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

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

On the recursive estimation of vehicular speed using data from a single inductance loop detector: a Bayesian approach

This paper investigates the recursive estimation of vehicular speed using the information provided by a single inductance loop detector (ILD). A statistical model for space-mean speed measured by an ILD is developed, upon which a Bayesian analysis is carried out to estimate vehicular speed. This results in a set of recursive formulae which is analytically nice and neat. The incurred computational cost for updating the estimate of vehicular speed is kept to be a minimum. As a by-product, a simple method for the calibration of the effective vehicle length of an ILD is also developed. The proposed method is illustrated using simulation studies and a practical example

Stochastic modeling for vehicle platoons: 2, Statistical characteristics

This two-part paper presents a new approach to stochastic dynamic modeling for vehicle platoons. Part I develops a vehicle platoon model to capture the dynamics of vehicles’ grouping behavior and proposes an online platoon recognition algorithm. On the basis of the developed platoon model, Part II investigates various important characteristics of vehicle platoons and derives their statistical distribution models, including platoon size, within-platoon headway, between-platoon headway and platoon speed. It is shown that the derived statistical distributions include some important existing models in the literature as their special cases. These statistical distribution models are crucial for us to understand the traffic platooning phenomenon. In practice, they can be used as the inputs for the design of traffic management and control algorithms for traffic with a platoon structure. Real traffic data is used to illustrate the obtained theoretical results

Stochastic modeling for vehicle platoons: 1, Dynamic grouping behavior and online platoon recognition

A vehicle platoon is a group of vehicles traveling together at approximately the same speed. Traffic platooning is an important phenomenon that can substantially increase the capacity of roads. This two-part paper presents a new approach to stochastic dynamic modeling for vehicle platoons. In part I, we develop a vehicle platoon model with two interconnected components: a Markov regime-switching stochastic process that is used to model the dynamic behavior of platoon-to-platoon transitions, and a state space model that is employed to describe individual vehicles’ dynamic movements within each vehicle platoon. On the basis of the developed stochastic dynamic model, we then develop an algorithm for online platoon recognition. The proposed stochastic dynamic model for vehicle platoons also provides a new approach to vehicle speed filtering for traffic with a platoon structure

Bayesian inference for origin-destination matrices of transport networks using the EM algorithm

Information on the origin-destination (OD) matrix of a transport network is a fundamental requirement in much transportation planning. A relatively inexpensive method for updating an OD matrix is to draw inference about the OD matrix based on a single observation of traffic flows on a specific set of network links, where the Bayesian approach is a natural choice for combining the prior knowledge about the OD matrix and the current observation of traffic flows. The existing approaches of Bayesian modeling of OD matrices include using normal approximations to Poisson distributions, which leads to the posterior being intractable even under some simple special cases, and using Markov chain Monte Carlo simulation, which incurs extreme demand of computational efforts. In this article, through the EM algorithm, Bayesian inference is reinvestigated for a transport network for estimating the population means of traffic flows, reconstructing traffic flows, and predicting future traffic flows. It is shown that the resultant estimates have very simple forms with minimal computational costs

A model of pedestrians' intended waiting times for street crossings at signalized intersections

For the purposes of both traffic-light control and the design of roadway layouts, it is important to understand pedestrian street-crossing behavior because it is not only crucial for improving pedestrian safety but also helps to optimize vehicle flow. This paper explores the mechanism of pedestrian street crossings during the red-man phase of traffic light signals and proposes a model for pedestrians’ waiting times at signalized intersections. We start from a simplified scenario for a particular pedestrian under specific traffic conditions. Then we take into account the interaction between vehicles and pedestrians via statistical unconditioning. We show that this in general leads to a U-shaped distribution of the pedestrians’ intended waiting time. This U-shaped distribution characterizes the nature of pedestrian street-crossing behavior, showing that in general there are a large proportion of pedestrians who cross the street immediately after arriving at the crossing point, and a large proportion of pedestrians who are willing to wait for the entire red-man phase. The U-shaped distribution is shown to reduce to a J-shaped or L-shaped distribution for certain traffic scenarios. The proposed statistical model was applied to analyze real field data

Recursive estimation of average vehicle time headway using single inductive loop detector data

Vehicle time headway is an important traffic parameter. It affects roadway safety, capacity, and level of service. Single inductive loop detectors are widely deployed in road networks, supplying a wealth of information on the current status of traffic flow. In this paper, we perform Bayesian analysis to online estimate average vehicle time headway using the data collected from a single inductive loop detector. We consider three different scenarios, i.e. light, congested, and disturbed traffic conditions, and have developed a set of unified recursive estimation equations that can be applied to all three scenarios. The computational overhead of updating the estimate is kept to a minimum. The developed recursive method provides an efficient way for the online monitoring of roadway safety and level of service. The method is illustrated using a simulation study and real traffic data

The multinomial logit model revisited: a semi-parametric approach in discrete choice analysis

The multinomial logit model in discrete choice analysis is widely used in transport research. It has long been known that the Gumbel distribution forms the basis of the multinomial logit model. Although the Gumbel distribution is a good approximation in some applications such as route choice problems, it is chosen mainly for mathematical convenience. This can be restrictive in many other scenarios in practice. In this paper we show that the assumption of the Gumbel distribution can be substantially relaxed to include a large class of distributions that is stable with respect to the minimum operation. The distributions in the class allow heteroscedastic variances. We then seek a transformation that stabilizes the heteroscedastic variances. We show that this leads to a semi-parametric choice model which links the linear combination of travel-related attributes to the choice probabilities via an unknown sensitivity function. This sensitivity function reflects the degree of travelers’ sensitivity to the changes in the combined travel cost. The estimation of the semi-parametric choice model is also investigated and empirical studies are used to illustrate the developed method

A new approach to cluster analysis: the clustering-function-based method

The purpose of the paper is to present a new statistical approach to hierarchical cluster analysis with n objects measured on p variables. Motivated by the model of multivariate analysis of variance and the method of maximum likelihood, a clustering problem is formulated as a least squares optimization problem, simultaneously solving for both an n-vector of unknown group membership of objects and a linear clustering function. This formulation is shown to be linked to linear regression analysis and Fisher linear discriminant analysis and includes principal component regression for tackling multicollinearity or rank deficiency, polynomial or B-splines regression for handling non-linearity and various variable selection methods to eliminate irrelevant variables from data analysis. Algorithmic issues are investigated by using sign eigenanalysis

Markov models for Bayesian analysis about transit route origin-destination matrices

The key factor that complicates statistical inference for an origin-destination (O-D) matrix is that the problem per se is usually highly underspecified, with a large number of unknown entries but many fewer observations available for the estimation. In this paper, we investigate statistical inference for a transit route O-D matrix using on-off counts of passengers. A Markov chain model is incorporated to capture the relationships between the entries of the transit route matrix, and to reduce the total number of unknown parameters. A Bayesian analysis is then performed to draw inference about the unknown parameters of the Markov model. Unlike many existing methods that rely on iterative algorithms, this new approach leads to a closed-form solution and is computationally more efficient. The relationship between this method and the maximum entropy approach is also investigated