A turning point-based offline map matching algorithm for urban road networks
Introduction
The past years have seen the popularity of Global Positioning System (GPS)-enabled devices being embedded in vehicles. This promotes the collection of a large amount of trajectory data that reflect vehicles’ positioning, speed, and direction information. In the Intelligent Transportation System (ITS), these GPS trajectory data are commonly integrated with the Geographic Information System (GIS) to provide individuals or companies with various services, such as vehicle navigation, tracking and recovering vehicles’ routes, and mapping new roads for the GIS [1]. In such integration with the GIS, a crucial step is to integrate trajectory data with spatial network data to identify the correct road segment on which a vehicle is travelling and to determine the vehicle’s location on the road segment, which is referred to as map matching [2]. Effective map matching is easy-to-achieve when the GPS trajectory data and the road network data are sufficiently accurate. However, real-world applications need effective map matching algorithms to handle GPS positioning errors and outdated road maps especially in dense urban road networks, where the road structure is very complicated and the road segments are usually dense.
Map matching can be performed in either online or offline mode in practice [3]. Online map matching algorithms are used to process real-time and streaming trajectory data and determine the road segment and/or the specific position (including lanes) where the vehicle is travelling [4], [5], [6]. They are used to facilitate some real-time services, such as vehicle navigation [7], driving trip path prediction [8], and taxi customer-searching [9]. In some other cases, we need to satisfy some trajectory-based services, such as travel route recommendation [10], anomalous taxi trajectory detection [11], and traversal time estimation [12]. These are the focuses of offline map matching algorithms that process stored and complete trajectory data and determine an entire best-matched path in the road network [13], [14], [15]. However, to ease the financial burden of transforming and storing raw data, the ITS typically reduces the sampling frequency of stored trajectory data [16]. For such low-sampling-rate trajectories, online map matching algorithms cannot guarantee complete and topologically feasible matched paths due to the so-called arc-skipping problem [17]. That is, the vehicle generally passes multiple road segments between two consecutive low-sampling-rate GPS points. Moreover, it is challenging to handle this in dense and complicated urban road networks, which is the focus of this paper.
A large number of offline map matching algorithms have been proposed for the case of low-sampling-rate trajectory data [13], [18], [19], [14]. To determine the specific travel path between two consecutive points, these matching algorithms typically first set multiple candidate matched positions for each trajectory point, and then calculate the shortest path between each pair of candidate positions of every two consecutive points. Although these algorithms can achieve high matching accuracies, they suffer from a long computation time caused by numerous shortest path calculations. Taking the algorithm proposed by Rahmani and Koutsopoulos [18] as an example, 71.18% of the matching time contributes to the shortest path calculations. A long computation time not only leads to a significant computation burden but also limits the application scenarios of these algorithms. For example, in the application of estimating the travel time of a path, existing route-based estimation methods need to call the map matching algorithm repetitively because they generally match and concatenate multiple historical and real-time trajectories that occurred in nearby areas during the current time period [20], [21], [12]. The resulting estimation process is thus inapplicable due to time-consuming repetitive map matching calculations. Therefore, it is crucial to improve the efficiency of the offline map matching. To address this challenge, this paper develops an efficient and effective offline map matching algorithm for low-sampling-rate trajectories.
Our map matching algorithm is designed based on the observation that a true travel path tends to be direct rather than roundabout [13]. In this case, before the vehicle turns, multiple consecutive trajectory points should be matched to the same road segment or the same approximately straight shortest path. Therefore, it is natural to match all trajectory points between two consecutive vehicle turns to a straight road segment or path at one time. This piecewise matching mechanism is promising to achieve a high computation efficiency because it eliminates the redundant shortest path calculations between every two consecutive trajectory points in the existing algorithms [13], [18], [6], [22]. Based on this mechanism, we develop a turning point-based map matching algorithm to perform piecewise map matching. The algorithm first identifies all vehicle turning points and separates the original trajectory into multiple sub-trajectories using the turning points. It then selects the best-matched path for each sub-trajectory from the corresponding K-shortest paths. To the best of our knowledge, this paper is the first to use turning points for piecewise matching in map matching. We will see in Sub-Section 5.3 that the proposed algorithm has clear advantages in both matching accuracy and efficiency compared with five state-of-the-art map matching algorithms [18], [3], [6], [23], [22].
This paper contributes to the literature by (1) introducing the concept of turning point into offline map matching to implement piecewise matching of travel trajectories, which leads to a substantial improvement of matching efficiency; (2) improving the performance of map matching by integrating piecewise matching with a K-shortest path solving method; and (3) finding that both correctly and incorrectly matched criteria are helpful to provide a comprehensive evaluation of the map matching performance.
The rest of this paper is organized as follows. Section 2 reviews related work in the literature. Section 3 introduces some notations and defines the offline map matching problem. Section 4 describes the proposed turning point-based map matching algorithm. Section 5 presents the results of numerical experiments. In Section 6, conclusions are made, and future research directions are discussed.
Section snippets
Related work
The research on map matching can be traced back to 1980’s [24]. According to the trajectory portion considered in each matching operation, existing map matching algorithms can be divided into three categories [14], including local algorithms [25], [4], [5], [26], incremental algorithms [17], [16], [6], [27], and global algorithms [28], [29], [13], [18], [30], [22].
The local map matching algorithm matches a single trajectory point at one time and does not care about its predecessors and
Notations and definitions
This section defines the preliminary notations and terms used for the offline map matching. Definition 1 (Trajectory Point): A trajectory point is a sampling point collected by a GPS device embedded in a vehicle to record the position of the vehicle. Let denote the ith trajectory point collected. is represented by a triple , which denote the longitude, latitude and timestamp of , respectively. Definition 2 (Trajectory): A trajectory T is a sequence of trajectory points ordered
Algorithm overview
Our turning point-based map matching algorithm is designed to match all trajectory points between two consecutive vehicle turns at one time. For each sub-trajectory between two vehicle turning points, the algorithm selects the best-matched path from the corresponding K-shortest paths. Fig. 1 presents the architecture of our algorithm, which consists of four steps: turning point-based separation, sub-network construction, K-candidate sub-path calculation, and the best sub-path selection.
Step 1:
Numerical experiment
We conduct extensive numerical experiments to evaluate the performance of our map matching algorithm, including the sensitivity analysis of algorithmic parameters and the performance comparison with five state-of-the-art map matching algorithms.
Conclusion
This paper proposed a novel turning point-based map matching algorithm to implement effective offline map matching based on the latitude, longitude, and timestamp information of GPS points. The proposed algorithm first separated the original trajectory into multiple sub-trajectories based on the identified turning points. Then, for each sub-trajectory, the algorithm constructed a sub-network to include all potential matched road intersections and road segments and calculated the -shortest
CRediT authorship contribution statement
Dongqing Zhang: Methodology, Investigation, Software, Validation. Yucheng Dong: Supervision, Methodology, Writing - review & editing. Zhaoxia Guo: Supervision, Methodology, Investigation, Funding acquisition, Resources, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
Guo would like to thank the financial supports from the National Natural Science Foundation of China (Grant No.: 71872118), the MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Grant No.: 18YJC630045), the Science and Technology Planning Project of Sichuan Province (Grant No.: 2020YJ0043), and Sichuan University (Grant No.s: 2018hhs-37, SKSYL201819). Zhang thanks the financial supports from the China Scholarship Council.
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