A Survey on Map-Matching Algorithms
AA Survey on Map-Matching Algorithms
Pingfu Chao , Yehong Xu , Wen Hua , and Xiaofang Zhou School of Information Technology and Electrical Engineering,The University of Queensland, Australia { p.chao,yehong.xu,w.hua } @uq.edu.au, [email protected] Abstract.
The map-matching is an essential preprocessing step for mostof the trajectory-based applications. Although it has been an active topicfor more than two decades and, driven by the emerging applications, isstill under development. There is a lack of categorisation of existing so-lutions recently and analysis for future research directions. In this paper,we review the current status of the map-matching problem and surveythe existing algorithms. We propose a new categorisation of the solu-tions according to their map-matching models and working scenarios.In addition, we experimentally compare three representative methodsfrom different categories to reveal how matching model affects the perfor-mance. Besides, the experiments are conducted on multiple real datasetswith different settings to demonstrate the influence of other factors inmap-matching problem, like the trajectory quality, data compression andmatching latency.
Nowadays, the ubiquity of positioning devices enables the tracking of user/vehicletrajectories. However, due to the intrinsic inaccuracy of the positioning systems,a series of preprocessing steps are required to correct the trajectory errors. Asone of the major preprocessing techniques, the map-matching algorithm findsthe objects travel route by aligning its positioning data to the underlying roadnetwork. It is the prerequisite of various location-based applications, such asnavigation, vehicle tracking, map update and traffic surveillance.The map-matching problem has been studied for more than two decades. De-spite hundreds of papers are proposed, to the best of our knowledge, only severalworks were conducted [4, 8, 14, 19] surveying them. More importantly, even themost recent surveys [8] fail to categorise the existing methods comprehensively.They either classify them based on applications [8] that are not very distinctiveto each other, or follow the previous categorisation [14] that is obsolete. Besides,various new techniques are introduced to the map-matching problem recently,including new models (weight-based [15], multiple hypothesis theory [16]), newtuning techniques (machine learning [12], information fusion [5, 9]), new datatypes (DGPS, inertial sensor, semantic road network) and new research topics(lane-level, parallel). Hence, it is about time to conduct a new survey to sum-marise existing solutions and provide guidance to future research.Note that the existing map-matching problem covers various scenarios, rang-ing from indoor to outdoor and from pedestrian, vehicle to multimodal. However, a r X i v : . [ c s . D B ] O c t P. Chao et al. to ensure a unified setting for survey and comparison, in this paper, we targetthe vehicle trajectory map-matching in an outdoor environment due to its pop-ularity. We categorise the existing work from technical perspective. In addition,we discuss the main properties of the methods and future research directionsaccording to the experiment results conducted on multiple matching algorithms.Overall, our contributions are listed as follows: – We review the map-matching solutions proposed since the last comprehensivesurvey [14] and propose a new categorisation of the algorithms based on theirmethodology. Our proposed categorisation can better distinguish the existingmethods from the technical perspective, which is beneficial for future study. – We enumerate several map-matching challenges that are caused by low-qualitytrajectory data. The challenges are exemplified and explained concretely, whichleads to future research directions. – To further demonstrate the challenges, we implement three representativemap-matching algorithms and conduct extensive experiments on datasets withdifferent sampling rate, map density and compression level. Our claims aboutthe relationship between data quality and map-matching quality are fullysupported by the experiments.The rest of the paper is organised as follows: In Section 2, we first formallydefine the map-matching problem and enumerate the existing surveys and theirlimitations. Then, we propose our new categorisation in Section 3. We furtherdiscuss the current challenges which are demonstrated through experiments inSection 4 and we draw conclusions in Section 5.
We first define the map-matching problem and relevant datasets, including tra-jectory (input), road network (input) and route (output):
Definition 1. (Trajectory) A trajectory
T r is a sequence of chronologicallyordered spatial points
T r : p → p → ... → p n sampled from a continuouslymoving object. Each point p i consists of a 2-dimensional coordinate < x i , y i > ,a timestamp t i , a speed spd i (optional) and a heading θ i (optional). i.e.: p i =
Definition 4. (Map-Matching) Given a road network G ( V, E ) and a trajectory T r , the map-matching find a route MR G ( T r ) that represents the sequence ofroads travelled by the trajectory. For simplicity, we omit the subscript G and use MR ( T r ) instead to repre-sent the matching result as different trajectories are usually map-matched onthe same map. In general, the map-matching route is expected to be continu-ous as it represents the vehicle’s travel history. However, it is quite often that MR ( T r ) contains disconnected edges due to incorrect map-matching, which willbe discussed in Section 4.
Intuitively, since the vehicle usually runs on the roads, a fully accurate trajectorysampled from a vehicle should always lie on the map. Therefore, apart from someunexpected map errors, which happens less frequently and is addressed by mapupdate process [2], the difficulty of map-matching problem solely depends on thequality of the input trajectories. As studied in many papers, the quality issues intrajectories are pervasive, which mainly caused by inaccurate measurement andlow sampling rate. In terms of the measurement error , due to the unstable con-nection between GPS device and satellites, the location of GPS samples usuallydeviate from its actual position by a random distance. Meanwhile, the samplingerror is mainly caused by lowering the sampling frequency.To deal with the quality issues, the map-matching problem has been studiedfor more than two decades. In terms of the working scenarios and applications,the current map-matching solutions can be classified into online mode and offlinemode. In online map-matching, the vehicle positions are sampled continuouslyand are processed in a streaming fashion, which means each time the map-matching is only performed on the current sample with a limited number ofpreceding or succeeding samples [3,21] as reference. The process is usually simpleand fast for interactive performance. In contrary, the offline map-matching isperformed after the entire trajectory is obtained, so it aims for optimal matchingroute with less constraint on processing time.From the methodology perspective, Quddus et al. [14] first conducted a com-prehensive review of the map-matching algorithms proposed before 2007. Thepaper classified the methods into four categories, namely geometric , topology , probabilistic and advanced . The geometric methods only focus on the distancebetween trajectory elements and the road network, while the topology methodstake into consideration the connectivity and shape similarity. The probabilistic methods try to model the uncertainty of trajectory, including the measurementerror and the unknown travel path between two samples, and they aim to finda path that has the highest probability to generate the given trajectory. The advanced category contains methods that are based on some advanced mod-els, like Kalman Filter, particle filter and fuzzy logic. This categorisation showsthe evolution of map-matching research, which starts from simple, fast but in-accurate geometric-based methods to more complicated but accurate probabil-ity/advanced solutions. It is by far the most comprehensive survey of this field. P. Chao et al.
However, after more than ten years’ development, most of the methods men-tioned in the paper has been outperformed by their new successors and theprevious categorisation also requires a revisit. Several surveys proposed after-wards reviewed the methods in certain perspectives. Hashemi et al. [4] targetedat the online map-matching scenario. Kubiˇcka et al. discussed the map-matchingproblem based on the applications [8], namely navigation , tracking and mapping .Other categorisations also appear recently ( incremental max-weight , global max-weight and global geometry [19]) which shows that there is still no consensus onhow to classify the algorithms technically. However, all of the existing categori-sations inherit the same idea from Quddus’ survey [14] with minor variations,which fail to categorise the recent methods for multiple reasons, explained inSection 3. According to our study, previous categorizations fail to classify the current so-lutions due to three main reasons: (1) Categories for some primary methods,such as geometric category [14], are no longer the focus due to their weak per-formance. (2) Application-based classification [4, 8] cannot fully distinguish themethods. Many of the map-matching algorithms, like the Hidden Markov Model(HMM) and Multiple Hypothesis Technique (MHT), apply to both online andoffline scenarios for different applications. (3) Classifying algorithms by embed-ded mathematical tools are not feasible since many recent algorithms employmultiple mathematical tools. Furthermore, the same tool implemented in dif-ferent algorithms may be used for different purposes, for example, an extendedKalman filter can be used to either estimate biases in GPS or fuse measurementsfrom different sources [9].Therefore, we establish a new classification that classifies the map-matchingalgorithms by their core matching model, which is employed to coordinate theirtechniques to finally achieve map-matching. In a map-matching algorithm, themap-matching model is the overall framework or matching principle for the map-matching process. A model usually consists of a set of computation components,like the calculation of distance, transition and user behaviour modelling, and aworkflow connecting them. Those components are fixed while their definition andimplementation vary among different methods. Existing map-matching modelscan be categorised into four classes: similarity model , state-transition model , candidate-evolving model and scoring model . The similarity model refers to a general approach that returns the vertices/edgesthat is closest to the trajectory geometrically and/or topologically. Intuitively,since a vehicle’s movement always follows the topology of the underlying roadnetwork and the vehicle can never leap from one segment to another, the tra-jectory should also similar to those of the true path on the map. Therefore, themain focus in this category is how to define the closeness . Survey on Map-Matching Algorithms 5
Distance-based
Most of the earliest point-to-curve and curve-to-curve match-ing algorithms [14] follow this idea. Specifically, the point-to-curve solutionprojects each trajectory point to the geometric-closest edge, whereas the curve-to-curve matching algorithms project each trajectory segment to the closest edgewhere the closeness is defined by various similarity metrics. Fr´echet distance isthe most commonly-used distance function [18] since it considers the monotonic-ity and continuity of the curves. However, it is sensitive to trajectory measure-ment errors since its value can be dominated by the outliers. As an alternative,Longest Common Subsequence (LCSS) [23] divide a trajectory into multiplesegments and find the shortest path on the map for each pair of start and endpoints of a trajectory segment. The shortest paths are then concatenated andform the final path while their corresponding LCSS scores are summed as the fi-nal score. Then, the path whose LCSS score is higher than a predefined thresholdis regarded as the final matching result.
Pattern-based
The pattern-based algorithms utilise the historical map-matcheddata to answer new map-matching queries by finding similar travel patterns [22].The assumption is that people tend to travel on the same paths given a pair oforigin and destination points. Therefore, by referring to the historical trajecto-ries that are similar to the query trajectory, its candidate paths can be obtainedwithout worrying about the sparseness of trajectory samples. Specifically, a his-torical trajectory or a trajectory obtained by concatenating multiple historicaltrajectories will be referred to if each point of this trajectory is in the safe regionaround the query trajectory. The algorithm finally uses a scoring function todecide the optimal route. However, due to the sparsity and disparity of histori-cal data, the query trajectory may not be fully covered by historical trajectoriesespecially in some rarely travelled regions, which leads to a direct matchingprocess.
The state-transition models build a weighted topological graph which containsall possible routes the vehicle might travel. In this graph, the vertices representthe possible states the vehicle may be located at a particular moment, while theedges represent the transitions between states at different timestamps. Differentfrom the road network, the weight of a graph element represents the possibilityof a state or a transition, and the best matching results comes from the optimalpath in the graph globally. There are three major ways of building the graphand solving the optimal path problem, namely Hidden Markov model (HMM),Conditional Random Field (CRF) and the Weighted Graph Technique (WGT).
Hidden Markov model
HMM is one of the most widely used map-matchingmodels as it simulates the road network topology meanwhile considers the rea-sonability of a path. HMM focuses on the case when states in the Markov chain
P. Chao et al. are unobservable (hidden) but can be estimated according to the given observa-tions associated with them. This model fits in the map-matching process nat-urally. Each trajectory sample is regarded as the observation, while the vehicleactual location on the road, which is unknown, is the hidden states. In fact,due to the trajectory measurement error, all the roads near the observation canpotentially be the actual vehicle location (state), each of which with a probabil-ity (emission probability). As the trajectory travels continuously, the transitionbetween two consecutive timestamps is concluded by the travel possibility (tran-sition probability) between their candidate states. Therefore, the objective is tofind an optimal path which connects one candidate in every timestamp. The fi-nal path is obtained by the Viterbi algorithm which utilises the idea of dynamicprogramming. The major difference between various HMM-based algorithms istheir definition of emission probability and transition probability. Unlike theemission probability, which is defined identically in most papers, the definitionof the transition probability varies since the travel preference can be affected byplenty of factors. Some works [11] prefers a candidate pair whose distance is sim-ilar to the distance between the observation pair, while others consider velocitychanges [3], turn restriction [12], closeness to the shortest path, the heading mis-match and travel penalty on U-turns, tunnels and bridges. Besides, HMM is alsoapplied to online scenario [3]. However, to build a reasonable Markov chain, on-line HMM-based algorithms usually suffer from latency problems, which meansa point is matched after a certain delay.
Conditional random field
CRF is utilized in many areas as an alternativeto HMM to avoid the selection bias problem [6]. As both CRF and HMM arestatistic models, the major difference is that CRF models interactions amongobservations while HMM models only model the relation between an observationwith the state at the same stage and its closest predecessor. Hunter et al. [6]proposed a CRF-based map-matching algorithm that can be applied to bothonline and offline situations with high accuracy. Its overall approach is similar toHMM-based algorithms but with different transition probability which considersthe maximum speed limit and the driving patterns of drivers. However, theproblem shared by both HMM and CRF is the lack of a recovery strategy forthe match deviation. Since once a path is confirmed, it will be contained by allfuture candidate paths, which hurts the online scenarios especially.
Weighted graph technique
WGT refers to a model that infers the matchingpath from a weighted candidate graph, where the nodes are candidate road pointsof location measurements and edges are only formed between two nodes corre-sponding to two consecutive samples. In most WGT-based algorithms, candidatepoints are the closest points on road segments in a radius of measurements [5,10],which is similar to HMM. The process of the WGT can be summarized as threesteps: (1) Initializing the candidate graph. (2) Weighting edges in the graphusing a scoring function. (3) Inferring a path based on the weighted graph.
Survey on Map-Matching Algorithms 7
Algorithms fall in this category mainly differs from each other in weightingfunctions. Lou et al. [10] firstly propose the WGT. It weights an edge simplybased on a spatial cost and a temporal cost, where the spatial cost is modelledon the distance between candidate c i to its observed position p i and the shortestlength between c i and c i +1 whereas the temporal cost is modelled on the ve-locity reasonability. Based on Lou’s design, the following work further considersmutual influences between neighbouring nodes, road connectivity, travel timereasonability [5] and other road features (traffic lights, left turns, etc.). Candidate-evolving model refers to a model which holds a set of candidates (alsoknown as particles or hypotheses) during map-matching. The candidate set isinitiated based on the first trajectory sample and keeps evolving by adding newcandidates propagated from old ones close to the latest measurements whilepruning irrelevant ones. Interpreting a candidate as a vote, by maintaining thecandidate set, the algorithms are able to find a segment with the most votes,thereby, determining the matching path. Compare to the state-transition model,the candidate-evolving model is more robust to the off-track matching issue sincethe current matching is influenced not only by a previously defined solution, butalso by other candidates. The particle filter (PF) and the Multiple HypothesisTechnique (MHT) are two representative solutions.
Particle filter
PF is a state estimation technique that combines Monte Carlosampling methods with Bayesian Inference. This technique has been utilized tosupport map-matching by the way of sensor fusion and measurement correction[17], while it is also applicable to directly address map-matching problem [1].The general idea of the PF model is to recursively estimate the ProbabilityDensity Function (PDF) of the road network section around the observation astime advances. Here, the PDF is approximated by N discrete particles, eachparticle maintains a weight representing how consistent it is to the locationobservation. The process of a PF can be summarized as follows: Initially, N particles are sampled with the same weight representing different locations inthe local road network. The weight of each particle keeps getting updated as newobservations are received. Then the PDF for the road network section aroundthe new observations is calculated and the area with the highest probability isdetermined as the matched region. A resampling stage starts afterwards, wherea new set of particles are derived based on the current set. The particles withhigher weights are more likely to propagate according to moving status to feedparticles for the next cycle, while those with low weights are likely to die out. Multiple hypothesis technique
Similar to PF, the MHT also tries to main-tain a list of candidate road matches for the initial trajectory point and the listis expected to be as large as possible to ensure correct result coverage. However,different from the PF which iterate through all possibilities over time, the MHT
P. Chao et al. is a much simpler model that inherits the idea of maintaining hypotheses butmanages to reduce computation during the process. An MHT evaluates eachcandidate road edge (or point) based on a scoring function instead of trying toapproximate the complicated PDF for the neighbour map area. Thereby, thecomputation cost of the MHT is dramatically reduced. According to the intu-ition, the MHT can be easily adopted in online scenario [16]. Moreover, sinceit possesses all the possibility of previous hypotheses, Taguchi et al. [16] pro-pose a prediction model which extends the hypotheses to further predict thefuture route, which can achieve better online map-matching accuracy withoutintroducing latency.
A group of algorithms [13,15] apply the weight without usinga particular model. Instead, they simply assign a group of candidates to eachtrajectory segment (or location observation) and find a road edge from eachgroup that maximizes the predefined scoring function. The found segment inevery timestamp is either returned if applied to the online scenario or waited tobe joint with other matched segments if applied in the offline scenario. Most re-cent work in this category [15] achieves a lane-level map-matching performance.The algorithm first identifies lanes in each road by utilising the road width in-formation in the map and partition them into grids accordingly. The algorithmthen finds candidate lane grids around the observed location and scores thesegrids at each timestamp. The grid results in the maximum score are then re-turned. The scoring function is a linear combination of four features, i.e. theproximity between the grid and trajectory sample, the estimated location of thevehicle at the next time stage, the reachability from the grid and the intentionof a turn. These features are modelled individually, their scores can be obtainedfrom the corresponding models in every timestamp. In addition, feature scoresare weighted differently in the scoring function whose coefficients are computedby a training process before map-matching starts.
Despite various of map-matching models are proposed to deal with trajectoryquality issues, the current solutions still fail to achieve decent matching qualityin all scenarios. Therefore, in this section, we will discuss several major chal-lenges caused by data quality issues that are affecting the map-matching results.We will demonstrate them both visually and experimentally to exemplify theirsignificance.
As listed in Table 1, we use four datasets for our experiments. The
Global [7]dataset is a public dataset for map-matching evaluation. It contains 100 GPStrajectories sampled from 100 different areas all over the world, each of which is
Survey on Map-Matching Algorithms 9 provided with a dedicate underlying map. Besides, we extract three sub-areas,namely
Beijing-U , Beijing-R and
Beijing-M , from a commercial dataset whichcontains taxi trajectories in Beijing. The reason for choosing these four datasetsis their diversity in terms of trajectory quality and map density. The
Global dataset has the best trajectory accuracy and its maps are also very sparse. The
Beijing-U and
Beijing-R represent two maps extracted from urban and ruralareas, respectively. They have roughly the same size but different map density(27 . vs . Beijing-M is a larger map area with more trajectories forlarge-scale performance test.
Table 1.
Summary of experiment datasets
Name Input Trajectory Road Network
Trajectory Trajectory Sampling km ) ( km/km )Global 100 1 N/A N/A N/A N/ABeijing-U 7,905 247,544 11.0 7,672 4,484 9.9 27.3Beijing-R 3,106 119,612 8.6 3,927 1,326 9.9 13.9Beijing-M 73,072 3,285,934 10.3 41,353 22,580 57.0 24.2 Our experiments are performed on a single server with two Intel(R) Xeon(R)CPU E5-2630 with 10 cores/20 threads at 2.2GHz each, 378GB memory andUbuntu 16.04. Both the route matching result MR ( T r ) and the correspondingground-truth are regarded as sets of road edges and are evaluated by F-measure,which is commonly used in map-matching evaluation [15,19]. The candidate map-matching algorithms used in the experiments include the most popular offlineHMM map-matching [11], the most-recent offline WGT algorithm [20] and anonline Scoring method [13].
According to our observations from the experiments, the current data qualityissues affect the map-matching in three major ways: the unnecessary detours,the matching breaks and the matching uncertainty.
Unnecessary detour
As an example shown in Fig. 1a, the matching resultsometimes may contain unnecessary detours, which happens more frequentlywhen the trajectory sampling rate is very high. In most scenarios, the detouris caused by two consecutive trajectory samples being too close to each otherso that the succeeding point happens to be matched to the upper stream of itspreceding point. Therefore, the shortest path between these two points has togo through a long detour. To avoid such issue, the measurement error shouldbe considered when finding the shortest path, which means a certain degree ofbacktrace should be allowable. Alternatively, instead of simply project trajec-tory samples to the candidate roads to find candidate points, the actual match-ing point should follow a distribution, according to the trajectory measurementerror, along the candidate road. (a) Unnecessary detour (b) Matching break
Fig. 1.
Example of map-matching challenges
In general, as depicted in Fig. 2a, the detour problem strongly affects thematching quality when the sampling rate is high. The result shows that it is notalways the case that a higher sampling rate leads to higher matching qualityespecially when the measurement error becomes the major problem. Therefore,a better way of modelling the measurement error is still required. (a) Accuracy over differentsampling rate (b) Down-sample v.s. com-pression (c) Influence of map densityand trajectory quality
Fig. 2.
Experimental results
Matching break
The matching break is a common problem in map-matching,which is mainly caused by trajectory outliers. This happens more frequentlyin the state-transition matching model when the correct state falls out of thecandidate range of the outlier. In this case, the states of two consecutive obser-vations may be unreachable, leading to disconnected matching route, as shownin the green circled area in Fig. 1b. Currently, most of the solutions [11] try toovercome this problem by identifying and removing the outliers to remedy thebroken route. In Fig. 2b, we apply online scoring method on
Beijing-M withrandom down-sample and trajectory compression (Douglas-Peucker algorithm),respectively. The result shows that simple trajectory compression fails to pruneoutliers as they are usually preserved as outstanding point, which means morepreprocessing step is required to remove such outliers. However, considering thedetour problem in high sampling rate data, the trajectory compression achievesbetter performance compared with simply down-sample the trajectory as it bet-ter preserve the shape of the trajectory, which is still beneficial.
Survey on Map-Matching Algorithms 11
Matching uncertainty
Although the main goal of map-matching algorithmsis to reduce the uncertainty of trajectory, the matching uncertainty varies indifferent scenarios. One of the main factor, which is not mentioned by any ofprevious work, is the map density. Intuitively, the map-matching of trajectory ismuch harder when the map area is full of roads compared with an emptier region.As shown in Fig. 2c, the map density can significantly affect the matching qualityas the
Beijing-U has much worse performance than
Beijing-R given both ofthem have a similar trajectory quality. On the other hand, the trajectory qualityalso plays an important role since the performance on
Global is better than on
Beijing-U with similar map density. Therefore, achieving decent performance ondense map area is still a challenging task for future map-matching research.
In this paper, we conduct a comprehensive survey of the map-matching problem.We reveal the inability of all previous surveys in classifying new map-matchingsolutions. On top of that, we propose a new categorisation of existing meth-ods from the technical perspective, which consists of similarity model, state-transition model, candidate-evolving model and scoring model. In addition, welist three major challenges (unnecessary detour, matching break and matchinguncertainty) that the current map-matching algorithms are facing. To exem-plify and demonstrate their influence on the current map-matching algorithms,we conduct extensive experiments over multiple datasets and map-matching al-gorithms. Overall, this paper concludes the current state of the map-matchingproblem and provides guidance to future research directions.
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