THE MA MATCHING ALGORITHM OF GS DATA WITH RELATIVELY LONG OLLING TIME INTERVALS Jae-seok YANG Graduate Student Graduate School of Engneerng Seoul Natonal Unversty San56-, Shllm-dong, Gwanak-gu, Seoul, 5-74 Korea Fax: +8-0-889-003 E-mal: bluedge0@snu.ac.kr Seung-pl KANG Assocate rofessor Graduate School of Engneerng Seoul Natonal Unversty San56-, Shllm-dong, Gwanak-gu, Seoul, 5-74 Korea Fax: +8-0-889-003 E-mal: kangsp@snu.ac.kr Kyung-soo CHON Full rofessor Graduate School of Engneerng Seoul Natonal Unversty San56-, Shllm-dong, Gwanak-gu, Seoul, 5-74 Korea Fax: +8-0-889-003 E-mal: chonks@snu.ac.kr Abstract: Many map matchng algorthms have been developed to match GS ponts to a dgtal map n prevous studes. But the prevous studes assume short pollng tme ntervals(about second) of the GS data. And the map matchng algorthms of such studes are not approprate for the GS data wth relatvely long pollng tme ntervals(about ~5 mnutes). In ths paper, we wll revew the prevous map matchng algorthms and dscuss the map matchng algorthms whch can be used under crcumstances of relatvely long pollng tme ntervals. Key Words: Map matchng, GS, ollng tme. INTRODUCTION Roles of the GS n obtanng the traffc nformaton wll become sgnfcant more and more. To generate traffc nformaton of better qualty, the accuracy of GS data and dgtal maps should be guaranteed. Although the SA(Selectve Avalablty) was removed on May, 000, the postonal error of GS wthout addtonal error correcton methods goes up to about 30 meters. In case of dgtal maps, varous factors lke errors n dgtzng map and the dstance from the road centerlne to the both end of the road makes the postonal error of nearly 0 meters. As a result, the drect overlay of postonal data obtaned from GS does not reconcle wth a dgtal map. Therefore GS data need to be corrected wth varous methods to match wth a dgtal map and we call ths procedure a map matchng. Algorthms of the map matchng have been developed contnuously and they can be classfed nto two categores roughly. Frst, map matchng algorthms whch consder only geometrc relatonshps between GS data and a dgtal map. Secondly, map matchng algorthms whch 56
consder not only geometrc relatonshps but also the topology of the road network and the hstory of GS data. It has been reported that the latter worked better mostly. The frst map matchng algorthms can be classfed agan nto the map matchng algorthm usng the dstance of pont-to-curve, one usng the dstance of curve-to-curve and one usng the angle of curve-to-curve. Some past studes used the dstance of pont-to-pont. But these vertex-based map matchng algorthms are approprate when one pursues smplcty rather than accuracy. The second map matchng algorthms use the result of map matchng at tme t- for the map matchng of GS data at tme t. And for the selecton of canddate segments whch GS data wll be matched, the topology of the road network s nputted as a constrant. But these algorthms should be used under partcular prudence. For example, f the result of map matchng at tme t- s wrong then the result of map matchng after that tme wll be wrong also. Thus, t should be guaranteed that the result of map matchng at tme t- s exact to use these algorthms. Besdes, f the vehcles wth a GS recever follow abnormal routes(e.g. the left turn on the left turn restrcted ntersecton) we cannot expect the rght result of map matchng because the normal topology respects traffc regulatons. Most of prevous studes of map matchng was under crcumstances of very short pollng tme nterval(about second). The shorter the pollng tme nterval s, the better the performance of the map matchng algorthm s, because the avalablty of the GS data hstory wll be ncreased. But n practce, varous problems restrct the shortenng of the pollng tme nterval. For example, there should be some telecommuncaton method to collect the GS data of many persons on real tme. And f the telecommuncaton s accomplshed by the thrd telecommuncaton company, very short pollng tme wll nevtably accompany wth a vast cost as f you use your cellular phone for a long tme, you wll have to pay hgh cost. Therefore, we wll revew the prevous map matchng algorthms and dscuss the map matchng algorthms whch can be used under crcumstances of relatvely long pollng tme ntervals(about ~5 mnutes). And the focus wll be lad on the map matchng algorthm consderng not only geometrc relatonshps but also the topology of the road network and the hstory of GS data.. LITERATURE REVIEW. Dscrmnaton of Vertex-based and Segment-based Map Matchngs Nodes, vertces, lnks and segments should be defned clearly before the lterature revew. Nodes and lnks are relatvely well known. For example, an ntersecton s a node. A lnk s a secton of road between ntersectons. Whte ponts n Fgure are nodes and there s only one lnk n Fgure. When the real road network s dgtzed, a curve s descrbed wth a set of many straght lnes. Vertces are ponts whch separate these straght lnes, and each straght lne s a segment. Fgure. The Composton of the Road Network 56
The clear defnton of the composton of the road network helps us to understand prevously studed map matchng algorthms whch can be roughly classfed nto two categores; vertex-based map matchngs and segment-based map matchngs. The Fgure shows these two map matchng algorthms. Fgure. Vertex-Based and Segment-Based Map Mathcngs If the real poston of the vehcle wth a GS recever s 0, the vertex-based map matchng mples a postonal error of d e. Whle the segment-based map matchng does not have ths error. In fact, the Fgure shows map matchngs under the deal condton. There can be another postonal error although a GS pont s matched to a segment properly(e.g. the real poston of the vehcle can be the vcnty of 0 ), but ths knd of error s not dealt n ths paper. Sometmes vertex-based map matchngs are used even though the weakness mentoned above. There can be many reasons for ths; for the smplcty of the map matchng process or the data structure whch s not approprate for the segment-based map matchng. Nowadays, there s no reason to use vertex-based map matchngs because the performance of computers and GIS packages s sgnfcantly mproved.. Map Matchngs Usng the Geometrc Relatonshp The basc form of the prevous map matchng algorthms s the map matchngs usng the geometrc relatonshps between the GS ponts and the network. Noh and Km(998) classfed such map matchngs nto three categores; the map matchng usng the dstance of pont-to-curve, one usng the dstance of curve-to-curve and one usng the angle of curve-to-curve. a a b b Fgure 3. The Map Matchng Usng the Dstance of ont-to-curve 563
The map matchng usng the dstance of pont-to-curve matches a GS pont to the nearest segment. Because t s the smplest form of the map matchngs, t has many problems. Fgure 3 shows the example of the problem. a and a are the vertce of the road A. b and b are the vertce of the road B. and are the two consecutve GS ponts. If the GS ponts are matched to the nearest segment, s matched to the road B whle s matched to the road A. That s to say, the map matchng concluded the unrealstc result that the car jumped from the road A to the road B. Map matchng algorthms whch use the nformaton of only one pont wll frequently meet such a problem. To overcome ths problem, the map matchngs usng the dstance of curve-to-curve or the angle of curve-to-curve was developed. a l a a l a l b b l b b Fgure 4. The Map Matchng Usng the Dstance of Curve-to-Curve The map matchng usng the dstance of curve-to-curve matches two GS ponts to the segment whch has the shortest dstance from the reference lne. The reference lne s the lne whch connect two GS ponts. There are many methods of measurng the dstance between the reference lne and the segment. The smplest method s to sum up the dstances between two end ponts. For example, and are matched to the road A because l + l ) < ( l + l ) n Fgure 4. ( a a b b a α β b b a Fgure 5. The Map Matchng Usng the Angle of Curve-to-Curve The map matchng usng the angle of curve-to-curve matches two GS ponts to the segment whch has the smallest angle from the reference lne. The reference lne s the lne whch 564
connect two GS ponts, too. For example, and are matched to the road A because α < β n Fgure 5..3 Map Matchngs Usng the Network Topology and the Data Hstory Most map matchng algorthms usng the network topology and the data hstory, whch also use the geometrc relatonshps, have smlar man algorthm. Greenfeld(00) matched the GS ponts to the nearest lnk usng only the geometrc relatonshps when the pont s the frst GS pont or the dstance between the prevous pont( ) and the present pont( t ) s too long. On the other hand, when the dstance between and t s under a partcular threshold, the algorthm evaluates the proxmty and the orentaton between the reference lne whch connects these two ponts and the segment( S ) to whch the prevous GS pont( ) was matched. And t s matched to S when the evaluaton crtera s met. When the evaluaton crtera s not met, segments whch are drectly connected to S s evaluated through the same process. Whte et al.(000) also suggested a smlar algorthm. When the result of the map matchng of s guaranteed, the result s referred to the map matchng of t, and t s matched to one of the segments whch s drectly connected to S..4 The Lmtaton of the revous Map Matchng Algorthms Frst, the avalablty of the geometrc relatonshps should be examned. The map matchng algorthm usng the dstance of curve-to-curve or the angle of curve-to-curve are more refned algorthms than the map matchng algorthm usng the dstance of pont-to-curve. But under the crcumstance of relatvely long pollng tme ntervals, the map matchng algorthm usng the dstance of curve-to-curve s not approprate because there can be many lnks between two consecutve GS ponts. Fgure 6. The roblem of Relatvely Long ollng Tme Intervals Fgure 6 shows such a problem, and t s not clear whch segment should be evaluated wth the reference lne n those case. The map matchng algorthm usng the angle of 565
curve-to-curve has the same problem. Secondly, the avalablty of the network topology and the data hstory s also lmted for the same reason. For the map matchng of t, to evaluate the segments whch s drectly connected to S as Greenfeld and Whte dd, s not approprate. In ~5 mnutes, the vehcle wth a GS recever can reach the segment whch s very far from S. 3. A NEW MA MATCHING ALGORITHM Wth relatvely long pollng tme ntervals of ~5 mnutes, the hstory of GS data can not fully utlzed lke the prevous studes whch assume short pollng tme ntervals of second. So, the full utlzaton of the geometrc relatonshps between the GS ponts and the road network becomes more mportant. But the map matchng algorthms usng the dstance of curve-to-curve or the angle of curve-to-curve are not approprate wth relatvely long pollng tme ntervals as mentoned above. Therefore, the map matchng algorthm usng the dstance of pont-to-curve wll be used n ths paper. 3. The Utlzaton of the Dstance to the Nearest Lnk and Secondly Nearest Lnk But the map matchng usng the dstance of pon-to-curve has problem of abnormal result whch was shown n Fgure 3. To overcome ths problem and to ncrease the accuracy of the map matchng, not only the dstance from a GS pont to the nearest lnk(wll be abbrevated as NL), but also the dstance from the GS pont to the secondly nearest lnk(wll be abbrevated as NL) wll be examned together. For example, when was matched to and was matched to, the latter can be sad to be more accurate, and ths logc wll be utlzed n the new map matchng algorthm. a a b b Fgure 7. The Utlzaton of the Nearest Lnk and the Secondly Nearest Lnk To nclude ths logc to the map matchng algorthm, the partcular threshold s needed. If the rato of the dstance from a GS pont to NL to the dstance from the GS pont to NL s larger than the threshold, the GS pont can be matched to NL. In ths paper, the threshold s set up as. In other words, f the dstance from a GS pont to NL s more than twce as large as the dstance from the GS pont to NL, the GS pont s matched to NL. The threshold of does not have some theoretcal base. Ths threshold can be rased to faster the process of the map matchng and can be lowered to ncrease the accuracy of the map matchng. 566
It s also possble that the dstance to NL s not long enough to match the GS pont to NL. For example, f the dstance to NL s 0m and the dstance to NL s m, the GS pont should not be matched to NL. Ths problem occurs under two crcumstances whch are descrbed below. One s the GS pont whch s n the vcnty of an ntersecton and the other one s the GS pont whch s between two nearly parallel lnks. shows the former case, and n Fgure 8 shows the latter case n Fgure 8. b a a a 3 c b c Fgure 8. The Crcumstances under whch the Map Matchng s Lkely to Fal 3. The roblem n the Vcnty of an Intersecton Ths problem can be resolved by matchng the GS pont to the nearest node. In other words, create a buffer wth partcular radus around a node. And f a GS pont s lad wthn the buffer, the GS ponts s always matched to the node. Obvously, ths process should be followed by the map matchng usng the NL-NL relatonshp. But, f the GS pont s matched to the nearest node, the result nevtably has some postonal error whch was shown n Fgure. If we assume the pollng tme nterval of mnutes and the vehcle speed of 0kph, the buffer of a 0m radus wll generate the maxmum postonal error of ±.5%. If the pollng tme nterval becomes longer or the vehcle speed becomes faster, ths error becomes lower. And such a low postonal error does not matter mostly. Now, the radus of the buffer should be determned. If there s an ntersecton on whch two four-lane roads cross, the extent whch s overlad by the two roads can be completely covered wth a buffer of 0m radus. But a GS pont has maxmum error of about 0m. So, t s reasonable to set up the radus of a buffer as 0m. Obvously, ths radus can be changed wth the number of lanes whch s connected to the ntersecton. If t s possble, the result of the map matchng can be more accurate. But ths paper assumes that there s no nformaton about the number of lanes. Instead, the accuracy of the map matchng wll be evaluated respectvely usng the buffer of 0m radus and 0m radus n the feld test. 3.3 The roblem between Two Nearly arallel Lnks Ths problem can be resolved by the utlzaton of the network topology and the data hstory. Before the descrpton of the method, some notatons have to be ntroduced to avod 567
confuson. : : : : th GS pont whch s not map matched yet th GS pont whch s map matched permanently th GS pont whch s map matched to NL temporarly th GS pont whch s map matched to NL temporarly + L = R 650m L m R 600 = + Fgure 9. The Utlzaton of the Network Topology and the Data Hstory The map matchng of a GS pont whch s between two nearly parallel lnks s done as follows. At frst, the map matchng of s deferred and + s map matched to fnd +. And then, the shortest path from to t and the shortest path from t to + are searched respectvely. And the sum of the dstance of these two shortest path s named as L R. Smlarly, L R s calculated wth respect to, t and +. If L R < LR, s matched to t and t becomes permanently, and vce versa. Fgure 9 shows ths process. Because the dstance from to NL s 0m and the dstance to the NL s 30m, the GS pont can not be matched to NL. In addton, no node have the buffer whch can contan the GS pont. But the result of the calculaton of L R and L R says that L R < LR, so s matched to NL. Ths methodology s based on the assumpton that the drver do not choose the farther route when he move from to +. The shortest path above means that of physcal dstance, and the lnk-labelng Djkstra algorthm(noh and Nam, 995) s used to fnd the shortest path. Usng the physcal dstance means that ths map matchng algorthm assumes the all-or-nothng assgnment. Needless to say, f one can use the travel tme nstead of the physcal dstance, the accuracy of ths algorthm wll be largely mproved. But f t s hard to attan the travel tme data on real tme, to use the physcal dstance s recommended as the second best method. artcular care should be taken to use and +. If the or + are the result of 568
ncorrect map matchngs, the result of the map matchng of whch use and + also can be ncorrect. Therefore, the correctness of and + should be guaranteed. And n ths paper, f a GS pont was matched by the NL-NL relatonshp or the node buffer, the result s treated as a correct result. When the accuracy of or + can not be guaranteed, s used nstead of or + s used nstead of +. But ths stuaton dd not occur so many tmes n the feld test. There s one more problem n ths process. The frst GS pont does not have a prevous GS pont and the last GS pont does not have a next GS pont. If they fall n the one of the node buffers fortunately, t does not matter. If not, the GS pont has no way but to be matched to NL despte the probablty of an error. There s stll a problem. If the frst GS pont was not map matched by the NL-NL relatonshp or the node buffer, now the second GS pont wll be under the same stuaton whch was experenced by the frst GS pont. In ths case, the second GS pont s map matched wth the same process whch matched the frst GS pont. GS ponts after the second GS pont wll be map matched wth the same process f t s necessary. Fgure 0. The Flowchart of the New Map Matchng Algorthm Fgure 0 shows the flowchart of the new map matchng algorthm whch was descrbed untl now. It uses the notatons below. 569
(): th GS pont (): th GS pont whch s map matched to NL temporarly (): th GS pont whch s map matched to NL temporarly C(): guarantee ndex, () can be used to fnd the shortest path f C()=TRUE rev: prevous GS pont whch s used to fnd the shortest path Next: next GS pont whch s used to fnd the shortest path DstFN(): dstance to the nearest node from () DstFL(): dstance to the NL from () DstFL(): dstance to the NL from () IsExst(): functon whch returns FALSE f th GS pont does not exst Routng[()~(j)]: functon whch returns the dstance of the shortest path between () and (j) 4. FIELD TEST To evaluate the accuracy of the new map matchng algorthm, totally about 9,500 GS ponts was collected by the vehcle equpped wth a GS recever(da: Compaq AQ H3630, GS module: Royaltek RGM-000) for three tmes. The study area was Gwanak-gu, Seoul. Table and Fgure show the routes, tme perods and numbers of GS ponts of the feld test. Table. Tme erod and the Number of Collected GS onts Route Tme perod Number of GS ponts 04/09/9 00::37~00:49:38 8 04/09/ 9:48:9~0:8:35 87 3 04/0/ 00:06:~0:0:3 4443 Fgure. The Route for the Collecton of GS onts 570
Actually, the GS ponts were collected every second, but the focus of ths paper s the map matchng of GS data wth relatvely long pollng tme ntervals. So, whole GS ponts were fltered every, 3, 4 and 5 mnutes respectvely. And these four groups were map matched by the new map matchng algorthm respectvely to evaluate the accuracy of the algorthm. Fgure shows the example of the GS ponts whch were fltered every mnutes. Fgure. The GS onts whch were Fltered Every Mnutes Before the exhbton of the result, the measure whch can evaluate the accuracy of the map matchng algorthm should be defned. The result of the map matchngs usng the NL-NL relatonshp or the network topology and the data hstory can be sad to be accurate when a GS pont s matched to the lnk on whch the vehcle really exsted at that tme. The result of the map matchng usng the node buffer should be vewed wth partcular care. Although a GS pont was matched to a node, t does not mean the GS pont was on that node accurately. Instead, t means that the GS pont was n the vcnty of that node. That s to say, t says that the GS pont was on the one of the lnks whch s drectly connected to that node. What matters s the fact that the map matchng usng the node buffer scarcely fals f we consder ths result as a success. Therefore the dstance from the matched node to the real poston of the vehcle at that tme can be more approprate measure for the evaluaton of the map matchng usng the node buffer. But, t s very hard to know the real poston of the vehcle at partcular tme. So, n ths paper, the map matchng algorthm usng node buffer s treated as successful f the GS pont was on the one of the lnks whch s drectly connected to the matched node even thought the weakness mentoned above. Table shows the result of the new map matchng algorthm when the radus of the node buffer s set up as 0m. The type of map matchng, and 3 are respectvely the map matchng usng the node buffer, the map matchng usng the NL-NL relatonshp and the map matchng usng the shortest path. The fgure before the slash(/) s the number of GS ponts whch was map matched successfully and the fgure after the slash s the number of GS ponts whch was not map matched successfully. 57
Table. The Result of the Map Matchng (the Radus of the Node Buffer s 0m) Interval(mn.) Type of map matchng Number of 3 total ponts 7/0 5/3 8/0 70 3 6/0 34/ 4/ 47 4 /0 9/ /0 35 5 /0 5/0 /0 8 The number of GS ponts whch faled to properly map matched s 8 totally. And t was found that each of them was n the vcnty of an ntersecton. Ths result says that the radus of the node buffer was too short. Table 3 shows the result of the same map matchng algorthm when the radus of the node buffer s set up as 0m. Table 3. The Result of the Map Matchng (the Radus of the Node Buffer s 0m) Interval(mn.) Type of map matchng Number of 3 total ponts 3/0 44/0 3/0 70 3 6/0 9/0 /0 47 4 9/0 5/0 /0 35 5 7/0 /0 0/0 8 All the GS ponts were map matched successfully. In addton, the number of GS ponts whch were matched usng thrd type of map matchng s decreased from 6 to 6 and the number of GS ponts whch were matched usng frst type of map matchng s ncreased from 7 to 55 compared to the map matchng wth the 0m radus of buffer node. Because the thrd type of map matchng requres more tme than the frst type of map matchng, t can be sad that the effcency of the map matchng algorthm also ncreased. 5. CONCLUSION The new map matchng algorthm whch s approprate for the GS data wth relatvely long pollng tme ntervals(~5 mnutes) was suggested n ths paper. The process of the algorthm s as follows. Frst, a GS pont whch s wthn the node buffer of partcular radus s matched to that node. Secondly, compare the dstance from a GS pont to the nearest lnk and the dstance from the pont to the secondly nearest lnk. If the rato of these two dstances s larger than the partcular threshold, the GS pont s matched to the nearest lnk. Thrdly, a GS pont whch can not map matched wth both of the process above, the map matchng of the GS pont( ) s deferred and the next GS pont( + ) s map matched. And then, the result of the shortest path search usng, and + s utlzed to map match the. The feld test whch was accomplshed n ths paper shows the good performance of the new map matchng algorthm. But, more feld tests are needed to frmly verfy the performance of the new map matchng algorthm and to determne the effcent radus of the node buffer and the threshold of the rato between the dstance to the nearest lnk and the dstance to the secondly nearest lnk from a GS pont. 57
REFERENCES Chung, Y.S. et al. (000) Classfcaton of map-matchng technques and a development, Journal of the Korean Socety for Geospatal Informaton System, Vol. 8, No., 73-84. Greenfeld, J.S. (00) Matchng GS observatons to locatons on a dgtal map, roceedngs of the 8 th Annual Meetng of the Transportaton Research Board, Washngton, DC, January 00. Noh, J.H. and Nam, K. S. (995) Development of shortest path fndng technque for urban transportaton network, The Journal of Korea lanners Assocaton, Vol. 30, No. 5. Noh, S.H. and Km, T.J. (998) A comprehensve analyss of map matchng algorthms for ITS, Hongk Journal of Scence and Technology, Vol. 9, 303-33 Whte, C.E. et al. (000) Some map matchng algorthms for personal navgaton assstants, Transportaton Research art C, Vol. 8, 9-08 573