Kalman filtering estimation of traffic counts for two network links in tandem

Gazis, Denos C.; Liu, Chiu

doi:10.1016/s0191-2615(02)00059-0

Cited by 46 publications

(48 citation statements)

References 2 publications

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“…For traffic density estimation, for instance, Gazis and Liu (2003) assumed that lane changes of vehicles were not common and hence lane-change maneuvers, as the inputs of their state space model, were ignored. As a result, the modeling errors will become large for the roadways with substantial lane-changes.…”

Section: Gillins and De Moormentioning

confidence: 99%

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State estimation with partially observed inputs: A unified Kalman filtering approach

2013

Automatica

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For linear stochastic time-varying state space models with Gaussian noises, this paper investigates state estimation for the scenario where the input variables of the state equation are not fully observed but rather the input data is available only at an aggregate level. Unlike the existing filters for unknown inputs that are based on the approach of minimum-variance unbiased estimation, this paper does not impose the unbiasedness condition for state estimation; instead it incorporates a Bayesian approach to derive a modified Kalman filter by pooling the prior knowledge about the state vector at the aggregate level with the measurements on the output variables at the original level of interest. The estimated state vector is shown to be a minimum-mean-square-error estimator. The developed filter provides a unified approach to state estimation: it includes the existing filters obtained under two extreme scenarios as its special cases, i.e., the classical Kalman filter where all the inputs are observed and the filter for unknown inputs.

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Section: Gillins and De Moormentioning

confidence: 99%

“…Here we focus on a road segment with n lanes that is a detection zone with an upstream detector and a downstream detector at the entrance and exit of each lane respectively (see, e.g. Gazis and Liu (2003)). The two detectors count the vehicles passing through.…”

Section: Estimation Of Traffic Densitiesmentioning

confidence: 99%

State estimation with partially observed inputs: A unified Kalman filtering approach

2013

Automatica

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“…The macroscopic models [10] representing the average traffic behavior in terms of aggregated variables (flow, density and speed at different locations) are the most suitable models for on-line implementations. Many of the proposed solutions for estimation of aggregated traffic variables are based on Extended Kalman filtering applied to such macroscopic models [26], [8], [20]. In [26] an Extended Kalman filter (EKF) is proposed (and validated by simulation) to estimate the unknown parameters and states of a stochastic version of METANET, a well-known macroscopic model [19].…”

Section: Motivationmentioning

confidence: 99%

“…In [26] an Extended Kalman filter (EKF) is proposed (and validated by simulation) to estimate the unknown parameters and states of a stochastic version of METANET, a well-known macroscopic model [19]. In [8] an EKF is designed for estimating the number of vehicles for two roadway sections in tandem. These estimators, [26], [8], and [20] have all the advantages and disadvantages of the EKF technique: computationally cheap, but relying on a linearization of the state and measurement models which can cause filter divergence.…”

Section: Motivationmentioning

confidence: 99%

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A particle filter for freeway traffic estimation

Mihaylova

Boel

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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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

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Spectral and time‐frequency analyses of freeway traffic flow

Sun

2013

J of Advced Transportation

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SUMMARYThis paper uses spectral and time-frequency analyses to treat three macroscopic traffic characteristics, namely, time mean speed, volume and occupancy as stochastic processes. Spectral and time-frequency analyses are performed to characterize power spectral density (PSD), cross-PSD, autocorrelation and cross-correlation of these characteristics using TransGuide traffic data collected from four different freeways. It is found that low-frequency components dominate the PSDs of speed, volume and occupancy at all times. The magnitude of PSDs decreases dramatically as frequency increases and remains almost at a constant level in high-frequency regimes. A power law is found to exist, which describes the relationship between the frequency and the PSD of traffic characteristics. It is also found that speed can be properly modeled by a narrowband low-pass stochastic process in a low-frequency regime and by a nonzero mean white noise in a high-frequency regime. Strong periodicities and synchronization are both shown in traffic flow. A variety of frequencies can be excited by congestion, and there is no dominant frequency found in stop-and-go traffic.

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Kalman filtering estimation of traffic counts for two network links in tandem

Cited by 46 publications

References 2 publications

State estimation with partially observed inputs: A unified Kalman filtering approach

State estimation with partially observed inputs: A unified Kalman filtering approach

A particle filter for freeway traffic estimation

Spectral and time‐frequency analyses of freeway traffic flow

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