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

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.