Map Matching with Simplicity Constraints

We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path according to this measure. However, these methods cannot guarantee that the result is simple (i.e. it does not intersect itself) even if the given curve is simple. In this paper, we prove that it is in fact NP-complete to determine the existence a simple cycle in a planar straight-line embedding of a graph that has at most a given Fr\'echet distance to a given simple closed curve. We also consider the implications of our proof on some variants of the problem

A Force-Directed Approach for Offline GPS Trajectory Map Matching

We present a novel algorithm to match GPS trajectories onto maps offline (in batch mode) using techniques borrowed from the field of force-directed graph drawing. We consider a simulated physical system where each GPS trajectory is attracted or repelled by the underlying road network via electrical-like forces. We let the system evolve under the action of these physical forces such that individual trajectories are attracted towards candidate roads to obtain a map matching path. Our approach has several advantages compared to traditional, routing-based, algorithms for map matching, including the ability to account for noise and to avoid large detours due to outliers in the data whilst taking into account the underlying topological restrictions (such as one-way roads). Our empirical evaluation using real GPS traces shows that our method produces better map matching results compared to alternative offline map matching algorithms on average, especially for routes in dense, urban areas.Comment: 10 pages, 12 figures, accepted version of article submitted to ACM SIGSPATIAL 2018, Seattle, US

Transformer-based Map Matching Model with Limited Ground-Truth Data using Transfer-Learning Approach

In many spatial trajectory-based applications, it is necessary to map raw trajectory data points onto road networks in digital maps, which is commonly referred to as a map-matching process. While most previous map-matching methods have focused on using rule-based algorithms to deal with the map-matching problems, in this paper, we consider the map-matching task from the data-driven perspective, proposing a deep learning-based map-matching model. We build a Transformer-based map-matching model with a transfer learning approach. We generate trajectory data to pre-train the Transformer model and then fine-tune the model with a limited number of ground-truth data to minimize the model development cost and reduce the real-to-virtual gap. Three metrics (Average Hamming Distance, F-score, and BLEU) at two levels (point and segment level) are used to evaluate the model performance. The results indicate that the proposed model outperforms existing models. Furthermore, we use the attention weights of the Transformer to plot the map-matching process and find how the model matches the road segments correctly.Comment: 25 pages, 9 figures, 4 table

Investigating the mobility habits of electric bike owners through GPS data

This paper investigates the mobility habits of electric bike owners as well as their preferred routes. Through a GPS tracking campaign conducted in the city of Ghent (Belgium) we analyze the mobility habits (travel distance, time spent, speed) during the week of some e-bike users. Moreover, we propose the results of our map matching, based on the Hausdorff criterion, and preliminary results on the route choice of our sample. We strongly believe that investigating the behavior of electric bikes’ owners can help us in better understanding how to incentivize the use of this mode of transport. First results show that the trips with a higher travel distance are performed during the working days. It could be easily correlated with the daily commuting trips (home-work). Moreover, the results of our map-matching highlight how 61% of the trips are performed using the shortest path

Integrity of map-matching algorithms

Map-matching algorithms are used to integrate positioning data with digital road network data so that vehicles can be placed on a road map. However, due to error associated with both positioning and map data, there can be a high degree of uncertainty associated with the map-matched locations. A quality indicator representing the level of confidence (integrity) in map-matched locations is essential for some Intelligent Transport System applications and could provide a warning to the user and provide a means of fast recovery from a failure. The objective of this paper is to determine an empirical method to derive the integrity of a map-matched location for three previously developed algorithms. This is achieved by formulating a metric based on various error sources associated with the positioning data and the map data. The metric ranges from 0 to 100 where 0 indicates a very high level of uncertainty in the map-matched location and 100 indicates a very low level of uncertainty. The integrity method is then tested for the three map-matching algorithms in the cases when the positioning data is from either a stand-alone global positioning system (GPS) or GPS integrated with deduced reckoning (DR) and for map data from three different scales (1:1250, 1:2500, and 1:50 000). The results suggest that the performance of the integrity method depends on the type of map-matching algorithm and the quality of the digital map data. A valid integrity warning is achieved 98.2% of the time in the case of the fuzzy logic map-matching algorithm with positioning data come from integrated GPS/DR and a digital map data with a scale of 1:2500

Map matching queries on realistic input graphs under the Fr\'echet distance

Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the trajectory, where spatial similarity is measured using the Fr\'echet distance. A shortcoming of existing map matching algorithms under the Fr\'echet distance is that every time a trajectory is matched, the entire road network needs to be reprocessed from scratch. An open problem is whether one can preprocess the road network into a data structure, so that map matching queries can be answered in sublinear time. In this paper, we investigate map matching queries under the Fr\'echet distance. We provide a negative result for geometric planar graphs. We show that, unless SETH fails, there is no data structure that can be constructed in polynomial time that answers map matching queries in $O((pq)^{1-\delta})$ query time for any $\delta > 0$, where $p$ and $q$ are the complexities of the geometric planar graph and the query trajectory, respectively. We provide a positive result for realistic input graphs, which we regard as the main result of this paper. We show that for $c$-packed graphs, one can construct a data structure of $\tilde O(cp)$ size that can answer $(1+\varepsilon)$-approximate map matching queries in $\tilde O(c^4 q \log^4 p)$ time, where $\tilde O(\cdot)$ hides lower-order factors and dependence of $\varepsilon$.Comment: To appear in SODA 202

Advanced Map Matching Technologies and Techniques for Pedestrian/Wheelchair Navigation

Due to the constantly increasing technical advantages of mobile devices (such as smartphones), pedestrian/wheelchair navigation recently has achieved a high level of interest as one of smartphones’ potential mobile applications. While vehicle navigation systems have already reached a certain level of maturity, pedestrian/wheelchair navigation services are still in their infancy. By comparing vehicle navigation systems, a set of map matching requirements and challenges unique in pedestrian/wheelchair navigation is identified. To provide navigation assistance to pedestrians and wheelchair users, there is a need for the design and development of new map matching techniques. The main goal of this research is to investigate and develop advanced map matching technologies and techniques particular for pedestrian/wheelchair navigation services. As the first step in map matching, an adaptive candidate segment selection algorithm is developed to efficiently find candidate segments. Furthermore, to narrow down the search for the correct segment, advanced mathematical models are applied. GPS-based chain-code map matching, Hidden Markov Model (HMM) map matching, and fuzzy-logic map matching algorithms are developed to estimate real-time location of users in pedestrian/wheelchair navigation systems/services. Nevertheless, GPS signal is not always available in areas with high-rise buildings and even when there is a signal, the accuracy may not be high enough for localization of pedestrians and wheelchair users on sidewalks. To overcome these shortcomings of GPS, multi-sensor integrated map matching algorithms are investigated and developed in this research. These algorithms include a movement pattern recognition algorithm, using accelerometer and compass data, and a vision-based positioning algorithm to fill in signal gaps in GPS positioning. Experiments are conducted to evaluate the developed algorithms using real field test data (GPS coordinates and other sensors data). The experimental results show that the developed algorithms and the integrated sensors, i.e., a monocular visual odometry, a GPS, an accelerometer, and a compass, can provide high-quality and uninterrupted localization services in pedestrian/wheelchair navigation systems/services. The map matching techniques developed in this work can be applied to various pedestrian/wheelchair navigation applications, such as tracking senior citizens and children, or tourist service systems, and can be further utilized in building walking robots and automatic wheelchair navigation systems