Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

Abstract

This paper proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described in this paper using a mode-dependent first order autoregressive (AR) stochastic process. The parameters of the AR-process take different values depending on the mode of traffic operation -free flowing, congested, or faulty -making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain, and hence we call this hybrid process a jump Markov process. This paper proposes an expectationmaximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied in this paper to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inferences algorithms and an online particle filter (PF). We also develop an EM parameter estimation that, in combination with a time window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator. The proposed parameter estimation technique can thus be used as part of an adaptive model-based filter for feedback control of traffic lights.Keywords: Hybrid system, parameter estimation, particle filter, stochastic system, fault detection, urban traffic networks. 2 IntroductionUrban traffic congestion is a problem that significantly affects many aspects of the quality of life. A more efficient use of the existing road infrastructure, using advanced traffic control strategies, can lead to reduced congestion, reduced emissions, reduced fuel consumption, and improved safety. The model based control strategies that are needed in order to achieve such an improvement depend strongly on the quality and the accuracy of the dynamic model of the system, on the availability of reliable online data and also on the ease of implementation of the control strategy. The model must describe the variability over time of the traffic flow, allowing model based estimation of the current state, fusing noisy traffic data from various traffic sensors. This estimation together with the model in turn allows probabilistic prediction of future traffic flows, so that control actions -selecting switching times of traffic lights in the application we have in mind -can properly anticipate future traffic flow. In this paper we use a stochastic hybrid model to effectively describe the evolution over time of the arrival and flow rates of vehicles in an urban traffic network as stochastic processes. We define the flow rate as the number of vehicles that pass a location per red/green cycle, divided by the length of this cycle (veh./sec). The random value of the continuous v...

Integrating Model-Based Observer and Kullback–Leibler Metric for Estimating and Detecting Road Traffic Congestion

“…They are very helpful for estimating data that are difficult to measure [13]. However, these approaches depend on the accuracy of the model used [14]. Several filter-based traffic estimation approaches are proposed in the literature, including Kalman filters [29], such as extended Kalman, particle Kalman [30], and Monte Carlo mixture Kalman filters [31].…”

“…On another hand, model-based state estimation approaches are based on analytical models describing the traffic dynamics. In literature, model-based estimation approaches have been shown good abilities in traffic estimation in terms of accuracy and the representation of several traffic phenomena [13], [14]. There are numerous model-based state estimation techniques in the literature, such as Kalman filtering (KF) and its extensions such as Duel extended KF [15] and mixture KF [16], particle filter [17] and adaptive smoothing filter [18].…”

Developing a Stochastic Model of Queue Length at a Signalized Intersection

“…Most of the past work related to traffic signal control design is based on the assumption that traffic flow is deterministic. Paper [6] proposes FFM with a discrete-event max-plus model while an FFM with the stochastic hybrid model is proposed in [7]. The FFM in [6] does not consider a random variation of the flow rates, whereas the FFM in [7] assumes that the evolution of arrival flow rate and departure flow rate are well defined by the parameters of the certain stochastic processes that have the capability to describe varying of intensity flow.…”

“…Their broad modeling expressivity has enabled various researchers to use stochastic hybrid systems as models in various application domains such as system biology, urban traffic networks [4], [7], [8], air traffic control [13] and smart grids. Paper [4] proposed hybrid models are represented by timed, discrete Petri nets.…”

“…Paper [4] proposed hybrid models are represented by timed, discrete Petri nets. Jump Markov model with the autoregressive process of traffic flow, for time update scales of the order several red/green cycles of the traffic light, and its parameter estimation is proposed in [7]. Paper [8] proposed hidden Markov models (HMM) with Gaussian distribution for time update scales of the order 15 minutes.…”