simple model describing the location of vehicles in the network. Many different models for both freeway traffic and for urban traffic have been developed. Urban traffic, the topic of this paper, can be described by macroscopic models [4], [5] representing the average traffic behavior in terms of the aggregated variables density and flow, as measured at different locations, or by microscopic models that represent the behavior of each vehicle individually. Microscopic models are suitable for very low density traffic, where no feedback control is necessary, while macroscopic models are suitable for oversaturated traffic where control actions select cycle times, red/green split, and offset. Our work deals with the intermediate traffic load case, and we aim at selecting the actual switching times of the individual traffic lights using local feedback, but trying to maintain as much as possible the green wave, so as to postpone the onset of saturation as much as possible. This requires PF traffic state estimators and MPC controllers that depend on a fast simulations models that can approximately locate all vehicles. In order to efficiently achieve this goal our model groups vehicles into platoons. A platoon consists of vehicles that Nicolae Marinic˘a is with the SYSTeMS Research Group, Faculty of Engineering, University of Ghent, B-9052 Zwijnaarde, Belgium
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