Arterial Travel Time Estimation Based On Vehicle Re-Identification Using Magnetic Sensors: Performance Analysis

Transcription

1 Arteral Travel Tme Estmaton Based On Vehcle Re-Identfcaton Usng Magnetc Sensors: Performance Analyss Rene O. Sanchez, Chrstopher Flores, Roberto Horowtz, Ram Raagopal and Pravn Varaya Department of Mechancal Engneerng Unversty of Calforna, Berkeley, CA 9472, US Emals: and Sensys Networks, Inc, Berkeley, CA 9471, US Emals: and Department of Cvl and Envronmental Engneerng Stanford Unversty, Stanford, CA 9435, US. Emal: Abstract Two versons of an arteral travel tme estmaton method based on vehcle re-dentfcaton usng wreless magnetc sensors were studed across an arteral segment wth multple ntersectons. Both methods are based on the same travel tme estmaton system, but one of them uses the so called orgnal sgnal processng algorthm whle the other one uses a recently modfed verson of t. Both methods were tested on a.51 km (.32 mle)-long segment of West 34th Street n New York, NY, under harsh drvng condtons (.e. rght after a wnter storm). The orgnal and modfed system results were compared aganst ground truth data obtaned from vdeo. Based on the ground truth data t was possble to determne the travel tme dstrbuton and the percentage of vehcles that each of the dfferent methods was able to re-dentfy. Durng an analyss perod of 45 mnutes, 318 vehcles were regstered to go across the arteral segment. The orgnal method has a 62% re-dentfcaton rate, whle the modfed method has a 69% rate. Based on comparsons of travel tme dstrbuton and emprcal cumulatve dstrbuton functons, t was observed that the modfed method travel tme dstrbuton s closely related to the ground truth dstrbuton, whle the orgnal method sgnfcantly dverges from the ground truth at long travel tmes. Keywords: Vehcle Re-Identfcaton; Real-Tme Travel Tme Estmaton; Arteral Performance Measures; Magnetc Sgnature I. INTRODUCTION The work presented n ths paper s a contnuaton of the work n [1], where the vehcle re-dentfcaton algorthm used n the arteral travel tme estmaton system, dscussed n [2] and consdered for ths analyss, was revsed, mproved and valdated at a sngle lane loop on-ramp. The modfed vehcle re-dentfcaton algorthm that resulted from [1] showed an mproved vehcle re-dentfcaton rate and accuracy at the test ste. In heavly used arteral streets, where stop-and-go traffc s smlar to the one observed n on-ramps under congested condtons, the modfed vehcle re-dentfcaton algorthm explaned n [1] has the potental to mprove travel tme estmaton. In order to determne the effect of the modfed method on arteral travel tme estmaton, a feld test was performed n a segment of West 34th Street n New York Cty (Fgure 1). The performance of the orgnal system and the system wth the modfed vehcle re-dentfcaton algorthm s studed usng ground truth data obtaned from vdeo. The paper s organzed as follows: the arteral travel tme estmaton system s summarzed n Secton II. The test ste and vehcle detecton nstallaton are descrbed n Secton III. The ground truth (GT) and the magnetc sensor array data are explaned n Secton IV. An analyss of the ground truth and the vehcle detecton system data s presented n Secton V. Secton VI contans the results of the arteral travel tme estmaton methods and the performance analyss of both methods based on ground truth. Conclusons are presented n Secton VII. II. ARTERIAL TRAVEL TIME ESTIMATION SYSTEM The system reles on matchng vehcle sgnatures from wreless sensors. The sensors provde a magnetc sgnature of a vehcle and the tme when the magnetc sgnature s measured. A re-dentfcaton of sgnatures between two locatons gves the correspondng travel tme of the vehcle. The travel tmes for all matched vehcles yeld the travel tme dstrbuton. The travel tme estmaton method summarzed n ths secton s descrbed n [2]. A. Vehcle Magnetc Sgnature The magnetc vehcle sgnature conssts of a collecton of peak value sequences (local maxma and mnma) extracted from the raw magnetc sgnals measured by an array of sensors. Each sensor has a three-axs magnetometer that measures the x, y and z drectons of the earth s magnetc feld as a vehcle goes over t. Each sensor generates three peak sequences extracted from the x, y and z component sgnals, whch consttute a sgnature slce X =(X x,x y,x z). For ths analyss, fve slces consttute a vehcle s sgnature, snce there are fve sensors n each array. B. Vehcle Re-Identfcaton Algorthm Summary The vehcle re-dentfcaton s done n two steps: 1) Sgnal Processng Step: In ths step, each par (X,Y ) of start and end vehcle sgnatures s compared to produce a dstance d(, )=δ(x,y ) between them. The smaller δ(x,y ) the more lkely t s that X,Y are sgnatures of the same vehcle. Ths step reduces the two sgnature arrays X =

2 {X, = 1,,N} and Y ={Y, = 1,,M} to the N M dstance matrx D={d(, ) 1 N,1 M}. Ths step of the vehcle re-dentfcaton method was modfed n [1] n order to enhance the matchng rate and accuracy durng congested condtons, when vehcles travel slowly or stop whle gong over the array of sensors. For ths analyss, orgnal method refers to the arteral travel tme estmaton system as descrbed n [2], whle modfed method refers to the same system wth the enhanced sgnal processng step descrbed n [1]. 2) Matchng Step: In the second step a matchng functon assgns to each dstance matrx D a matchng µ : {1,...,N} {1,...,M,τ}, wth the followng nterpretaton: µ()= means that the start (upstream) vehcle s declared to match (be the same as) end (downstream) vehcle ; µ()=τ means s declared not to match any downstream vehcle. In ths step, a constraned matchng functon s used, whch does not permt vehcle overtakng. The algorthm matches the largest number of vehcles that satsfy the Frst In, Frst Out (FIFO) condton. Note that ths constrant slghtly affects the matchng rate (e.g. less potental vehcles avalable to re-dentfy) but greatly mproves accuracy f vehcle overtakng s not sgnfcant [2]. C. Travel Tme Estmaton Every tme a vehcle sgnature s measured, a correspondng tme stamp s pared to the sgnature. The start and end sensor array data correspond to a collecton of data pars of the form (s,x ) and (t,y ), respectvely. When two sgnatures (X,Y ) are determned to be a match by the vehcle re-dentfcaton algorthm, the travel tme across the segment s determned to be t s. In a deployment lke the one shown n Fgure 1, where the arteral segment s composed of multple lanes, the vehcle re-dentfcaton algorthm s tradtonally used wth upstream and downstream array data comng from the same lane. For the NY test ste, the tradtonal way to run the algorthm would nvolve usng data from the fast lane start and end arrays, represented by f ast f ast, ndependently of the data comng from the slow lane start and end arrays, depcted by slow slow. Ths practce s based on the assumpton that for the most part, vehcles tend to stay n ther same lane as they go through the segment. III. TEST SITE The New York Cty arteral test ste s a.51 km (.32 mle)-long segment of West 34th Street that ntersects the 7th and 8th avenue (see Fgure 1). The segment s formed by three lanes, however, ths analyss focuses on the travel tme estmaton of vehcles n the fast and slow lanes. The thrd one, a bus only lane, was not transted durng the analyss perod because t was blocked at dfferent locatons along the segment as shown n Fgure 2 (b). Ths test ste s a sutable locaton to study the performance of arteral travel tme estmaton systems, snce t has a Fg mle segment of 34th Street n New York Cty confguraton and drvng dynamcs that encompasses what can be encountered n arteral streets n many bg ctes: drvers are aggressve, lane changng s sgnfcant, taxs and buses stop as they go across the segment, people double park, and there s vehcle queueng at the detector locatons. Furthermore, vehcles get n and out of the segment not only at the start and end locatons, but also at the ntersectons n between. If a travel tme estmaton system yelds accurate results under these traffc condtons, then t can be expected to have a comparable or better performance n arteral streets where traffc condtons are more ordered and less congested. The locatons of the sensor arrays at ths test ste do not follow the manufacturers gudelnes. The sensors were nstalled at the locatons where tag readers had been nstalled n order to be able to make a comparatve analyss between dfferent arteral travel tme estmaton systems. Ths resulted n vehcles gong over the detector at fast and slow speeds, and even restng on top of them whle watng for the vehcles on the queue to move. Normally sensor arrays are nstalled ust after the ntersecton to maxmze free flow. There was a wnter storm wth heavy snowfall that ended one day before the analyss perod. Ths resulted n dffcult drvng condtons that are not typcally encountered at many nstallaton stes. The snow on the street blocked part of the bus lane along the segment due to snow beng plowed to the sde of the street, whch resulted n vehcles (e.g. taxs) stoppng or double parkng n the slow lane. Ths led to consderable lane changng from the slow to the fast lane and to vehcles travelng off the center of the lane. These condtons are smlar to the condtons descrbed n [1] for on-ramps, for whch the modfed method mproved performance. A. Vehcle Detecton System The vehcle detecton system deployed at the New York test ste and used for ths study was developed by Sensys Networks, Inc. Ths system conssts of two access ponts and 2 wreless magnetc sensors nstalled n a fve sensor array confguraton n the mddle of the fast and slow lanes at the start and end locaton, as shown n Fgure 2. See [3] for detals on ths vehcle detecton system.

3 TABLE I VEHICLE COUNT BASED ON GROUND TRUTH AND SENSOR ARRAYS DATA START locaton END locaton GT Array GT Array N f ast M f ast N slow M slow 1 22 N M Fg. 2. (a) Segment Start Locaton (b) Segment End Locaton Fg. 3. (a) Camera recordng vehcles at the START Locaton. (b) Camera recordng vehcles at the END locaton. TABLE II CHOSEN VEHICLES k l Veh. Type Lane : Start End Travel Tme [sec] 11 τ Tax, car 12 τ SUV Tax, car f ast f ast SUV f ast slow Car f ast f ast τ Tax, prus 17 τ Car Bus slow f ast τ Car 2 2 Tax, car slow f ast SUV f ast slow Tax, mnvan f ast f ast Bus slow f ast Car slow f ast τ Mnvan A. Ground Truth Data IV. DATA Ground Truth (GT) data was obtaned from vdeos recorded on January 28, 211 from 1:54 am to 11:41 am. A tme stamp, transted lane, vehcle type, and the vehcle poston wth respect to the mddle of the lane were recorded for each vehcle enterng or leavng the arteral segment at the start and end locatons. Two ndependent cameras were used to obtan the ground truth data. From the frst camera (Fgure 3 (a)) t was possble to obtan the tme s lane GT k when vehcle k entered the arteral segment at the start locaton and went across the sensor array located on ether the f ast or the slow lane, where s lane GT 1 s lane GT 2 s lane GT NGT. From the second camera (Fgure 3 (b)) t was possble to get the tme tgt lane l when vehcle l exted the arteral segment and went through the downstream array located on ether the f ast or the slow lane, where tgt lane 1 tgt lane 2 tgt lane MGT. The data used to obtan a GT travel tme dstrbuton conssts of two vectors {s lane GT k,k = 1,,N GT = 495} and {tgt lane l,l = 1,,M GT = 434}. The GT matchng of upstream to downstream vehcles k l was done vsually and resulted n 318 matches. 177 enterng vehcles k dd not have a matchng extng vehcle l (e.g. vehcles turned or parked before reachng the end locaton) whle 117 extng vehcles l were not matched to any enterng vehcle k (e.g. vehcles got nto the segment at an ntersecton or were orgnally parked nsde of t). B. Vehcle Detecton System Data Consder a lnk formed by one of the start arrays, lanes, and one of the end arrays, lanee. Durng the vdeo recordng tme nterval, detecton events ndexed =1,,N lanes were regstered by lanes at tmes s lanes 1 < s lanes 2 < s lanes. Ths N lanes array measured a sgnature X lanes each tme there was a vehcle detecton event together wth the tme s lanes. Detecton events ndexed = 1,,M lanee were regstered by lanee at tmes t1 lanee < t2 lanee < t lanee. Ths array M lanee measured a sgnature Y lanee each tme there was a detecton event together wth the tme t lanee. For ths study, the vehcle detecton system data conssts of four arrays: (s slow,x slow ), (s f ast,x f ast ), (t slow,y slow ) and (t f ast,y f ast ). Table I summarzes the vehcle detecton system counts and compares them aganst the ground truth. Note that detecton errors cannot be avoded and may create multple sgnatures of the same vehcle at one locaton or may result on mssng sgnatures due to undetected vehcles, as dscussed n [4]. The vehcle re-dentfcaton algorthm summarzed n Secton II can be ndependently appled to the followng combnatons of data arrays: f ast f ast, f ast slow, slow f ast, and slow slow, even though tradtonally only the frst and the fourth combnatons are used. 1) Subset of Vehcles: In order to be able to analyze the system performance n detal, a platoon of 15 contnuous vehcles were chosen from the 495 vehcles that entered the arteral segment at the start locaton. These vehcles are shown n Table II. From ths subset, a few vehcles were chosen to analyze ther vehcle sgnatures.

4 V. GROUND TRUTH AND VEHICLE DETECTION SYSTEM DATA ANALYSIS A. Lane Changng Lane changng can have a sgnfcant degradng effect on the travel tme estmaton system performance f t contnuously occurs as vehcles are gong over the sensor arrays. If vehcles are travelng evenly n between lanes as they are gong through the start or end locaton, the sgnature s splt between both arrays at that locaton, and the mddle part of the sgnature, whch s generally the most useful, s not correctly measured by any of them. When ths happens vehcles are very lkely to be unmatched by the algorthm, reducng the vehcle re-dentfcaton rate. Lane changng was very common durng the analyss perod. The man reason why people where changng lanes at the arteral segment was to overtake vehcles obstructng the slow lane. A large porton of the vehcles that changed lanes close to the end locaton trggered a detecton event at both the fast and slow sensor arrays. Ths s reflected n the data from Table IV, that shows that 122 vehcles that entered the segment through the slow lane, exted t through the fast lane, whle only 22 vehcles entered n the fast lane and exted n the slow one. Furthermore, Table I shows an overall 25% vehcle countng error by the vehcle detecton system at the end locaton, whle countng error n the start locaton was only 2.3%. The large dscrepancy n vehcle countng and the contnuous lane changng were the result of vehcles double parked for extended perods of tme n the slow lane downstream of the end locaton. Ths forced vehcles on the slow lane to change to the fast lane as they were extng the segment. Many of these vehcles were almost completely changed to the fast lane as they were gong over the end locaton, but some of the sensors from the slow array were also trggered by them. The extng sgnatures of vehcles k = 15, 18 and 23 lsted n Table II were some of the sgnatures studed because they were detected by both arrays as they were extng the segment. Sgnatures from the slow lane array under ths condton contaned no useful data; most of the vehcle sgnature nformaton was captured n the sgnature data measured by the fast lane array. After ths analyss t was observed that when a vehcle trggers detecton events at multple arrays at the same locaton whle gong mostly n one lane, sgnfcant vehcle countng error n one of the lanes may result. However, ths would barely affect the travel tme estmaton results because sgnatures comng from the unused lane array would yeld large dstances n the sgnal processng step of the vehcle re-dentfcaton algorthm (see Secton II) whch would make them unmatched. B. Frst In, Frst Out Condton As t was mentoned n Secton II, the matchng algorthm s constraned and does not allow overtakng. In other words, when the matchng step s performed, the sequence of matched vehcles satsfes the FIFO condton. Wth the k th Start Vehcle (SLOW Lane) k slow l fast Matchng Matrx: Ground Truth Matches (122) l th End Vehcle (FAST lane) k th Start Vehcle (SLOW lane) k slow l fast Matchng Matrx: Longest GT FIFO Match Sequence (95) l th End Vehcle (FAST lane) Fg. 4. Synthetc Dstance Matrx (left) Complete Data Set (rght) Largest Vehcle Sequence Satsfyng the FIFO condton ground truth data collected from vdeo t s possble to determne the effect of the FIFO constrant on the matchng rate upper bound. Note that snce the vehcle re-dentfcaton algorthm s run ndependently for dfferent array combnatons, the FIFO constrant s only mposed among vehcles gong on the same lnk. Fgure 4 (left) s the gray scale codng of a matrx that relates the start sgnatures measured by the slow lane array to the end sgnatures measured by the fast lane array (.e. lnk slow f ast) based on GT data. If the k th sgnature (row) and the l th sgnature (column) correspond to the same vehcle, the pxel s black, otherwse t s whte. A perfect matchng algorthm would re-dentfy 122 vehcles across ths lnk. However, f a FIFO constraned vehcle re-dentfcaton algorthm s used nstead, t would be possble to match only 95 vehcles, whch corresponds to the number of elements n the largest vehcle sequence, out of the 122 vehcles, that satsfy the FIFO constrant. Fgure 4 (rght) shows the gray scale codng of the matrx wth ths vehcle sequence. For ths partcular lnk, 72 % s the upper bound on the matchng rate that could be expected from the re-dentfcaton algorthm summarzed n Secton II assumng perfect accuracy. Table IV lsts, n the second and thrd column, the number of vehcles that went across each of the lnks n the arteral segment. In the fourth and ffth column ths table lsts the maxmum number of vehcles that satsfy the FIFO constrant n each of the lnks, whch correspond to the upper bound on the number of re-dentfed vehcles for a FIFO constraned matchng algorthm. From ths table t can be seen that out of the 318 vehcles that crossed the segment, only 27 could be matched by the vehcle re-dentfcaton algorthm f perfect performance s assumed, whch accounts for 85 % of the vehcles. The FIFO constrant mproves accuracy of the system, as mentoned n [2], wthout sgnfcantly reducng the maxmum possble number of matches. C. Travel Tme by Vehcle Category The travel tme dstrbuton estmates are affected by the FIFO constrant. If there s a partcular vehcle group wth sgnfcant presence along the arteral segment under consderaton, and a large percentage of the vehcles n the

5 group volates the FIFO condton as they go across, then dscrepances between the ground truth and the estmated travel tme dstrbutons should be expected. The algorthm would be able to predct accurately the travel tme nformaton of vehcles that want to go across the segment wthout stopng, snce t s assumed that these are the maorty of the vehcles and for the most part follow the FIFO condton. Taxs or buses are vehcle groups that have a tendency to stop and end up volatng the FIFO constrant. If the percentage of vehcles n these groups s large wth respect to the total number of vehcles gong across the segment, and f there are consderable bus routes wth multple stops and common locatons for taxs to drop off and pck up passengers, then the travel tme dstrbuton based on the ground truth data wll be sgnfcantly dfferent from the estmated one. Nevertheless, as far as a traffc agency and drvers that rely on travel tme estmaton are concerned, ths should not represent a problem, snce the nformaton that can be extracted from the estmated travel tme dstrbuton would be useful and representatve of the traffc condtons at the arteral segment under consderaton. Table III lsts the dfferent types of vehcles and the number of them that entered the segment at the start locaton, exted through the end locaton and went across t. The Table also lsts nformaton about the travel tme dstrbuton dvded by vehcle type. For the most part, all the vehcles have smlar travel tme characterstcs. For the test ste n New York Cty, tax presence s sgnfcant, accountng for 3.5 % of the vehcles that went across the segment. Note that ther travel tme dstrbuton s 25th percentle, medan and 75th percentle are very close to those of the total dstrbuton. The buses travel tme dstrbuton has the larger 25th percentle, medan and 75th percentle, whch s expected, snce there are several bus stops along the segment. Snce buses only represent 5.3 % of the total number of vehcles that crossed the segment, ther nfluence s not sgnfcant. Fgure 5 (top) shows the travel tme dstrbutons based on GT data for taxs and buses whle Fgure 5 (bottom) shows the travel tme dstrbuton of all the vehcles except taxs and buses. Note that both dstrbutons look smlar wth almost the same medan, but a larger dfference at the 9th percentle, whch s the result of long travel tmes correspondng manly to buses. The travel tme dstrbuton of taxs and buses, across the test ste and durng the analyss perod, seems to reflect street traffc condtons. Based on the results from ths secton, an accurate travel tme dstrbuton based on the matchng algorthm descrbed n Secton II should be smlar to the one obtaned based on the ground truth data. Slghtly lower percentles n comparson to the GT dstrbuton are expected due to outlers and travel tmes from vehcles not satsfyng the FIFO condton wth travel tmes n between the 5 and 1 seconds (e.g. taxs makng short stops but not stoppng at any red lght)..2.2 TABLE III GROUND TRUTH DATA BY VEHICLE TYPE Vehcle Start End GT 25th Medan 75th Type Counts Counts Matched Perc TT [sec] Perc bcycle bus car mnvan pck up SUV tax truck van TOTAL Travel Tme Dstrbuton: Taxs and Buses (114 Vehcles) Medan: 99 sec 9 Percentle: 149 sec Mn TT: 39 sec Max TT: 289 sec Travel Tme Dstrbuton: All Vehcles EXCEPT Taxs and Buses (24 Vehcles) Medan: 98 sec 9 Percentle: 127 sec Mn TT: 32 sec Max TT: 56 sec Fg. 5. Travel Tme Frequency Dstrbuton by Vehcle Type (top) Taxs and Buses. (bottom) All Vehcles except Taxs and Buses. VI. TRAVEL TIME RESULTS In ths secton the GT travel tme dstrbuton s compared to the travel tme dstrbutons computed wth the orgnal method and the modfed method. Table IV shows the results obtaned from the vehcle re-dentfcaton algorthm for the orgnal method and the modfed method. The total number of matched vehcles for each method s lsted as well as the number of re-dentfed vehcles per lnk (e.g. f ast f ast, f ast slow, slow f ast and slow slow). Tradtonally only f ast f ast and slow slow lnks are used, snce t s assumed that most vehcles stay n the same lane as they go through an arteral street. However, the GT data shows that 122 vehcles that entered the segment through the slow lane exted through the fast lane, whch accounts for 38% of the vehcles that crossed the arteral segment. For ths reason t was decded to use the four lnks to estmate vehcle travel tmes. As t can be seen from Table IV, for both of the methods, the TABLE IV MATCHING RESULTS COMPARISON Ground GT Orgnal Modfed Truth (FIFO) Method Method Start\End Fast Slow Fast Slow Fast Slow Fast Slow Fast Slow Total

6 number of matched vehcles obtaned usng the slow f ast lnk accounts for a large percentage of the number of redentfed vehcles. The f ast slow lnk s not as mportant, but t ncreases the matchng rate for both methods. The vehcle re-dentfcaton rate for the orgnal method s 62%, whle for the modfed method t s 69%. Table IV (columns 4 and 5) shows the vehcle re-dentfcaton upper bound for each of the lnks. Note that a consderable percentage of the matched vehcles n the slow slow lnk s expected to be naccurate for both estmaton methods, snce the number of matched vehcles exceeds the upper bound based on the FIFO constrant. The orgnal method overestmates the number of matched vehcles by at least 14, whle the modfed method does t by 12. At least 7% of total travel tme estmates calculated wth the orgnal method are naccurate whle at least 5 % are naccurate for the modfed method results. Fgure 6 compares the orgnal method travel tme dstrbutons aganst the GT. The orgnal method estmated dstrbuton seems to capture the GT dstrbuton at short travel tme values. However, the number of estmated travel tmes above 15 seconds exceeds the ones observed n the GT data. Ths suggests that some of these long travel tmes were calculated from X,Y vehcle sgnature pars that were ncorrectly matched. Fgure 7 shows that the GT and the orgnal method cumulatve dstrbuton functons (CDF) correlate well at short travel tmes, but start dvergng rght after the medan, reachng an error of 17% at the 75th percentle and 52% at the 9th percentle. Fgure 6 compares the modfed method travel tme dstrbutons aganst the GT. The modfed method travel tme dstrbuton correlates well wth the GT data. Fgure 7 shows that the GT and the modfed method cumulatve dstrbuton functons (CDF) have a smlar shape. The estmated CDF s shfted to the left of the GT CDF, wth a maxmum error of 17% close to the medan. The error between both CDFs s very small rght after the 65th percentle, wth a 3.5% error at the 75th percentle and 2.3% error at the 9th percentle. The dfferences observed between the GT and the estmated travel tme dstrbutons wth the modfed method correspond to the dfferences expected n Secton V for an accurate FIFO constraned matchng algorthm at the test ste. VII. CONCLUSION A vehcle travel tme estmaton system was studed on an arteral segment n New York Cty usng ground truth data collected from vdeo. The ground truth data was valuable to understand the traffc phenomena that occur at arteral streets lke lane changng, vehcle overtakng, vehcles travelng n between lanes, among others, whch drectly relate to the performance of the travel tme estmaton system. It was possble to apply the vehcle re-dentfcaton algorthm usng sensor array data from dfferent lanes, f ast slow and slow f ast, somethng that has not been tred before wth ths system and that led to an ncrease on the vehcle re-dentfcaton rate. Furthermore, t was shown that the Travel Tme Dstrbuton: Ground Truth (318 Data Ponts) 25th Percentle: 51 sec Medan: 98 sec 75th Percentle: 115 sec 9th Percentle: 132 sec Travel Tme Dstrbuton: Orgnal Method (198 Data Ponts) 25th Percentle: 53 sec Medan: 1 sec 75th Percentle: 135 sec 9th Percentle: 21 sec Travel Tme Dstrbuton: Modfed Method (221 Data Ponts) 25th Percentle: 47 sec Medan: 85 sec 75th Percentle: 111 sec 9th Percentle: 129 sec Fg. 6. Travel Tme frequency dstrbuton for the ground truth, the orgnal method and the modfed method Emprcal Cumulatve Travel Tme Dstrbuton Ground Truth CDF (318 Data Ponts) Orgnal Method CDF (198 Data Ponts) Modfed Method CDF (221 Data Ponts) Travel Tme [sec] Fg. 7. Emprcal Cumulatve Travel Tme Dstrbuton for the GT, Orgnal Method and Modfed Method FIFO assumpton that constrans the matchng algorthm s adequate at arteral mplementatons. The matchng rate for the orgnal method was 62% whle that of the modfed method was 69%. Even though there s not a bg dfference n the matchng rate, t seems that the modfed method s more accurate, snce ts travel tme dstrbuton and cumulatve dstrbuton functon are closely related to the ground truth ones. The orgnal method travel tme CDF does not match the GT, especally at long travel tmes, whle the modfed method has an mproved performance n ths aspect. At the 75th percentle, the orgnal method error s around 17%, whle the modfed method error s less than 3.5%. REFERENCES [1] R. O. Sanchez, C. Flores, R. Horowtz, R. Raagopal, and P. Varaya. Vehcle Re-Identfcaton Usng Wreless Magnetc Sensors: Algorthm Revson, Modfcatons and Performance Analyss, n Proceedngs of the IEEE Internatonal Conference on Vehcular Electroncs and Safety, Beng, Chna, July 211. [2] K. Kwong, R. Kavaler, R. Raagopal, and P. Varaya. Arteral travel tme estmaton based on vehcle re-dentfcaton usng wreless magnetc sensors, n Trans. Res. Part C: Emergng Technol., vol. 17, no. 6, pp , 29. [3] A. Haou, R. Kavaler, and P. Varaya, Wreless magnetc sensors for traffc survellance, n Transp. Res. Part C: Emergng Technol., vol. 16, no. 3, pp , 28. [4] R. O. Sanchez, R. Horowtz, and P. Varaya, Analyss of queue estmaton methods usng wreless magnetc sensors, accepted for publcaton at the Trans. Res. Rec., Journal of the Transportaton Research Board, 211.