Real Time Destination Prediction Based On Efficient Routes

Transcription

1 Paper Number Real Tme Destnaton Predton Based On Effent Routes John Krumm Mrosoft Researh Copyrght 26 SAE Internatonal ABSTRACT Ths paper presents a novel method for predtng the loaton of a drver s destnaton durng the drve. Suh a predton an be used to help dede whh nformaton to automatally present to the drver, dependng on where the drver s gong. The predton s based on the ommon ntuton that drvers tend to hose effent routes. We quantfy ths preferene for effeny probablstally based on a database of drvng trps we gathered wth GPS reevers. We show how to use ths probablty along wth a map of drvng tmes to ompute the probablty of any anddate destnaton. Our tests show that halfway through the drve, we an predt the destnaton to wthn about 1 km, and at three quarters of the way, the error drops to about 3 km. INTRODUCTION Knowledge of a drver s destnaton s an mportant parameter for delverng useful nformaton durng the drve. For nstane, an n-ar navgaton system ould automatally show traff ams, gas statons, restaurants, and other ponts of nterest that the drver s expeted to enounter along the way. If the navgaton system an make an aurate guess about the general regon to whh the drver s headng, then t an ntellgently flter the nformaton t dsplays, redung the ogntve load. Whle t would be possble to expltly ask the drver about hs or her destnaton, drvers would lkely not bother to provde ths nformaton at the begnnng of every trp. It would be muh more onvenent to automatally predt the destnaton. Toward ths end, we have developed an algorthm to predt drvng destnatons based on the ntuton that the drver wll take a moderately effent route to the destnaton. Usng GPS data we gathered from 118 drvng volunteers who made about 43 dfferent loal trps n the Seattle area, we derved a probablty dstrbuton for the amount of drvng tme drvers normally waste by takng less-than-optmal routes. We used ths probablty dstrbuton to repeatedly ompute the probablty of a grd of anddate destnatons as the drve progresses. The probablty omputaton s set up to redue the probablty of destnatons for whh the drver has passed up effent routes. We tested the algorthm on our GPS data and found that we an predt the destnaton to wthn about 1 km at the trp s halfway pont, and at three quarters of the way, the error drops to about 3 km. Fgure 1: On the left s the GPS reever that we loaned to volunteers to ollet drvng data. On the rght s the vewng program that volunteers were gven to revew ther traks.

2 Our work dffers from prevous work n destnaton predton n that we do not use a model of an ndvdual s travel behavor. For nstane, Ashbrook and Starner[1] use GPS traes to fnd a user s meanngful loatons and then apply a seond-order Markov model to predt whh of these loatons a user wll go to next. In a body of work represented by [2], Patterson, Lao et al. present dynam Bayes networks that learn about a user s travel behavor to predt where the user wll go among a set of prevously learned destnatons. Our work s dfferent n that we assume no pror knowledge of a drver s usual destnatons (e.g. work, home, shool). Ths means that our system an work out of the box n a new ar, a rental ar, or n a ty the drver has not vsted before. Another relevant area of researh s predtng loatons for users of moble wreless deves, lke ell phones and W-F[3]. These algorthms are desgned to predt where a wreless user wll go to faltate effent handoffs between antennas. In ontrast, our work s desgned to predt the ultmate destnaton of a drver, not the next few loatons. Also, our loatons are defned geographally, not n terms of antenna loatons, whh means we an be senstve to road networks and drvng behavor. MULTIPERSON LOCATION SURVEY We developed our model of effent drvng and took our test data from the Mrosoft Multperson Loaton Survey (MSMLS)[4]. The MSMLS s an ongong proet amed at gatherng data about where people go n ther daly lves. Volunteer subets for our survey are loaned one of 4 Garmn Geko 21 GPS reevers (Fgure 1) for nomnally two weeks. The default use of the reever s to power t from the garette lghter n the subet s vehle, wth the reever restng on the dashboard or some plae wth a lear vew of the sky for GPS satellte reepton. Our GPS reevers are apable of reordng up to 1, tme-stamped (lattude, longtude, alttude) trples. The Geko 21 an be programmed to reord at regular ntervals n tme or dstane. We used a thrd mode that adaptvely reords more ponts when the reever s aeleratng or turnng, presumably by thresholdng on the devaton between the measured pont and the reever s nternally extrapolated estmate. Ths mode offers fve resoluton settngs varyng from hghest to lowest. We hose the hghest settng. For the approxmately 48, ponts we reorded, the medan dstane between the ponts was 62. meters, and the medan tme between ponts was 6. seonds. Our GPS reever uses the wde area augmentaton system Gender Age male female % male Average age about 36 Famly Chldren sngle partner 4 2 none toddler(s) -2 kd(s) 3-8 youth(s) 9-11 adolesent(s) % wth domest partner 48% wth hldren Fgure 2: Demographs of the 118 subets n our GPS loaton study.

3 Number of Trps Trp Duraton Hstogram Trp Duraton (mnutes) Trp Count Number of Trps per Day Trps per Day Fgure 3: Hstogram of trp tmes. The mean trp tme s 14.4 mnutes. (WAAS), whose RMS error has been measured as 1.13 meters[5]. We solted volunteer subets prmarly from Mrosoft Researh, but some volunteers were other Mrosoft employees and spouses. The demographs of the subets are shown n Fgure 2. Overall, of the 118 subets, 75% were male, 71% had a domest partner, 48% had hldren, and the average age was about 36. For the purpose of determnng trp destnatons, we segmented eah subet s data nto dsrete trps. After downloadng from the GPS nto our database, eah subet s raw data onssted of a sequene of tmestamped (lattude, longtude) oordnates. (We gnored alttude.) We splt these sequenes nto dsrete trps by lookng for plaes n the sequene that met ether of the followng rtera: Gap of at least fve mnutes Ths ndates that the GPS was not movng and, beause of ts adaptve reordng mode, not reordng new ponts. Suh a gap an also ome from vehles whose garette lghter turns off wth the ar, whh would turn off the garette lghterpowered GPS. At least fve mnutes of speeds below two mles per hour Ths aounts for the fat that, even when parked, GPS nose an make t appear that the vehle s movng slghtly. Fve mnutes or more of ths extremely slow apparent movement s onsdered a splt between trps. Segmentaton resulted n a total of 43 dsrete trps. To hek the plausblty of our segmentaton sheme, we omputed statsts about the trps to see f the results were reasonable. One statst s the average temporal length of eah trp, whh was 14.4 mnutes. A hstogram of trp tmes s shown n Fgure 3. Lakng any other soure of trp length statsts, ths result appears reasonable. Another statst s the average number of trps per day, whh we omputed as 3.3, also a Fgure 4: Hstogram of number of trps per day. The mean s 3.3. reasonable number. A hstogram of the number of trps per day s shown n Fgure 4. GRID REPRESENTATION The omputatonal substrate for our assessment of drvng behavor and destnaton predtons s a grd plaed over the Seattle area, as shown n Fgure 5. Ths grd s 41 km X 41 km, wth eah square ell beng 1 km on a sde. Eah ell s represented as an nteger ndex, = 1,2,3, K, N, wth N = 1681 beng the total number of ells n our ase. We represent eah trp through the grd as a sequene of traversed ells, as shown n Fgure 6. We onvert from a sequene of (lattude, longtude) oordnates to a sequene of ell ndes by makng a tme-ordered lst of all the traversed ells. Then we replae all subsequenes of repeated ells wth a sngle nstane of the repeated ell, gvng a lst of traversed ells wth no adaent repeats. Our destnaton predton s based on the assumpton that drvers hose effent routes. We quantfy effeny usng the drvng tme between ponts on the drver s path and anddate destnatons. Thus, for eah par of ells (, ) n our grd, we estmate the drvng tme T, between them. A frst approxmaton to the drvng tme ould ome from a smple Euldan dstane and speed approxmaton between eah par of ells. Instead, we used the Mrosoft MapPont desktop mappng software to plan a drvng route between the enter (lattude, longtude) ponts of pars of ells. MapPont provdes a programmat nterfae whh returns the estmated drvng tme of planned routes. Usng a drvng route planner takes nto aount the road network and speed lmts between ells, gvng a more aurate drvng tme estmate. For N ells, there are N ( N 1) dfferent ordered pars, not nludng pars of dental ells. Our route plannng software plans routes at the rate of about four per seond on a 2.8 GHz PC, meanng t would take about 196 hours to plan routes for all 6 N ( N 1 ) pars. We ut ths tme n half by assumng that the travel tme from ell to s the

4 Fgure 5: We used a grd as the bass for modelng drver behavor and destnaton predtons. The left map shows the area wthout the grd. same as from ell to,.e. T, = T,. The omputaton tme for route plannng was the man barrer to nreasng the resoluton of our grd. Fortunately, ths omputaton must be done only one for the grd. The results an be stored on vehle s omputer. DRIVERS ABILITY FOR EFFICIENT ROUTING Our ntuton says that drvers wll not pass up an opportunty to get to ther destnaton qukly. For nstane, f a drver omes lose to hs or her destnaton at one pont durng the trp, he or she s unlkely to subsequently drve farther from the destnaton. In other words, as a trp progresses, we expet the tme to the destnaton to derease monotonally. We tested ths assumpton usng our trp data. We frst onverted eah trp nto a sequene of ells (as explaned above) and examned eah sequene one ell at a tme. As we went Fgure 6: Trps are represented as a sequene of ells. On ths grd, ths trp would be represented as S = {2, 7, 12, 11, 16, 21, 22, 23, 24, 19, 2, 19, 14, 13, 12, 13, 8}. There are no adaent repeats, although ells 12, 13, and 19 appear twe. through eah sequene, we kept trak of the mnmum tme to the sequene s last ell (the destnaton ell) enountered so far. An effent route would redue ths mnmum tme as the sequene progresses. For eah ell transton n the sequene, we omputed t, the hange n estmated drvng tme aheved by transtonng to the new ell over the mnmum tme to the destnaton enountered so far. We would expet ths tme to be usually negatve, meanng that the ell transton redued the tme to the destnaton. We tested ths by omputng all the t s for all the ell transtons from our GPS data. The normalzed hstogram of these t s s shown n Fgure 7. The normalzed hstogram of t s s an estmate for p t t, whh gves the probablty of the hange n trp ( ) Probablty Drvers' Ablty for Effent Routng Change n Tme to Destnaton on Trp (seonds) Fgure 7: As a trp progresses, drvers sometmes redue the tme to ther destnaton (negatve tme hanges) and sometmes nrease the tme to ther destnaton (postve tme hanges).

5 tme that a drver s transton to the next ell wll ause, wth referene to the losest the drver has been to the destnaton so far. The probablty that the drver wll redue the mnmum tme to the destnaton s p = p t ( t) d t =. 625 based on our data. Surprsngly, t < ths means that 1 p =. 375, or 37.5% of the tme, the drver s move to a new ell atually nreased the tme to the destnaton. Most of our volunteer drvers lve and work wthn the test grd, so we expeted ther famlarty wth the area would lead to more effent drvng. However, ths number may be artfally hgh due to drvers spealzed knowledge that our route planner ddn t have, suh as shortuts, hanges n the road network, and traff ondtons. Also, the mean and medan of p t ( t) are seonds and -39. seonds, respetvely, so on average the data shows that drvers do proeed toward ther destnatons wth eah transton to a new ell n the grd. DESTINATION PREDICTION Our goal s to assgn a destnaton probablty to eah ell n the grd, wth hgher probabltes meanng more lkely destnatons. In partular, we want to estmate p( S ) for = 1,2,3, K, N, where represents ell and S = { s1, s2, s3, K, s N s } represents the sequene of ells traversed so far. Thus, for any sequene of traversed ells S, p( S ) gves the probablty of the destnaton beng ell. Applyng Bayes rule, we get p ( S ) = p( S ) p( ) N p S p = 1 ( ) ( ) The terms of the rght sde are: p ( S ) the lkelhood of the sequene S gven the destnaton. p ( ) the pror probablty of ell beng the destnaton. Sne we have no pror bas about the destnaton, we use = 1 N, gvng all the ells the same pror probablty. N p( S ) p( ) = 1 N = 1 ( S ) = 1 p. a normalzaton fator to make To ompute p ( S ), we ompute the probablty of the sequene of traversed ells, assumng the drver s ablty to move toward the destnaton s probablstally ndependent at eah step. Ths leads to the followng smple formula: p N ( S ) = s = p f s 2 1 p otherwse s loser to than any prevous ell n For eah ell transton n the sequene of ells traversed so far, ths formula multples the probablty p f the transton moved loser to the anddate destnaton than the losest pont so far n the sequene, otherwse t multples 1 p f the transton moved farther away from the anddate destnaton. As long as p >. 5 ths formula wll favor anddate destnatons that the drver s more often drvng toward. An example of the results of these omputatons s shown n the three maps n Fgure 8. In the frst map, the trp starts at the hghlghted square near the mddle of the S (a) (b) () Fgure 8: Probabltes of some ells are redued sgnfantly as a trp progresses. Darker ell outlnes represent hgher probabltes. In (a), the trp has started at the hghlghted ell near the mddle of the grd. The probablty dstrbuton s unform. After travelng four ells south n (b), most of the northeast upper trangle s elmnated. After gong further south, all but the southwest quadrant s elmnated n ().

6 Perentage of Trp Completed Number of Test Trps Medan Error (km) 25% % % % Table 1: Medan error of destnaton predton as a funton of the perentage of the drvng trp ompleted. map. The omputed destnaton probablty of all the ells s equal. After traversng four squares south n the seond map, nearly the entre northeast upper trangle of the grd s elmnated as a destnaton. The probabltes omputed for these anddate loatons are low beause the drver has onsstently transtoned to ells that would nrease the travel tme to these ells. After ontnung south n the thrd map, all but the southwest quadrant of the grd s elmnated, beause the drver would have lkely taken dfferent routes to get to destnatons n the other three quadrants. We tested the auray our destnaton predtons usng a randomly seleted 2% of our GPS trp data to ompute p (the probablty of an effent transton) and the other 8% to test. The tranng data led to a value of p =.684, lose to p =. 625 that we omputed earler from all the data. For testng, we omputed the destnaton probablty of eah ell n the grd for eah ell of eah of the test trps. To quantfy the performane, we omputed the medan error between the atual destnaton and the mode (maxmum peak) of p( S ) on the grd of ells. For eah test trp, as the trp progresses, we an ompute the fraton of the trp that has been ompleted for eah traversed ell. For nstane, a 4-ell trp wll have fratons {.,.33,.67, 1.}, and a 5- ell trp wll have fratons {.,.25,.5..75, 1.}. We aggregated destnaton errors for all the observed trp fratons. For nstane, there were 756 test trps where one traversed ell represented exatly 25% of the trp. The medan error of the destnaton predton for these 756 trps was 21 km. For the 1428 trps at 5%, the medan error dropped to 1 km. Table 1 gves some of the results. Results from all the trp fratons wth 1 or more representatve trps are plotted n Fgure 9. As expeted, the predton error drops as the trp progresses, beause the drver s passng up more and more destnatons. CONCLUSION A smple model of drvng effeny over a known road network s an effetve tehnque for predtng a drver s destnaton. Our predton s based on the ntuton that drvers wll usually follow an effent route, and we quantfed ths behavor usng atual drvng data and omputed route tmes. The ablty to predt destnatons ould be used to flter out rrelevant data presented to drvers, onentratng nstead on nformaton onernng plaes and stuatons the drver s most lkely to enounter durng the trp. Error (km) There are other soures of nformaton that an be used to make destnaton predtons, suh as a dstrbuton of lkely trp tmes, lkely destnaton types (e.g. drvers rarely end up n lakes), and a hstory of past destnatons. We plan to nvestgate these other soures and ombne them wth the drvng effeny method used n ths paper to nrease the auray of our predtons. REFERENCES Medan Error of Destnaton Predton Fraton of Trp Completed Fgure 9: The medan error of the predted destnaton drops as the trp progresses. The gray urve s a smoothed verson of the results. 1. Ashbrook, D. and T. Starner, Usng GPS To Learn Sgnfant Loatons and Predt Movement Aross Multple Users. Personal and Ubqutous Computng, 23. 7(5): p Patterson, D.J., et al. Opportunty Knoks: A System to Provde Cogntve Assstane wth Transportaton Serves. n UbComp 24: Ubqutous Computng. 24. Nottngham, UK: Sprnger. 3. Cheng, C., R. Jan, and E.v.d. Berg, Loaton Predton Algorthms for Moble Wreless Systems, n Wreless Internet Handbook: Tehnologes, Standards, and Applatons. 23, CRC Press: Boa Raton, FL, USA. p Krumm, J. and E. Horvtz, The Mrosoft Multperson Loaton Survey (MSR-TR-25-13). 25, Mrosoft Researh. 5. Coyne, P.I., S.J. Casey, and G.A. Mllken, Comparson of Dfferentally Correted GPS Soures for Support of Ste-Spef Management n Agrulture. 23, Kansas State Unversty Agrultural Experment Staton and Cooperatve Extenson Serve.