Vehicle density estimation of freeway traffic with unknown boundary demand–supply: an interacting multiple model approach

Abstract

As distributed parameter systems, dynamics of freeway traffic are dominated by the current traffic parameter and boundary fluxes from upstream/downstream sections or on/off ramps. The difference between traffic demand-supply and boundary fluxes actually reflects the congestion level of freeway travel. This study investigates simultaneous traffic density and boundary flux estimation with data extracted from on-road detectors. The existing studies for traffic estimation mainly focus on the traffic parameters (density, velocity etc.) of mainline traffic and ignore flux fluctuations at boundary sections of the freeway. The authors propose a stochastic hybrid traffic flow model by extending the cell transmission model with Markovian multi-mode switching. A novel interacting multiple model filtering for simultaneous input and state estimation is developed for discrete-time Markovian switching systems with unknown input. A freeway segment of Interstate 80 East (I-80E) in Berkeley, Northern California, is chosen to investigate the performance of the developed approach. Traffic data is obtained from the performance measurement system. IntroductionReal-time knowledge about the traffic conditions of freeway transportation systems is critical for traffic management and control. There are many well-established technologies for collecting vehicle speed and traffic flux, including loop detectors or automatic vehicle identification systems. Recently, the novel ubiquitous sensing technologies, such as dedicated probe vehicles or smartphone-based applications, have the potential of unprecedented data collection at any positions of large-scale traffic networks. However, the equipped measurement is typically low and not representative of the urban network as a whole, which leaves the traffic conditions in most of the network unknown. Estimate unknown states of freeway traffic with filtering have been extensively studied in the past two decades. In the literature [1], Wang and Papageorgiou proposed the extend Kalman filter (EKF) based on the stochastic version of macroscopic traffic flow model, METANET. A particle filter (PF) is developed in [2] using the extended stochastic cell transmission model (CTM) [3][4][5]. Sun et al. [6] propose a solution to the traffic estimation by a sequential Monte Carlo algorithm, the so-called mixture Kalman filter. A switching mode model (SMM) is developed in [7] to represent freeway traffic with two distinct traffic phenomena, as a free-flow mode and a full congestion mode, respectively. A fuzzy observer is designed in [8] based on SMM to estimate vehicle densities of a freeway link. Most recently, the PF method is developed in [9] to real-time estimate traffic states with a jumped Markov traffic model coming from a variant of CTM. While, all of the above methods assume that the boundary flux of the estimated freeway traffic is known or available (as system measurement model) in advance.In practise, however, when using mobile sensing technologies to perform measurement, it is reasonable difficult ...

Traffic state estimation on highway: A comprehensive survey

“…This might be because such route choice behavior is uncertain and makes the problem complex (Tampère and Immers, 2007). Regarding boundary demand, some studies have incorporated demand estimation/prediction in their TSE methods, and the importance of demand estimation has been pointed out (e.g., Wang and Papageorgiou, 2005;Wang et al, 2006;Zhang and Mao, 2015).…”

“…Traffic demand, both at boundaries and junctions (c.f., Section 3.3), is often neglected by TSE studies (e.g., simply assumed to be observed or inferred from historical-data). This is partially accounted for by existing studies, such as the estimation of boundary flow (e.g., Wang et al, 2006;Zhang and Mao, 2015); however, demand responsive to traffic has not been well investigated in TSE. This problem would be significant for TSE in large-scale networks.…”

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

“…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]. Recently, Zhang and Mao proposed using interactive multiple model filtering to estimate the traffic state and input variables [32]. This approach is based on Switched Mode Model (SMM), which takes into account only the fully free and fully congested modes.…”

Stochastic stability of Markov jump hyperbolic systems with application to traffic flow control

“…Motivated by the development of stochastic traffic flow models, see Boel and Mihaylova (2006), Zhang and Mao (2015), we deduce the quasi-linear hyperbolic equation (48) to a MJLH system.…”