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Abstract

Using perception data to excavate vehicle travel information has been a popular area of study. In order to learn the vehicle travel characteristics in the city of Ruian, we developed a common methodology for structuring travelers’ complete information using the travel time threshold to recognize a single trip based on the automatic license plate reader data and built a trajectory reconstruction model integrated into the technique for order preference by similarity to an ideal solution and depth-first search to manage the vehicles’ incomplete records phenomenon. In order to increase the practicability of the model, we introduced two speed indicators associated with actual data and verified the model’s reliability through experiments. Our results show that the method would be affected by the number of missing records. The model and results of this work will allow us to further study vehicles’ commuting characteristics and explore hot trajectories.

Keywords

Trajectory reconstruction automatic license plate reader data technique for order preference by similarity to an ideal solution depth-first search vehicle travel

Introduction

The mobile trajectory can be defined as the path generated by the moving entity in space, Spaccapietra et al.¹ had defined “trajectory” with “space-time path,” which is recognized by other scholars.^2–4 With the rapid development of location tracking and storage technology, people have been able to collect a large number of vehicle and human mobile trajectory data (abbreviated trajectory data), the analysis of trajectory data can effectively help people understand the traffic conditions of a city and the law of people’s movement. Trajectory data contain both space and time attributes, large data volume, and high dimensions; now, the relevant researches mainly include evaluation and prediction of the road network state,^5–9 mining individual travel characteristics,¹⁰ inferring the home/work locations,^11–16 the commuting characteristic analysis,¹⁷ and so on.

However, most trajectory data from these researches were acquired from the mobile traffic sensors, including data from the Global Positioning System (GPS),^18–21 smart phones,^22,23 and smart cards.^24–26 There are also trajectory data from fixed sensors, called the automatic license plate reader (ALPR) data. Through advanced optoelectronic, computer, image processing, pattern recognition, and remote data access technologies, intelligent ALPR systems achieve the all-weather real-time monitoring of motor vehicle and bicycle lanes in the monitored sections; with the analysis of captured images, front-end processing systems automatically obtain the vehicles’ recorded time when they pass by the test point, as well as their location, direction, plate number, plate color, body color, and other data, and this information is then transferred to the database of the ALPR system control center for data storage, query, comparison, and processing by the computer network (Figure 1).

Figure 1.

Intelligent ALPR system structure.

Different from the trajectory data above, the ALPR data were easy to acquire and have a rich data format; currently, the equipment has been installed and used in many cities of China. While these ALPR data have been widely used in violation accident monitoring, their utilization rate is still not very high, leading to a high necessity to mine ALPR data in vehicle trajectory reconstruction.

However, the ALPR data also have some flaws, due to the limitations of license plate recognition technology;^27,28 the equipment that were installed in vehicle and roadside are affected by environment and the performance of sensors. The incomplete and abnormal deviation of trajectories is obtained. Using these unhandled data would impact the accuracy and reliability of the results. Therefore, it is significant to reconstruct the missing vehicle trajectories.

There are already some trajectory reconstruction methods^29–31 for mobile sensors data, while most methods do not take the actual road network and the validation with measured data into account.

Based on the research situation, this article will propose trajectory reconstruction method combining traffic characteristics to solve the vehicle trajectory missing, and we would use the ALPR data to verify this method.

The rest of this article is organized as follows: section “Data description and preprocessing” summarizes the existing trajectory reconstruction methods. Then, we introduce the data source and some preprocessing approaches. Section “The trajectory reconstruction model” proposes the reconstruction model and parameter calculation. Section “Empirical validation of the model” presents the numerical experiment results based on the empirical ALPR data. Conclusions and future research directions are discussed in section “Concluding remarks.”

Literature review

For the problem of trajectory data missing, we summarized the existing solutions and divided them into three categories:

The first category does not consider the missing ALPR data,^18,32,33 but this may cause large errors when missing many samples.

The second category is to fix the lost data separately combined with specific analysis. For example, Castillo et al.³⁴ proposed a traffic flow prediction method based on Bayesian networks, which could effectively reduce the omission of or errors in license plate recognition. However, this method is only suitable for adjacent road sections in a small-scale city network.

The third is the reconstruction of vehicle trajectory, a more extensive method of interpolation. Through the effective interpolation algorithm, we track and restore the space–time trajectory. The current interpolation method mainly adopts linear interpolation algorithm.

Frentzos et al.³⁵ proposed query processing algorithms to perform nearest neighbor (NN) search on R-tree-like structures³⁶ storing historical information about moving objects. Although this linear interpolation algorithm could solve some trajectory reconstruction problems, in practice, even if the vehicle runs on a straight road, its trajectory would not be completely straight.

Kim et al.³⁷ described an iterative refinement method for approximating a cubic B-spline interpolation of unit quaternions to construct the curve trajectory; however, the calculation procedure is complex and just for some special curves.

Yu and Kim³⁸ used the high-order polynomial to interpolate the curve, but Loan³⁹ proved that the high-order polynomial tends to cause the vibration of the curve, and the convergence of interpolation is not good. Yu et al.⁴⁰ proved that using curves to indicate the space–time trajectory of moving objects is more accurate than line segment, and proposed a piecewise polynomial method to interpolate trajectory, these require quantity and thus is not suitable for high-dimension expansion.

All these studies represent a moving trajectory as a sequence of connected segments in space–time, and each segment has two end points that are consecutively reported factual states.

There is another method⁴¹ treating vehicle travel as a consequence of the choice of different routes. Wang et al. created a direct access network model, based on which constructed the track patching set, and finally made optimal decision to the track patching set using track utility function. However, the assumption is not verified using large-scale real-life data.

This article proposes a trajectory reconstruction method for the ALPR data, which does not need microscopic representation of vehicle running trajectory; the model is simple and convenient to calculate. And we demonstrated its scalability and efficiency through an extensive experimental study using large synthetic and real datasets.

Data description and preprocessing

Data description

We utilized the vehicle identification data of Ruian, Zhejiang province, China, where ALPR facilities have been installed in 108 intersections. Figure 2 shows the distribution of the 108 data collection points, and all of the 108 intersections data have been used in calibration and validation in this article. These detectors cover the major roads in Ruian seen on the map, and the data clearly reflect the vehicles’ running state. The database receives millions of records every day. In total, two data collection periods are used in this study: one between 29 December 2015, 00:00:00 and 4 January 2016, 23:59:59, and another between 1 March 2016, 00:00:00 and 21 March 2016, 23:59:59.

Figure 2.

The distribution of the detectors.

Data preprocessing

There were 20 working days and 8 testing days in the two datasets. We used SQL server to finish the data preprocessing. After importing the data into the database and storing them in a table named “dbo.source,” we selected useful columns from the original 38 fields. The filtered dataset format is shown in Table 1.

Table 1.

Summary of the datasets.

Column name	Explanation	Sample data
HPHM	Vehicle license plate number (the first character is the provincial capital and the second number is for the city; these are followed by four numbers and letters)	“zheCFXXX”
HPZL	Types of license plate number (01 or 02; 01 is a large car and 02 is a small car)	01
GCSJ	The time the vehicles pass the test point	30 December 2015, 12:16:20
CLLX	Vehicle type (0/1; 0 is a small car; 1 is a large car)	1
CDBH	Lane number (1, 2, or 3, beginning with the center line from left to right)	2
DDBH	Location number (from 1 to 108)	100
DDMS	Location description	Wangsong East Road and Anyang Road
XSFX	Driving direction	South to North
FXMS	The direction to describe	Anyang Way South to North

Due to the limitations of the image recognition technology, some vehicles’ plate numbers could not be clearly captured, so it was necessary to remove these unidentified records from our datasets. These records were dropped by an execute statement: “delete from dbo.source where HPHM like ‘identified.’” Finally, we deleted approximately 10% of the data. Since there was a red light in the intersections, some of the uploaded data from certain facilities were repeated. As a result, there were many duplicate records that needed to be removed from the datasets. Our approach for recognizing duplicate records included the following steps:

The same records include the same time.

In total, two adjacent records are the same except for the time, and the time interval of two records is less than threshold A.

We found that threshold A depends on the all red time of the intersection, and the vehicle stopped for the all red light and was detected repeatedly at the same location; here, we assumed A = 5 s, which would represent the all red time in this article.

Vehicle trip extraction

In the process of mining, the vehicle travel information is based on the ALPR data; it is imperative to obtain complete vehicle travel trajectories, so this section organizes the data according to the vehicle itself and identifies the vehicle’s single trip through the travel time threshold. We include a vehicle trajectory reconstruction model with the technique for order preference by similarity to an ideal solution (TOPSIS) algorithm,⁴² which effectively completes the vehicle travel information based on the ALPR data. We then show the complete single vehicle trip information. The reliability of our model was demonstrated by experiments.

Data organization

Before we mined the travel information of each vehicle, we first constructed the individual vehicle’s travel portfolio: a list of complete records, ranked by the time. All these records were connected to a series of integral travel trajectories. All research in this article were based on the individual vehicle’s travel information. Faced with an enormous amount of data, we first divided the data by the record time. We then grouped these records according to license plate number.

Single-vehicle trip recognition

The record for a vehicle contained multiple single trips in 1 day. We segmented all the single trips of each vehicle using the travel time threshold B every day. We defined the single trip as meeting the condition that the time interval between the current trip and adjoining trips exceed B. We obtained the time interval by computing the time gap of two consecutive records. If the time gap was larger than B, we distinguished the two records into two different trips. We were able to obtain a vehicle’s travel information and determined the value of B using formula (1)

B = max {T}

(1)

where $T$ is the travel time set of all sections of the researched road network $T = {t_{1}, t_{2}, t_{3}, \dots, t_{n}}$ . We obtained this value by calculating the ratio of the road section length and speed limit.

The trajectory reconstruction model

In this section, we proposed a method to solve vehicle trajectory missing for the ALPR data. According to original data and actual road network, we found all incomplete vehicle trajectory records and used depth-first search (DFS)⁴³ to find all possible routes and finally solved the trajectory decomposition set decision with TOPSIS and achieved trajectory reconstruction (Figure 3).

Figure 3.

The trajectory reconstruction method flowchart.

The first step is to determine the research area; to facilitate the understanding of the model, we created a simple road network (Figure 4(a)) consisting of 16 nodes, 12 links, and we assumed that all the road sections are of the same nature, and the length of the section, road direction, and other network information are known.

We projected a vehicle’s travel data into the road network, which cannot form a complete route; this means that there is no direct link between some adjacent two records. This issue belongs to the vehicle trajectory missing, as shown in Figure 4(b), and the vehicle trajectory records (node 1, node 2, node 7, node 11, node 12, and node 16) are projected into the road network; it was first tested at locations 1 and 2 and then tested again at locations 7, 11, 12, and 16 apparently, and there were some missing records.

Figure 4.

Road network and incomplete vehicle trajectory: (a) is the road network and black circles with numbers are the detection locations, green circles in, (b) are the known vehicle trajectory records, the yellow, red and blue circles and sections in, and (c) are the vehicle's three possible routes.

Constructing trajectory patching set

We assumed that the vehicle does not appear two times in a location and used depth-first traversal (DFS) to search all possible alternative trajectories to construct trajectory patching set.

In combination with mentioned vehicle trajectory example above, the specific operation steps are as follows:

Input incomplete trajectory records: node 1, node 2, node 7, node 11, node 12, and node 16.

Get the start and end records of the trajectory: node 1 and node 16.

With the known research network and depth-first traversal, obtain all routes from the start point (node 1) to the end point (node 16): T1 = {node 1, node 2, node 6, node 7, node 11, node 12, node 16}, T2 = {node 1, node 2, node 3, node 7, node 11, node 12, node 16}, and T3 = {node 1, node 2, node 3, node 4, node 8, node 7, node 11, node 12, node 16}, as shown in Figure 4(c).

Determine whether the route in step 3 contains all initial incomplete record points in step 1 or remove this route; here, T1, T2, and T3 satisfy it.

Get the trajectory patching set.

Best trajectory

Based on the trajectory patching set, we defined some decision indicators and used TOPSIS method to make optimal decision and obtain the complete vehicle trajectory.

Decision attributes

By taking into consideration the factors influencing vehicle travel, we selected three indicators as the trajectory decision indicators: the path pattern matching degree, the path of tortuosity, and the consistent interval. For each trajectory, we set four attribute values: the section number, speed match degree, path pattern number, and vehicle turning number.

Section number. It means how many sections of the current trajectory.

Speed match degree. We calculated the actual speed and theoretical speed of each trajectory and obtained their difference as the speed match degree, and the calculation method is described in detail in the next section.

The path pattern number. It means the number of path pattern types in the trajectory. The vehicle travel path generally follows the step mode or straight line mode, as shown in Figure 5.

Vehicle turning number. The turning numbers of the vehicle in the corresponding trajectory.

Figure 5.

Mode of vehicle travel pattern in urban road network: (a)–(d) are the step mode and (e)–(h) are the straight mode.

Parameter calculation considering traffic operation characteristics

To make the model provide a better actualization, we obtained the actual and theoretical speeds of the alternative trajectory $T_{i}$ with processed data through SQL server. We selected useful rows, such as HPHM, DDBH, GCSJ, and XSFX, for the alternative trajectory $T_{i}$ , since these contain a series of recording spots, denoted as $(s_{1}, s_{2}, \dots, s_{k})$ , $0 < k < O$ . With a known network, we obtained the distances in the continuous recording spots as $(d_{12}, d_{23}, \dots, d_{k - 1 k})$ using the ArcGIS distance function. The theoretical speed $V_{i}$ was counted using formula (2)

V_{i} = \frac{(d_{12} + d_{23} + \dots + d_{k - 1 k})}{(t_{l} - t_{f})}

(2)

where $t_{f}$ is the researched vehicle’s first recorded time and $t_{l}$ is the last recorded time.

We denoted all sections in road network as $(l_{1}, l_{2}, \dots, l_{T})$ .We set the time interval as 30 min because the road sections did not obviously change during this time span. We calculated all the road sections’ average speed at every time interval throughout the day, so each section had 48 speed values, denoted as $(V_{1}, V_{2}, \dots, V_{T})$ , and the speed values set of section $i$ were $V_{i} = (V_{i 1}, V_{i 2}, \dots, V_{i 48})$ and $i \in T$ .

We queried an average speed of all road sections in the alternative trajectory $T_{i}$ between a time quantum spanning 30 min according to $t_{f}$ , which required us to find the time interval containing the time $t_{f}$ . We denoted the result as the actual speed, $V'_{i}$ .

Calculation process

We were able to choose the best trajectory from the alternative plans based on the close degree between the evaluation objects and idealized goal, as shown in formula (3)

C_{i +} = \frac{S_{i -}}{(S_{i +} + S_{i -})}

(3)

where $C_{i +}$ is the possibility of the evaluated object $i$ and $S_{i +}$ and $S_{i -}$ are the distances between the positive ideal, negative ideal, and evaluation object $i$ , respectively.

Here, we introduce the specific calculation steps, where the four attributes correspond to $M$ , $V$ , $P$ , $D$ , and $J$ for attributes, $I$ means trajectory:

Attribute normalization:⁴⁴ For speed matching degree, use $r_{ij} = 1 - (| a_{ij} - α_{i} | / max_{i} | a_{ij} - α_{i} |)$ ; for the remaining three attributes, use $r_{ij} = min_{i} (a_{ij}) / a_{ij}$ , obtain the initial decision matrix $R$ ;

Weighted calculation, $ω_{j} r_{ij}$ : We assume that four attribute weights are uniformly 0.25 and obtain $v_{ij}$ ;

Positive and negative solution calculations: $v_{j}^{+} = max_{i \in N} v_{ij}$ and $v_{j}^{-} = min_{i \in N} v_{ij}$ , where $v_{j}^{+}$ and $v_{j}^{-}$ are the positive and negative ideal solutions of all attribute values in all evaluation objects, respectively;

Object sort: $S_{i +} = \sqrt{\sum_{j = 1}^{n} {(v_{ij} - v_{j}^{+})}^{2}}$ , $S_{i -} = \sqrt{\sum_{j = 1}^{n} {(v_{ij} - v_{j}^{-})}^{2}}$ ;

Optimal trajectory: $max {C_{1 +}, C_{2 +}, \dots, C_{i +}}$ , the object with the maximum value for $C_{i +}$ is the optimum selection object.

Empirical validation of the model

In this section, we used the actual data to validate the proposed trajectory reconstruction model.

Initial road network

From the distribution of equipment without consideration of rural roads, we chose an initial network of Ruian as a research area, which could reflect the city’s traffic characteristics and consisting of 35 nodes and 108 road sections (Figure 6) and Table 2 shows the road length.

Figure 6.

Initial road network.

Table 2.

Partial information of road length.

Start location number	End location number	Length (m)	Start location number	End location number	Length (m)
62	61	515	51	52	638
61	60	411	51	64	407
81	80	500	52	53	394
80	82	469	52	63	536
77	78	477	63	64	514
78	79	550	53	62	632
67	66	885	62	63	643
…	…	…	…	…	…
62	81	375	57	56	320
81	77	351	56	42	618
77	67	584	56	60	1015
61	80	398	57	61	813
80	78	491	62	112	319
78	66	753	82	79	594
60	82	423	79	65	902

Data preparation

We extracted 1 week’s records from the preprocessed data in section 1 and finally found more than 2000 complete trajectories information combined with the research network. Figure 7(a)–(c) shows three complete routes from three vehicle trajectory record sets.

Figure 7.

Three vehicles’ trajectories: Green circles and black arrows in (a), (b), (c) are three vehicles' trajectories respectively.

To provide a contrast between our experimental results and a real situation, we need some incomplete trajectories. This article supposed the missing vehicle trajectory records are irregular; then, we set three sets of experiments based on the missing number of trajectory points. We erased part of the vehicle trajectories and reconstructed them with the model. According to the time of trajectory records, we sorted and numbered them from 1 to the last one and then we generated random numbers from the serial number and deleted the corresponding records:

Missing 30% information. In the first case, we assumed that the vehicle trajectory points are lost about; for each complete trajectory, we randomly dropped 30% of them, as shown in Table 3, case 1, and two records were dropped out.

Missing 60% information. In the second case, we thought that the vehicle lost about 60% information and then randomly erased trajectory points (Table 3, case 2).

Missing 80% information. In the third case, the vehicle lost most trajectory information, and we removed all records in addition to the start and end points (Table 3, case 3).

Table 3.

Vehicle travel information.

Group	Hidden records
Group	Case 1	Case 2	Case 3
Vehicle 1
Vehicle 2
Vehicle 2

With our method, we needed to obtain the actual speed and theoretical speed of each trajectory based on section 2. From the data and road network information, we calculated the average velocity per day of each section in the road network, as shown in Figure 8.

Figure 8.

Road average speed throughout a week.

Experimental results

Single-trajectory experiment

With our method, we needed to obtain the actual speed and theoretical speed of each trajectory based on section 2. We mainly described the calculation process of vehicle 1 (Figure 7(a) and case 1), and we received three possible trajectories of vehicle 1: T1 = {67, 77, 81, 80, 61, 60, 82}, T2 = {67, 77, 78, 80, 61, 60, 82}, T3 = {67, 77, 81, 62, 61, 60, 82}, and we obtained each section’s velocity profile every 30 min in the road network throughout the day. This vehicle first appeared at 12:16:20, so we obtained the road sections’ average speed of each alternative trajectory during the time period 12:00:00–12:30:00, corresponding to the 23 time intervals (the blue dotted line in Figure 9). We found that the actual speeds on the three routes were 26.9, 25.1, and 23. The theoretical speeds were 26.9, 28.3, and 26.8.

Figure 9.

The section speeds throughout the day in the road network.

Then, the initial decision matrix X was found: $X = \begin{matrix} T_{1} \\ T_{2} \\ T_{3} \end{matrix} [\begin{matrix} \begin{matrix} 5 \\ 5 \\ 5 \end{matrix} & \begin{matrix} 26.9 \\ 28.3 \\ 26.8 \end{matrix} & \begin{matrix} 4 \\ 3 \\ 2 \end{matrix} & \begin{matrix} 5 \\ 5 \\ 3 \end{matrix} \end{matrix}]$ . Using formulas (5) and (6), we found that the standardized decision matrix $R$ is $R = [\begin{matrix} \begin{matrix} 1 \\ 1 \\ 1 \end{matrix} & \begin{matrix} 1 \\ 0.16 \\ 0 \end{matrix} & \begin{matrix} 0.5 \\ 0.67 \\ 1 \end{matrix} & \begin{matrix} 1 \\ 1 \\ 1 \end{matrix} \end{matrix}]$ .

In this article, we defined the weight vector $ω = (0.25, 0.25, 0.25, 0.25)$ ; these four attributes were equally important, so we obtained the weighted criteria decision matrix $V$ , $V = [\begin{matrix} \begin{matrix} 0.25 \\ 0.25 \\ 0.25 \end{matrix} & \begin{matrix} 0.25 \\ 0.04 \\ 0 \end{matrix} & \begin{matrix} 0.125 \\ 0.1675 \\ 0.25 \end{matrix} & \begin{matrix} 0.25 \\ 0.25 \\ 0.25 \end{matrix} \end{matrix}]$ . Finally, three alternative trajectory possibilities are $[C_{1}^{+}, C_{2}^{+}, C_{3}^{+}] = [0.6667, 0.2055, 0.3333]$ .

These results indicate that the first alternative trajectory was chosen as the “best” one, and in fact, it is the vehicle’s true trajectory.

Large-scale trajectory experiments

For the three groups of experiments from 2000 trajectories, we calculated the accuracy separately. These results indicate that the first case has better efficacy with 85%, the value of second case is 64%, and the third case has the lowest value about 43%. With the missing information increase, the accuracy of trajectory reconstruction tends to reduce, and we found that the more the information was lost, the more alternative trajectories were generated in the reconstruction model. This means the vehicle has many possible routes, which would improve the likelihood of the nonreal trajectories and reduce the accuracy of the result.

As shown in Figure 10, there is no significant difference in the accuracy of workdays (days 1–5) and weekend (days 6 and 7). In order to analyze the accuracy of the model throughout peak time and off-peak time, we calculated the traffic flow every 5 min in day 1 (Figure 11); correspondingly, we can obtain the accuracy of model within each hour of this day (Figure 12), and from the result, we found that there is no special difference between different hours.

Figure 10.

The accuracy of three experiments throughout 7 days.

Figure 11.

The traffic flow every 5 min in day 1.

Figure 12.

The accuracy of the model within each hour in day 1.

For easy visual perception, we chose 10 trajectories from actual dataset and 3 experiments (Figure 13); case 1 is more similar to the actual. Furthermore, we have done more experiments to find the maximum missing rate 50%, and with this rate, we received an acceptable accuracy approximately 80%.

Figure 13.

The trajectories from three experiment results and actual dataset.

In this section, we explained a common method for obtaining the vehicles’ travel portfolios based on the ALPR data, and this method also applies to other data (such as GPS information).

Concluding remarks

Properly mining vehicle travel information from ALPR data improves the understanding of the characteristics of commuting vehicles and the traffic state of the roadway network. This study proposed a general method to obtain a vehicle’s complete travel information. Based on the vehicle identification data, we organized these records according to the vehicle plate number and recognized a single trajectory from the vehicle’s records based on the travel time threshold B. We proposed a model to reconstruct incomplete vehicle trajectories through depth-first traversal and TOPSIS algorithm, and through known records, we found possible routes and set four attributes to evaluate the best trajectory, which included the speed parameter highly depending on the ALPR data. A numerical experiment using identification data from Ruian, China, was conducted to validate the effectiveness of the proposed model, where we did three groups of contrast experiments according to the missing degree of trajectory records; the results demonstrated that with the increase in missing records, the accuracy of the model would fall, and we also found that the results of model would not be affected by date and time of day. Based on the trajectory reconstruction model, we could obtain complete vehicle records, which provide a very reliable data support. Therefore, our findings are important for mining ALPR data and the analysis of vehicle commuting characteristics; it can also provide the basis for road condition evaluation and planning.

Although the proposed methods are promising for constructing a vehicle’s trajectories, some improvement is necessary. For instance, the model of the trajectory construction should be procedural and applied to the complex roadway network. In addition, there should be more research on travel patterns for all vehicles, such as the commuting distance analysis, which may help with the analysis of the traffic state of the road network.

Footnotes

Handling Editor: Liping Jiang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This article is supported by the National Natural Science Foundation of China (51308021, U1564212, and 61773036), Beijing Natural Science Foundation (9172011), and Young Elite Scientist Sponsorship Program of the China Association for Science and Technology (2016QNRC001).

References

Spaccapietra

Parent

Damiani

et al . A conceptual view on trajectories. Data Knowl Eng 2008; 65(1): 126–146.

Hägerstraand

. What about people in regional science? Pap Reg Sci Assoc 1970; 24(1): 6–21.

Miller

. A measurement theory for time geography. Geogr Anal 2005; 37(1): 17–45.

Miller

. Modelling accessibility using space-time prism concepts within geographical information systems. Int J Geogr Inf Syst 1991; 5(3): 287–301.

Dai

et al . Learning traffic as images: a deep convolutional neural network for large-scale transportation network speed prediction. Sensors 2017; 17(4): 818.

Wang

et al . Large-scale transportation network congestion evolution prediction using deep learning theory. PLoS ONE 2015; 10(3): e0119044.

Song

Guan

et al . k-nearest neighbor model for multiple-time-step prediction of short-term traffic condition. J Transp Eng: ASCE 2016; 142(6): 04016018.

Wang

et al . Spatiotemporal recurrent convolutional networks for traffic prediction in transportation networks. Sensors 2017; 17(7): 1501.

Chen

et al . Probabilistic prediction of bus headway using relevance vector machine regression. IEEE T Intell Transp 2017; 18: 1772–1781.

10.

Simini

González

Maritan

et al . A universal model for mobility and migration patterns. Nature 2012; 484(7392): 96–100.

11.

Isaacman

Becker

Cáceres

et al . Identifying important places in people’s lives from cellular network data. In: Proceedings of the 9th international conference on pervasive computing, San Francisco, CA, 12–15 June 2011, pp.133–151. Berlin; Heidelberg: Springer.

12.

Liao

Fox

Kautz

. Extracting places and activities from GPS traces using hierarchical conditional random fields. Int J Robot Res 2007; 26(1): 119–134.

13.

Zhu

Cai

et al . Two-phase optimization approach to transit hub location—the case of Dalian. J Transp Geogr 2013; 33(4): 62–71.

14.

Liu

Zhou

Zhang

. Estimating users’ home and work locations leveraging large-scale crowd-sourced smartphone data. IEEE Commun Mag 2015; 53: 71–79.

15.

Yao

et al . An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Ann Oper Res 2016; 242(2): 303–320.

16.

Zhang

Wang

Sun

et al . The sightseeing bus schedule optimization under Park and Ride System in tourist attractions. Ann Oper Res. Epub ahead of print 7 November 2016. DOI: 10.1007/s10479-016-2364-4.

17.

Kung

Greco

Sobolevsky

et al . Exploring universal patterns in human home-work commuting from mobile phone data. PLoS ONE 2014; 9(6): e96180.

18.

Ashbrook

Starner

. Learning significant locations and predicting user movement with GPS. In: Proceedings of the 6th international symposium on wearable computers, Seattle, WA, 10 October 2002, pp.101–108. New York: IEEE.

19.

Vazquezprokopec

Bisanzio

Stoddard

et al . Using GPS technology to quantify human mobility, dynamic contacts and infectious disease dynamics in a resource-poor urban environment. PLoS ONE 2013; 8(4): e58802.

20.

Kong

Sun

et al . A bi-level programming for bus lane network design. Transport Res C: Emer 2015; 55: 310–327.

21.

Peng

Shan

Guan

et al . Stable vessel-cargo matching in dry bulk shipping market with price game mechanism. Transport Res E: Log 2016; 95: 76–94.

22.

Domenico

Lima

Musolesi

. Interdependence and predictability of human mobility and social interactions. Pervasive Mob Comput 2012; 9(6): 798–807.

23.

Becker

Hanson

Isaacman

et al . Human mobility characterization from cellular network data. Commun ACM 2013; 56(1): 74–82.

24.

Wang

Chen

et al . Transit smart card data mining for passenger origin information extraction. J Zhejiang Uni: Sci C 2012; 13(10): 750–760.

25.

Wang

et al . Mining smart card data for transit riders’ travel patterns. Transport Res C: Emer 2013; 36: 1–12.

26.

Chen

et al . Sustainable station-level planning: an integrated transport and land use design model for transit-oriented development. J Clean Prod 2018; 170(1): 1052–1063.

27.

Barroso

Dagless

Rafael

et al . Number plate reading using computer vision. In: Proceedings of the IEEE international symposium on industrial electronics, Guimarães, 7–11 July 1997, vol. 3, pp.761–766. New York: IEEE.

28.

Nelson

. License-plate recognition systems. In: Proceedings of the ITS world congress, Berlin, 21–24 October 1997, vol. 2, pp.26–29.

29.

Vajakas

Lillemets

. Trajectory reconstruction from mobile positioning data using cell-to-cell travel time information. Int J Geogr Inf Sci 2015; 29(11): 1941–1954.

30.

Sun

Ban

. Vehicle trajectory reconstruction for signalized intersections using mobile traffic sensors. Transport Res C: Emer 2013; 36(11): 268–283.

31.

Sun

Ban

Vehicle trajectory reconstruction for signalized intersections using mobile traffic sensors. Transport Res C: Emerg Tech 2013; 36: 268–283.

32.

Amir

Hedayat

Ardeshir

. Development of a delay model for unsignalized intersections applicable to traffic assignment. Transport Plan Techn 2011; 34(5): 497–507.

33.

Hanif

Jitamitra

Hesham

. A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times. Transport Res B: Meth 2006; 40(10): 857–871.

34.

Castillo

Menéndez

Sánchez-Cambronero

. Traffic estimation and optimal counting location without path enumeration using Bayesian networks. Comput-Aided Civ Inf 2008; 23(3): 189–207.

35.

Frentzos

Gratsias

Pelekis

et al . Algorithms for nearest neighbor search on moving object trajectories. Geoinformatica 2007; 11(2): 159–193.

36.

Manolopoulos

Nanopoulos

Papadopoulos

et al . R-trees: theory and applications (Advanced information and knowledge processing). London: Springer-Verlag, 2005.

37.

Kim

Shin

. A C2-continuous B-spline quaternion curve interpolating a given sequence of solid orientations. In: Proceedings of the computer animation’ 95, Geneva, 19–21 April 1995, pp.72–81. IEEE.

38.

Kim

. Interpolating and using most likely trajectories in moving-objects databases. In: Proceedings of the 17th international conference on database and expert systems applications (DEXA), Kraków, 4–8 September 2006, pp.718–727. Berlin; Heidelberg: Springer.

39.

Loan

CFV

. Introduction to scientific computing: a matrix-vector approach using MATLAB. Upper Saddle River, NJ: Prentice Hall, Inc., 1996.

40.

Kim

Bailey

et al . Curve-based representation of moving object trajectories. In: Proceedings of the database engineering and applications symposium, Coimbra, 9 July 2004, pp.419–425. New York: IEEE.

41.

Wang

Chen

et al . Track patching method for incomplete track in track-oriented traffic survey and analysis. Appl Res Comput 2014; 31(1): 162–165.

42.

Hwang

Yoon

. Methods for multiple attribute decision making. In: Hwang

Yoon

(eds) Multiple attribute decision making, vol. 186. Berlin; Heidelberg: Springer, 1981, pp.58–191.

43.

Dehne

Sack

Smid

. Algorithms and data structures. Berlin; Heidelberg: Springer-Verlag, 1991, pp.125–182.

44.

Howard

. Decision analysis: applied decision theory. In: Proceedings of the 4th international conference on operational research, Stanford Research Institute, 1966, p.57. New York: John Wiley & Sons.

Vehicle trajectory reconstruction from automatic license plate reader data

Abstract

Keywords

Introduction

Literature review

Data description and preprocessing

Data description

Data preprocessing

Vehicle trip extraction

Data organization

Single-vehicle trip recognition

The trajectory reconstruction model

Constructing trajectory patching set

Best trajectory

Decision attributes

Parameter calculation considering traffic operation characteristics

Calculation process

Empirical validation of the model

Initial road network

Data preparation

Experimental results

Single-trajectory experiment

Large-scale trajectory experiments

Concluding remarks

Footnotes

Declaration of conflicting interests

Funding

References