A map matching algorithm for intersections based on Floating Car Data Wenjie Liao1, Weifeng Lv, Tongyu Zhu, DongDong Wu State Key Laboratory of Software Development Environment, Beihang University, China
[email protected] and it is possible to estimate the accurate travel path of the vehicles by using traditional map matching algorithm to process the compact sampling data. In view of the cost of data transmitting and receiving, the sampling rate of the floating car is usually once per 30 seconds to once per 120 seconds in practice. The vehicle data that the traditional map matching algorithms[1] use have short distance between two adjacent sampling points, and two adjacent points are usually matched to the same or adjacent roads. However, under the sampling condition of the floating car, it is probable to match two points to two disjunct roads, in addition, the error of the GPS is usually over 15 meters[2], therefore the traditional map matching algorithms are incapable to figure out the travel path of the vehicle when it travels in the intersections, and the accuracy of map matching is greatly affected. In addition, the roads in the intersections are crowded, and the connectivity is complex, therefore the traditional map matching algorithms are unaccommodated to the complicated road network by way of regarding intersection roads as simple roads, and the estimated travel path is inaccurate. In conclusion, the traditional map matching algorithms can not adapt to the need of FCD processing. In the process of map matching, it is likely to make mistakes in the intersection area. So it has great limitation in describing road structure to use only nodes and links, and it is incapable to adjust the map matching algorithm to the different road structure. This paper designs a new road network structure, and the structure adds intersection nodes and links properties. Supported by the properties, network topology can be established, and route list of the intersections can be built. With the network topology, the new map matching algorithm process the two sampling points before and after the vehicle travel through the intersections, then find the route between two points by bidirectional search. This approach can decrease the effect of the GPS errors, and decrease the influence of
Abstract The traditional map matching algorithms consider little about the complicated structure of the road network, and regard all roads as the same. However, in the Transportation Information System using the Floating Car Data (FCD), the GPS sampling rate is low, and it is probable to figure out the incorrect result when the vehicle is in the intersection area. To solve this problem, this paper proposes a bidirectional heuristic map matching algorithm for intersections based on a data structure for intersections. This algorithm apply the data structure of intersections to separates the intersection part from common map matching, decreases the FCD map matching mistakes that caused by the complicated road network and the GPS errors, and increases the accuracy of map matching. Keywords: Floating Car Data (FCD), map matching, intersections, bidirectional heuristic search
1 Introduction With the continuous development of Intelligent Transportation System (ITS), the Floating Car Data (FCD) is used more and more as an advanced method to get traffic information of the roads. The Floating Cars System collects a large number of position, direction, speed information of vehicles, and process the data using map matching model and traffic information computing model, then it can figure out the travel time and travel speed information of the roads. In an Transportation Information System, the traffic information are all figured out from the Floating Car Data (FCD). And different from the GPS receivers of the Vehicle Navigation System, the sampling rate of the Floating Car Data is low. The sampling rate of the Vehicle Navigation System is usually once per second,
1 Supported by the National High-Tech Research and Development Plan of China Under Grant No.2006AA12Z315 (863) and the National Grand Fundamental Research 973 Program of China under Grant No. 2005CB321900
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the map matching errors to the following map matching.
2 Intersection network topology and data structure The main factors that affect the map matching in the intersection region are as follows: (1)The projecting errors caused by GPS errors; (2)The difficulties caused by the complicated traveling route of the vehicle; In the intersection area, the distances between roads are small, and the sampling points can be projected to several roads, which possibly do not include the actual traveling road because of the GPS error. In addition, the roads which the points are projected to are probable not adjacent, and the therefore the estimated traveling path of the vehicle can be incorrect. To solve the problems and adapt to the map matching algorithm for the intersections, this paper design a intersection structure. When building network topology, the intersection nodes and links besides common nodes and links are built at the same time. The intersection network model is describes as follows:
Figure 1 An intersection
3 Bidirectional heuristic map matching for intersections The traditional map matching algorithms match the sampling points according to the time order. This paper propose a bidirectional heuristic map matching algorithm, which firstly match the sampling points before and after the vehicle traveling through the intersection, then search links restrictedly by heuristic search criteria till reaching the intersection, finally find the travel route and match the points in the intersection using the intersection network topology.
I = ( N , L, T ) N = (N , N , N ) 1 2 3 L = {< n1 , n2 , id >| n1 , n2 ∈ N }, 且L = ( L1 , L2 , L3 ) T = {< id , l1 , l2 , R >| l1 ∈ L2 , l2 ∈ L3 , R = R '(l1 , l2 )} (1)
3.1 Heuristic search criteria
Where I describes intersections; N describes intersection nodes, N1 , N 2 , N 3 are internal nodes, entrance nodes and exit nodes; L describes intersection links , L1 , L2 , L3 are
In order to contract the range of search and improve the search efficiency, this paper restrict the bidirectional search by the relationship between vehicle traveling direction and the entrance and exit of the intersection, also by the distance from the sampling points to the intersection.
internal links, entrance links and exit links ， id describes the id which intersection the link belongs to; T describes a intersection list， id describes the intersection number, R '(l1 , l2 ) describes a route from the entrance link l1 to the exit link l2 。 Figure 1 is an intersection, N1 is internal node, N2 is entrance node, N3 is exit node, L1 is internal link, L2 is entrance link, L3 is exit link. When building network topology, the algorithm builds a list for all intersections, and every item in the list contains an intersection id, an entrance link, an exit link, and a route from the entrance link to the exit link. Every node has its properties besides the id which intersection it belongs to. Every link has several pointers pointing to the route which contains it in the intersection list.
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Figure 2
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In figure 2, assume the vehicle travels along the roads a, b, and according to the cosine theorem of triangle and limit theorem: a + b > 2c ⇒ cos C >
(2)
intersection list to find the route of the vehicle, then matches the sampling points in the intersection. After finding the entrance link l1 and the exit
3(a 2 + b2 ) 1 1 − ⇒ cos C > ⇒ C < 60° 2ab 4 2
link l2 , firstly search the list T , find the route that
R '(l1 , l2 ) represents, which is the route of the vehicle
then：
in the intersection. Then match the sampling points in the intersection to the links of the route. Equation 3 describes the match weight of a point to a link.
C ≥ 60° ⇒ a + b ≤ 2c
(3) When the deflection angle that the vehicle travels °
across is less than 120 , the distance between two adjacent sampling points can be regarded as longer than the route length that the vehicle passes through. When the vehicle travels into or out of the intersection,
f (d , θ ) = α ⋅
(5)
°
the included angle will not be larger than 120 , so by regarding the travel route as triangle, the forward and backward heuristic search criteria can be determined. the forward and backward heuristic search criteria are as follows： D θi < 90 lm1e + f (li ) < 2d p1i
D θ o < 90 lm2 s + f (lo ) < 2d p2o
d link, θ
1 1+
d
+ β ⋅ cos θ
σ2
is the distance from the sampling point to the
is the angle of traveling direction and the link direction. Presume that there are n sampling points in the intersection, and the match weight of a point to a link is f ( di , θi ) , then the equation 4 describes the total match weight of all points in the intersection:
(4)
Where p1 , p2 are the sampling points before traveling into and after travel through the intersection m1 , m2 are their matched points, e is the link that m1
n
W = ∑ f ( d i , θi ) i =0
(6)
is in, s is the link that m2 is in, l1 , l2 are the entrance link and exit link of the intersection; θi is the angle of the direction of p1 and l1 ， θ o
Presume that there are k match results, and the responding match weights are W1 , W2 ,..., Wk
is the angle of the direction of p2 and l2 ;
lm1e is the length between m1 and e , lm2 s is the
Wmax = max{W1 ,W2 ,...,Wk } (7) Then the match result which Wmax is responded to
length between m2 and s , f (li ) is the total length of all links from e to the entrance node of the
is final result, and the match point is the one that is nearest to the match link.
intersection, f (lo ) is the total length of all links from
3.3 The process intersection
the exit node of the intersection to s ， d p1i is the distance from p1 the entrance node of the intersection,
map
matching
for
When the vehicle travels into the intersection area, use the bidirectional heuristic algorithm to do map matching, and the functions to be performed as follows: （1）Read in the map data, and build the network topology I ; （2）When the sampling points are in intersection area, match the points p1 and p2 which are before and after vehicle traveling through the intersection, and m1 , m2 are their match point, then search afterwards and backwards separately.
d p2 o is the distance from p2 to the exit node of the intersection
3.2 Interior search in the intersections In order to reduce the effect of the complicated road structure and GPS errors to the map matching, the algorithm that this paper describes uses the definitive entrance and exit of the intersection that determined by the bi-directional heuristic search, and searches the
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（3）Search the subsequent links of e ,and find the entrance link conjoint with it; （4）Search the subsequent links of s ,and find the entrance link conjoint with it; （ 5 ） Search the intersection list T of I ， and
scheduled routes in daytime, and sent back their GPS data (include the vehicle id, time, longitude, latitude, traveling direction, speed) to be processed. The sampling rate is once per 90 seconds, and every route
find the route corresponding to R '(l1 , l2 ) , then figure
f (di ,θi ) and Wmax to match the sampling out points in the intersection area; （ 6 ） Connect the links outside and inside the intersection, and choose the best route. 3.4 Example of map matching intersection
for the
Figure 3 describes for four sampling points of a vehicle traveling through the intersection, and the first point is matched to links L1 and L2. As the second and third point are in intersection area, search till the fourth point and match it to the links L7 and L8. Search the subsequent links of L1 and L2 till reach the entrance link L3 and L4 of the intersection, and search the preceding links of L7 and L8 till reach the exit link L5 and L6 of the intersection. Then search the intersection list to find the route between L3, L4 and L5, L6, and figure out the matching links according to the matching weight. Finally the integral traveling path of the vehicle can be concluded. And Figure 4 describes the searching process of the links from the road network.
Figure 4 The bidirectional heuristic search
Figure 3 The sampling points in a intersection
which is 5-20 kilometers long is tested 3 or 4 times. Figure 5 describes the scheduled route of the vehicle. The accuracy of estimated traveling route is used to value the effect of the algorithm. Equation 8 describes the accuracy of estimated traveling route:
4 Experiment result and analysis In order to confirm the accuracy of the algorithm, an experiment was performed on the main intersections of Beijing such as SANYUAN Bridge and XIZHIMEN Bridge. Two taxis were chosen to traveling along 10
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accuracy =
t ot al l engt h of t he correct l y est i mat ed t ravel i ng l i nks t ot al l engt h of t he act ual t ravel i ng l i nks
Figure 5 The scheduled route of the vehicle The experiment compares the processing results of the bidirectional heuristic map matching algorithm to the heuristic map matching algorithm[3]. The heuristic algorithm uses the heuristic search method which is similar to A* algorithm, and select the vehicular possible traveling routes, and it has high accuracy in processing FCD on simple roads. Figure 6 describes the average accuracy of every route of two algorithms. We can make out that in most condition, this algorithm is better than heuristic map matching algorithm. Route
Route 1 Route 2 Route 3 Route 4 Route 5 Route 6 Route 7 Route 8 Route 9 Route 10
Total length of the route (km) 26.0 13.3 7.1 5.2 10.9 4.8 11.9 6.1 9.6
16.8
Accuracy of heuristic algorithm 30% 77% 16% 0% 48% 35% 68% 65% 38% 100%
Accuracy of bidirectional heuristic algorithm 93% 90% 89% 100% 95% 25% 81% 65% 74% 100%
Figure 7 heuristic map matching algorithm
Figure 6 Comparison result As shown in Figure 6, in the experiment, when the sampling rate of the FCD is low, the accuracy of the heuristic algorithm sometimes is low, especially when traveling across the intersection area. When the vehicle is in the intersection area, the heuristic algorithm may match the sampling points to the wrong road, and search the following roads. Then the estimated traveling route is incorrect or even can not be figured out. Compared to the heuristic algorithm, the
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bidirectional heuristic algorithm uses the intersection topology information and greatly reduces the effect of the low sampling rate and the road condition, and figure out the correct traveling path of the vehicle. Figure 7 and Figure 8 indicate an example of this situation. Figure 7 describes the estimated traveling path of the heuristic map matching algorithm. As shown in the figure, the roads are close and parallel, and the vehicle turns 270 degrees to travel from the west to the north. We can find that only the route before the vehicle turns south are figured out, and the turning part of the traveling route cannot be figured out. Figure 8 describes the estimated traveling path of the bidirectional heuristic map matching algorithm. By comparing the result of two figures, we can find that in Figure 8 the bidirectional heuristic map matching algorithm estimates the whole traveling path of the vehicle and in Figure 7 only a part of the path is figured out. In conclusion, this algorithm improves the accuracy of estimating.
Figure 8 bidirectional heuristic map matching algorithm
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[1]Christopher E. White, David Bernstein, Alain L. Kornhauser, Some map matching algorithms for personal navigation assistants Transportation Research Part C 8 (2000) 91-108 [2] D.Pfoser and C.S Jensen. Capturing the uncertainty of moving-object representations. In Proc. 6th SSD conf, pages 111-132, 1999 [3] Dongdong Wu, Tongyu Zhu, Weifeng Lv, Xin Gao, A Heuristic Map-Matching Algorithm by Using Vector-Based Recognition, Computing in the Global Information Technology, 2007. ICCGI 2007. International Multi-Conference on March 2007 Page(s):18 - 18
5 Conclusion This paper design a data structure of the intersections, and present a bidirectional heuristic map matching algorithm to solve the problem of low map matching accuracy in the intersections. This approach deduces the map matching errors caused by the GPS data, and improves the map matching accuracy without improve the sampling rate of the floating car.
Reference
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