Urban Road Traffic Spatiotemporal State Estimation

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1		Jian Gu	--	3272	2024-01-18 00:34:24	\|
2	layout & references	Sirius Huang	Meta information modification	3272	2024-01-18 02:18:38	\|

This entry is adapted from the peer-reviewed paper 10.3390/app132112079

The road traffic state is usually analyzed from a temporal and macroscopic perspective; however, traffic flow parameters, such as density and spacing, can explain the evolution of traffic states from the microscopic perspective and the spatial distribution of vehicles in lanes.

traffic state estimation phase space

1. Introduction

The operational status of urban road traffic reflects the degree of use of existing road resources by road users. The road traffic operational status has obvious temporal and spatial distribution characteristics, which are influenced by the method used to determine the operational status. The operational status of roads is generally divided into five levels, and the status is evaluated from different perspectives, such as links, roads, and road networks. Different indicators are selected for evaluation, most commonly the free flow speed, average travel speed, travel time, and other parameters. The evaluation results are distinguished by different colors to visually display the management department’s understanding of the road operations. However, from a research perspective, the evaluation results of the road traffic operational status are only static evaluations of quasi-real-time traffic operations based on detection data with a time interval of 5–15 min. Indicators such as speed and travel times are calculated, and the transformation and evolution processes of the macroscopic road traffic operational status must simultaneously be analyzed using other indicators. In addition, the change process of traffic from smooth to congested and then back to smooth at a node position cannot be analyzed without considering the temporal–spatial relationships between vehicles, such as headway and spacing. These relationships can be used to analyze the operational status of nodes at multiple locations and obtain the evolution law of traffic status at node positions, achieving the recognition of operational status for urban roads.

The current urban road traffic operational status assessment criteria focus primarily on the road sections between upstream and downstream detectors, using the vehicle travel time obtained within a certain time interval as the main evaluation index. Although this approach is simple and straightforward, it neglects the uneven distribution of vehicles arriving at adjacent road sections due to the periodic conversion of traffic rules at intersections. Therefore, the travel time index cannot reflect the local spatial evolution characteristics of the traffic operational status, namely, the uneven distribution of traffic flow density in upstream and downstream road sections, simultaneously. To address this issue, the periodic impact of intersections must be introduced into the assessment process by categorizing the arriving traffic into different lane directions. Vehicle arrival and departure times, vehicle-to-vehicle distances, and vehicle speeds should be extracted from detection information to obtain traffic characteristics such as headway and spacing. Microscopic traffic flow theory should be applied to analyze the inaccurate assessment of the traffic operational status caused by the uneven distributions of traffic density in upstream and downstream road sections.

Considering the nonlinear characteristics of detection data time series, a comprehensive prediction model should be developed based on a single parameter, such as the travel time, and incorporate microscopic traffic flow parameters. This involves reconstructing a multivariable space to analyze the nonlinear characteristics of traffic flow parameters. Based on this, a multivariable prediction model can be constructed to obtain the time-based evolution of the traffic operational status, estimate the congestion duration, estimate the spatial distribution of the traffic operational status, and determine the length of the affected road sections.

Phase space reconstruction is an important method for analyzing nonlinear time series and can restore the attractor of a dynamic system in a high-dimensional space. The reconstructed phase space represents the dynamic characteristics of the time series as the physical meaning of the original time series is weakened. Therefore, multivariable phase space reconstruction can be used to integrate multisource data.

The single physical quantity of traffic flow parameters has chaotic characteristics. When comprehensively analyzing traffic conditions, multiple traffic parameters and physical quantities must be analyzed together, that is, from the perspective of a comprehensive space–time analysis. However, when combined with the function of chaotic parameters, the orbit characteristics of multiple chaotic variables change, which affects the chaotic prediction accuracy of space–time parameters. Reducing or avoiding this requires further research.

2. Analysis of Spatiotemporal Operation Characteristics of the Traffic State

Much research has been conducted on typical traffic state classification parameters and methods, as shown in Table 1. Felix et al. ^[1] analyzed the spatiotemporal distribution characteristics of chronic traffic congestion by simplifying a complex traffic network into the most frequently congested parts (clusters) based on real-time collected data and introducing clustering methods. Ryo Inoue et al. ^[2] proposed a method based on frequent pattern mining in information science for analyzing traffic sensor data to understand traffic congestion patterns in cities. The feasibility and effectiveness of the proposed method were evaluated through an analysis of traffic sensor data in Okinawa (Japan). Rajvi Kapadia ^[3] created a model for mining traffic period patterns that accounted for the impact of monsoons on road traffic, presenting an overall traffic scenario analysis and more accurately analyzing the traffic patterns of developing cities with a high population density such as Mumbai. Based on the work by Qingdao, Sun ^[4] combined traffic performance index (TPI) data with a hierarchical clustering algorithm to extensively study traffic congestion in urban commercial districts. In a study in Beijing, Lei et al. ^[5]^[6] constructed a traffic state classification system based on the flow, speed, time occupancy, and road network redundancy and analyzed the system using an improved fuzzy clustering algorithm. Clustering of actual traffic parameters detected in some areas of the Beijing expressway network allowed the states of traffic flow data to be determined. Liu et al. ^[7] used floating vehicle data and real-time traffic data to analyze the traffic status of schools around roads through spatiotemporal clustering, revealing the distribution characteristics of traffic status around schools in Beijing. Fabritiis et al. ^[8] estimated traffic speeds from GPS traces and proposed algorithms based on artificial neural networks and pattern matching for short-term travel speed predictions in Italy. Wu et al. ^[9] considered the impact of road grades on congestion indicators, selected the INRIX road congestion index system, used taxi trajectory data to calculate the road congestion index, and proposed an abnormal judgment method for the road congestion index and a congestion index correction method based on regional continuity. He et al. ^[10] introduced the spatiotemporal cumulative index of traffic congestion to identify and quantitatively analyze the operational status of regional transportation; established a functional relationship between congestion sources and congestion evaluation points to construct a visual model; used gradient direction histograms and principal component analysis to extract features from traffic operation status data; and used the Gaussian mixture clustering method to cluster the feature data and classify the spatial distribution pattern of regional traffic congestion. D’Andrea et al. ^[11] presented an expert system for detecting traffic congestion and incidents from real-time GPS data collected from GPS trackers or drivers’ smartphones. Kan et al. ^[12] proposed an approach for detecting traffic congestion from taxis’ GPS trajectories at the turn level by analyzing features of GPS trajectories and identifying valid trajectory segments; they also detected congested trajectory segments of three different intensities.

Table 1. Data and parameters for traffic state classification.

No.	Data and Parameters	Methods	Typical Research
1	Traffic performance index (TPI) Data From Qingdao, China	Hierarchical clustering	Sun et al. ^[4]
2	Volume, speed, occupy, road network redundancy from urban expressway	Fuzzy clustering	Lei et al. ^[5]^[6]
3	Float car GPS and real-time data from Beijing, China	Temporal–spatial clustering	Liu et al. ^[7]
4	Float car data from metropolitan areas in Italy	Pattern matching	Fabritiis et al. ^[8]
5	Taxi trajectory data from Fuzhou, China	Abnormal judgment	Wu et al. ^[9]
6	Taxi data from Guangzhou, China	Gaussian mixed clustering	He et al. ^[10]
7	GPS traces from the city of Pisa	Speeds data mining	D’Andrea ^[11]
8	Taxis’ GPS data from Wuhan, China	Turn-level clustering	Kan et al. ^[12]

In addition, many scholars have explored traffic congestion from different perspectives. For example, Gao et al. ^[13] explored and analyzed the spatiotemporal distribution characteristics, laws, and causes of traffic congestion in Xuchang city based on the real-time traffic data over one week.Sun et al. ^[14] primarily studied the spatiotemporal distribution characteristics of traffic congestion caused by traffic accidents on urban roads, characterized the spatiotemporal features of traffic states from the perspective of congestion, and established a congestion determination model based on speed differences. Anbaroğlu et al. ^[15] proposed an NRC (non-recurrent congestion event) detection methodology to support the accurate detection of NRCs in large urban road networks by substantially estimating high link journey times on adjacent links.

Overall, significant progress has been made in the traffic congestion field worldwide, encompassing a variety of methods and fields. These studies provide important references for transportation planning and management and help to improve traffic congestion in cities.

3. Multivariate Phase Space Analysis and Its Applications

The complex nonlinear characteristics of road traffic operations make scientifically and accurately describing the traffic operation status with a single parameter difficult. Therefore, a rapidly developing technical method based on multivariate variable analysis has been proposed. Its theoretical basis is the phase space reconstruction technology based on a single variable, which constructs phase space reconstruction theory and a method for multiple variables. This method, based on phase space reconstruction technology, can more comprehensively reveal the mutual relationships between multiple traffic variables, thereby facilitating more accurate traffic operation status analyses. Traditional multivariate variable phase space reconstruction and prediction methods are shown in Table 2. Wang ^[16] proposed a coarse-grained algorithm for time series mapping to complex networks by combining phase space reconstruction and rough set technology. This algorithm transformed time series into complex networks to more accurately describe the evolution characteristics of time series. Li ^[17] proposed a multidimensional chaotic time series prediction method based on Bayesian theory, which integrated traffic measurement values (speed, occupancy, and flow) from different data sources through phase space reconstruction. Qian et al. ^[18] established a traffic flow prediction model based on phase space reconstruction and Kalman filtering theory to improve the urban traffic flow prediction accuracy. This model could effectively reflect the essential characteristics of traffic flow. Yang ^[19] used the maximum Lyapunov exponent to analyze the predictability of traffic flow and then reconstructed the phase space. The reconstructed phase points were introduced into the Kalman filter equation as the initial state points to establish a short-term traffic flow prediction model based on phase space reconstruction. Cheng ^[20] used multiple measurement parameters, such as the average speed, average occupancy, and average traffic flow, to describe a transportation system. A multisource and multi-measurement traffic flow prediction model was constructed using chaos theory and the support vector regression method. Chaotic time series of multiple measurements were integrated into a multidimensional phase space through phase space reconstruction by selecting embedding dimensions and delay times. Tang ^[21] proposed a hybrid prediction model (GQPSO-WNN) based on phase space reconstruction to quantitatively analyze the chaos characteristics and predictability of traffic flow changes. The advantages of the genetic algorithm (GA) and quantum particle swarm optimization (QPSO) were cleverly combined to enhance the model performance by optimizing the wavelet neural network parameters.

Table 2. Traditional methods of multivariate phase space reconstruction and prediction.

No.	Data	Main Methods	Typical Research
1	period time series	Complex network	Wang ^[16]
2	speed, occupancy, and flow	Bayes theory and phase space reconstruction theory	Li ^[17]
3	traffic flow data	Phase space reconstruction and Kalman filtering theory	Qian et al. ^[18]; Yang et al. ^[19]
4	speed, occupancy, and flow	Support vector machine and chaos theory	Cheng ^[20]
5	traffic flow time series	Phase space reconstruction and genetic algorithm (GA) and quantum particle swarm optimization with the wavelet neural network	Tang ^[21]

Shang ^[22] constructed a short-term traffic flow prediction model based on phase space reconstruction and regularized extreme learning machines to improve the short-term traffic flow prediction accuracy. The optimal time delay and embedding dimension of the traffic flow time series were determined using the C-C algorithm, and the phase space was reconstructed. The G-P algorithm was used to calculate the correlation dimension of the sequence, and chaos characteristics were identified for short-term traffic flow sequences. Wang et al. ^[23] introduced a multi-time series reconstruction method based on data fusion. A social cognitive algorithm and adaptive weighted fusion estimation were used to optimize the weight of each component. The phase space was reconstructed by fusing different phase spaces through data fusion, providing a new idea for the data fusion of heterogeneous sensors. To address the large number of monitoring variables and high redundancy in chemical production systems, Zhao et al. ^[24] proposed a multisource data fusion method based on phase space reconstruction. The parameters of phase space reconstruction were obtained using the mutual information and Cao methods, providing new insights into solving multisource heterogeneous sensor data fusion problems. Thonhofer et al. ^[25] presented a modular macroscopic traffic model with two traffic light formulations, and the proposed model allowed arbitrary functional forms of the fundamental diagram defined by a small number of parameters; then, the moving density gradients (jam fronts) were represented accurately, and the model parameters were physically meaningful and could readily be estimated from measurement data. Li ^[26] aimed to improve the accuracy of short-term traffic flow predictions by studying a prediction model based on phase space reconstruction and particle swarm optimization Gaussian process regression. To overcome the nonlinearity, complexity, and randomness of traffic flow time series, the phase space was reconstructed based on chaos theory to obtain the best delay time and embedding dimension of the original time series, which were used as the input–output data set of the model to maintain the same dynamic characteristics as the original data. Hou ^[27] proposed a method for predicting connected traffic flow data with chaotic characteristics by using an improved phase space reconstruction method to reveal chaotic dynamics in data and a hybrid deep learning model to extract features from phase space data and optimize model parameters, improving the prediction results.

4. Deep Learning Methods for Traffic Flow Parameter Prediction Applications

Traffic flow parameter prediction is an important component of urban traffic management and planning, and it is crucial for alleviating traffic congestion, improving road usage efficiency, and optimizing transportation system operations. Some researchers have combined machine learning with traditional linear methods, including the K-nearest neighbor algorithm (KNN), support vector regression (SVR), K-means, and artificial neural network (ANN) models, to predict traffic flow parameters. In recent years, the rapid development of deep learning technology has attracted widespread attention to its applications in traffic flow parameter prediction. Deep learning can automatically learn feature representations from large-scale traffic data by constructing complex neural network structures, thereby improving the accuracy and robustness of predictions. Researchers have applied deep learning to traffic flow parameter prediction, achieving significant results. These deep learning models can obtain more accurate prediction results than early machine learning models and statistical models. For time series data such as traffic flow, recurrent neural networks (RNNs) have been used to fully extract the information of each time step during spatial–temporal feature extraction. Typical multivariate variable phase space reconstruction and prediction methods are shown in Table 3. Liu et al. ^[28] presented a method for short-term traffic flow prediction based on an attention model that can extract spatiotemporal features and understand the influence of each unit of data. Zhang et al. ^[29] constructed a traffic flow prediction model based on image Motif-GCRNN, capturing spatiotemporal dependencies in road networks through graph convolutional learning. Yang et al. ^[30] proposed a stacked autoencoder Levenberg–Marquardt model to improve the prediction accuracy by learning traffic flow features through layer-by-layer unsupervised learning. Wu et al. ^[31] proposed a DNN-based traffic flow prediction model (DNN-BTF) that fully utilized the periodicity and spatiotemporal characteristics of traffic flows using convolutional neural networks and recurrent neural networks to extract spatial and temporal features. Du et al. ^[32] proposed an adaptive multimodal deep learning model, HMDLF, combining a convolutional neural network (CNN) and gated recurrent unit (GRU) models to capture local trends and long-term dependencies in traffic data, reducing the computational complexity. Tan et al. ^[33] proposed a new short-term traffic flow prediction method based on dynamic tensor completion (DTC), where traffic data were represented as dynamic tensor patterns. This method was able to capture more traffic flow information, including the time variability, spatial features, and multimodal periodicity, than traditional methods. A DTC algorithm was designed to use multimodal information for low-rank constraint prediction of traffic flow.

Table 3. Recent methods on multivariate predictions.

No.	Data	Main Methods	Typical Research
1	traffic speed	CNN combined with LSTM and attention mechanisms	Liu et al. ^[28]
2	traffic speed	Graph convolutional recurrent neural network	Zhang et al. ^[29]
3	traffic flow data from the M6 freeway in the U.K.	Self-encoded Levenberg–Marquardt model	Yang et al. ^[30]
4	PeMS database	Mixed methods on convolutional recurrent neural network	Wu et al. ^[31]
5	flow, speed, journey time from UK	CNN and GRU	Du et al. ^[32]
6	PeMS database	Dynamic Tensor Completion	Tan et al. ^[33]

Polson et al. ^[34] developed an innovative deep learning architecture for predicting traffic flow. The architecture combined linear models with a series of tanh layers to address the challenges of sharp nonlinear spatiotemporal effects produced by transitions between free flow, congestion, recovery, and gridlock. Kumar et al. ^[35] used the predictive scheme of seasonal ARIMA (SARIMA) models to overcome data availability issues and used limited input data for short-term traffic flow prediction. Lopez-Garcia et al. ^[36] proposed a method for optimizing the elements of fuzzy rule-based system (FRBS) hierarchies using a GA and cross-entropy (CE) hybrid, called GACE, for short-term traffic congestion prediction. Chen et al. ^[37] proposed a chaotic prediction method based on the Lyapunov exponent for traffic flow characteristics with chaos. Dong et al. ^[38] proposed an end-to-end trainable unified model that combines an autoencoder and a random forest to construct a random decision tree model for guiding parameter learning. Liao et al. ^[39] used Dest-ResNet to correct the original traffic speed prediction errors and solved the time series relationship problem caused by crowdsourcing map queries. Shao et al. ^[40] used a long short-term memory (LSTM) network and other models for traffic flow prediction. This model further improved the RNN and addressed gradient explosions caused by missing data in simple RNNs. Ma et al. ^[41] applied LSTM networks for traffic speed prediction, demonstrating that the LSTM structure can capture long-term time dependencies in traffic data and overcome the vanishing gradient problem by using memory blocks, demonstrating excellent performance in time series prediction with long-term dependencies. Zhang et al. ^[42] proposed a tree-based ensemble method that improved the performance of highway section travel time predictions by considering variables derived from historical data. Additionally, gradient boosting tree methods have also been developed, revealing hidden patterns in travel time data and improving the accuracy and interpretability of models. Deep learning technology has tremendous potential for traffic flow prediction. Future research could further explore deep-learning-based traffic flow prediction methods to improve the efficiency of traffic management and reduce the negative impacts of urban traffic problems.

In summary, numerous methods have been proposed to address traffic operating status estimation and classification. A comparative analysis of these methods has revealed the following characteristics: First, many studies focus on the parameters of either the time or spatial dimensions to conduct state classification or recognition research, and the selected methods rely primarily on pattern recognition or clustering methods. Second, prediction and estimation methods based on multivariate variable reconstruction have been continuously developed, with classic theories such as Bayesian theory, Kalman filters, support vector machine, and complex networks being applied widely. Additionally, with the rapid development of neural networks, deep learning, and other technologies, multivariate phase space reconstruction prediction and estimation methods have gradually become research hotspots. Third, the application of deep learning technology has improved traffic parameter prediction accuracy, but a single neural network type can capture only the features of either the time dimension or spatial dimensions of traffic data, and the predicted results cannot reflect the characteristics of traffic operation changes in multiple dimensions and levels.

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