Calibrating Car-following Model with Trajectory Data by Cell Phone

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1 Calibratig Car-followig Model with Trajectory Data by Cell Phoe Jiag Zeyu 1 jiagzy15@mails.tsighua.edu.c Wag Yog @qq.com Wag Gagqiao 1 wag-gq15@mails.tsighua.edu.c Zhag Xiagpeg @qq.com *Correspodig author Xig Ha 2 xh @163.com Liu Yi 1* liuyi@tsighua.edu.c 1 Istitute of Public Safety Research, Dept. Eg. Phy. Tsighua Uiversity Beijig , CHINA 2 College of Iformatio Istitute,Beijig Uio Uiversity Beijig ,CHINA 3 School of Geodesy ad Geomatics,Wuha Uiversity Wuha ,CHINA ABSTRACT This paper discussed the possibility of usig trajectory data by cell phoe i calibratio of car-followig model. Experimetal study of car followig behaviors is performed with both GNSS devices ad cell phoes used for trajectory data collectio. GM model is applied i model calibratio. The results of this paper idicate possibility of rapid modelig usig cell phoe data ad proved the feasibility of real-time modelig. CCS Cocepts Computig methodologies Model verificatio ad validatio Huma cetered computig Mobile phoes. Keywords Car-followig model; Trajectory data; Cell phoe; GNSS; Model calibratio 1. INTRODUCTION With the icreasig i temporal ad spatial scales of disasters, emergecy evacuatio lies more ad more o vehicles. Large scale traffic evacuatio becomes oe of the key issues i emergecy respose ad maagemet. Decisio-makig for large scale traffic evacuatio is complex ad difficult due to the complexity of road etworks, emergecy coditios, ad behavior differeces amog idividuals [1,2,3]. Aget-based simulatio is believed to be effective tool for decisio-makig support [4], while challege exists i the drivig behavior models i emergecy coditios. Geeral drivig behavior models have bee studied ad developed such as Gipps model [5] ad GM model[6], which are widely used i trasportatio researches. Whe applyig these models to emergecy cases, it is ot clear if the models work or ot. Murray- Tuite P[7] ad Pel A J[8] discussed behavior differeces betwee geeral cases ad emergecy cases, ad Yua[9] developed a itegrated way i dyamically selectig models for differet cases. For drivig models i certai emergecy cases, there are ot much studies curretly. Challeges also exist i the ucertaities of emergecies. Due to the great ucertaities of emergecies, it is ot reasoable usig a fixed model to simulate dyamic drivig behavior, which may differ greatly. I this paper, the authors developed a real-time modelig idea based o data collectio ad aalysis. There are two widely used way i collectig drivig data, oe is by Global Navigatio Satellite System (GNSS) devices, ad the other is by cell phoes. The idea of real-time modelig is to some exted like the big-data aalysis methods. By collectig real-time drivig data of idividuals, simulatio system may develop models with data-miig ad modify models dyamically with real-time data. This paper provides experimetal study results of how the idea works ad compares effectiveess betwee GNSS data ad cell phoe data i drivig behavior model developmet. 2. EXPERIMENTAL STUDY I traffic simulatio, it is oe of the key issues to deal with ucertaity, which caused maily by the aturally existed heterogeeity of drivig behaviors icludig both iter-driver variability ad itra-driver variability. Car-followig model calibratio based o trajectory data has bee raised i literature[10,11] I this paper, research idea is focused o that if the trajectory data collected from cell phoe may work well for model calibratio. Geerally, trajectory data is collected by professioal equipmet or devices, i.e., the GNSS devices. Cell phoes, although may serve as trajectory data collectio devices, does ot meet the data accuracy requiremets well. While from aother poit of view, cell phoe with applicatio software is more coveiet i data collectio tha the professioal GNSS devices, especially for cases of large driver populatio ad real time data

2 collectio. I this paper, experimetal study is performed to fid how cell phoe data works i car followig model calibratio. A sigle lae loop roadway is selected as testig road with a straight road part of 90m i legth. Two cars are applied i the experimet deoted as car A ad car B respectively. Car A served as leader ad the drivig behavior is totally uder cotrol i the experimet. For the drivig of car A, the acceleratio or deceleratio will follow commads from a guide perso. Car B served as follower ad the driver of car B drive the car by his ow experiece, judgemet ad cotrol. Figure.1 shows the road ad cars i experimet. There fixed a GNSS device ad a cell phoe i each car. The GNSS devices support GPS (Global Positio System, GPS), BEIDOU, ad GLONASS(Global Navigatio Satellite System, GLONASS) ad the positioig accuracy is about 2m. Data is sampled i 1hz. Cell phoes are both with Adroid system ad use applicatio software to collect trajectory data. Data is sampled i about 1hz. Positioig accuracy of cell phoe is supposed to be about 10m. two variables ca be expressed by distace differece ad velocity differece. Eq. (1) shows the GM model as follow. where m v t a t T a l v1 t v t x 1 t x t x 1 t x time t respectively, t v 1 (1) refer to follower s ad leader s locatios at t v t refer to follower s ad leader s velocities at time t respectively, T is the time step, a t T refers to follower s acceleratio at time t+t, a, m ad l are model parameters. 3.2 Data aalysis After data pre-processig, there are 576 groups of data available for data aalysis. Each group of data icludes velocity data, acceleratio data, ad leadig-followig vehicle distace data. (1) Error aalysis Error aalysis of both GNSS data ad cell phoe data are show i Figure. 2 ad Tab.1, which shows the precisio differece betwee GNSS data ad cell phoe data. Figure. 1 Drivig experimet scee As data collected by GNSS ad cell phoe directly is of latitude ad logitude coordiate, data pre-processig with followig three steps are doe before data aalysis: 1) Trasform the origial data with Ellipsoidal earth coordiates to the pla-metric rectagular coordiates by Gauss projectio, i.e., B, L X, Y. 2) With built-i high precisio clock, GNSS devices collect data by time step of 1s strictly. While the samplig iterval of cell phoes with applicatio software shift from 0.5s-2s. Iterpolatio is used to reduce the measuremet error. 3) Both GNSS data ad cell phoe data provides trajectory data while parameters used i car-followig model are velocity ad acceleratio. Calculatio is doe with trajectory data for model parameters. 3. MODEL CALIBRATION 3.1 Car-followig model Car-followig models describe drivig behaviors of motor vehicles movig o the driveway. It is geerally assumed that velocity of followig car is determied by velocity ad acceleratio of leadig car ad the distace betwee them. Widely accepted car-followig models iclude stimulus-respose model [6], safety based model [12], physio-psycho model [13], ad models based o fuzzy theory [14]. I this paper, GM model is selected to verify whether cell phoe data will meet the requiremets of model calibratio. The GM model is a stimulus-respose model, which believes that driver s reactio i a certai momet depeds o his sesitivity to stimulus ad the itesity of the stimulus by leadig driver. These (a) Error of leader s speed (b) Error of follower s speed (c) Error of leader s acceleratio

3 (d) Error of follower s acceleratio Figure. 2 Error distributio of GNSS data ad cell-phoe data Table 1. Error compariso betwee GNSS ad cell-phoe data v(l) v(f) a(f) a(f) distace Max Mea Stadard Deviatio (a) Use the first group of data for model calibratio ad get the value of parameters a, m, ad l. (b) Apply the parameters value to GM model ad calculate with the secod group of experimetal data to get the acceleratio i GM model. a t T (c) Compare the calculated a t T by GM model with experimetal data of the secod data group to verify effectiveess of experimetal data i model calibratio. Table 3 shows the calibrated parameters of a, m, l with radomly selected 288 data sets of the first data group from GNSS data ad cell phoe data separately. The results ad relative error lie i reasoable rage ad differ ot much from Table 2. Table 3. Calibratio of GM model a m l GNSS Cell-phoe Figure 2 ad Tab 1 show that due to the precisio limitatio of cell phoes, the data accuracy of measured parameters by cell phoes does ot match that by GNSS devices satisfactorily. Eve though, will the results of car-followig model calibratio based o cell phoe data be trusted? (2) Model calibratio To aswer the questio above, model calibratio is performed with both GNSS data ad cell phoe data, ad GM model is selected as metioed i sectio 3.1. The Global Optimality Algorithm (GOA) is applied i parameter calibratio, ad the results are show i Table 2. As the precisio of GNSS data is acceptable, calibratio result with GNSS data are cosidered reasoable ad correct. With such assumptio, the calibratio result by cell phoe data is compared with that by GNSS data. From Table 2 oe ca fid that the calibratio results by cell phoe data fit well with parameter l, with which the relative error is about 0.05% compared with that by GNSS data. Calibratio result of parameter a got a higher relative error of about 17.4%, which is ot good but acceptable. Result of parameter m got a very high relative error of 290%, eve though it still fit the value rage of parameter m, which is geerally -1.0 to 2.0. (a) GNSS (GR-GC) Table 2. GM model calibratio results a m l r GNSS cell phoe relative error % 290.4% 0.054% (b) Cell-phoe (CR-CC) Figure. 3 Compariso betwee experimetal data ad calculated data with GM model To further validate the effectiveess of cell phoe data, both GNSS data ad cell phoe data are radomly separated ito two groups, ad each group has 288 data set. Followig steps are doe with both GNSS data ad cell phoe data separately: Figure.3 shows the compariso of real experimetal data from the secod data group ad the calculated data with GM model usig calibrated parameters with the secod data group. I Figure.3(a),

4 the red lie is results of GNSS data from experimet, deoted as GR i the Figure ad the black lie refers to calculated results with GM model i which parameters are calibrated with GNSS data from experimet, deoted as GC i the Figure. I Figure.3(b), the red lie is results of cell phoe data from experimet, deoted as CR i the Figureure ad the black lie refers to calculated results with GM model i which parameters are calibrated with cell phoe data from experimet, deoted as CC i the Figureure. X-Y charts are show i Figure. 4 to make further discussio about the effectiveess of cell phoe data i calibratig car-followig model. Figure.4(a) shows the compariso betwee real experimetal data of GNSS ad cell phoe. As has bee metioed about with Figure.2 ad Table 1, if GNSS data is assumed to be high precisio ad almost correct, the cell phoe data do ot fit well with GNSS data. However, for Figure.4(b), the calculated results with calibrated model by experimetal data show less differece betwee result by GNSS data ad that by cell phoe data. Figure.4 idicated that eve trajectory data by cell phoe is less precise, the ability i model calibratio shows to be acceptable ad satisfactory. Error distributio is show i Figure. 5. Comparig with Figure.2 oe ca fid that the error reduced greatly after model calibratio. Figure.6 shows the compariso betwee experimetal GNSS data ad calculated results with GM model calibrated by cell phoe data, which shows less differece. A weighted Euclidea distace is used to fid similarity. Similarity betwee two group of o-dimesioal data ai ad bi is defied as: Where Similarity a, b i i 1 disai, bi 1 (2) (b) GC-CC Figure. 4 X-Y chart of GNSS data ad cell phoe data (a) GR-GC i disa, b a b 2 (3) i i i i i1 Table 4 provides the error ad similarity aalysis results which shows that there is about 4.23% icreasig i similarity betwee CC-GR ad GR-CR, which further proves that cell phoe data may perform satisfactorily i model calibratio. (b) CR-CC Figure. 5 Error distributio of GR-GC ad CR-CC (a) GR-CR Figure. 6 Compariso betwee cell phoe ad GNSS

5 Table 4. Absolute error of GM model output CR- GR GC- CC GR- GC CR- CC CC- GR Max Mea Stadard Deviatio Similarity CONCLUSIONS This paper discussed the possibility of usig trajectory data by cell phoe i calibratio of car-followig model. Experimetal study of car followig behaviors is performed with both GNSS devices ad cell phoe used for trajectory data collectio. GM model is applied i model calibratio. It is show that the precisio of cell phoe data is ot accuracy eough. Locatio iformatio obtaied directly by cell phoe ad the calculated velocity ad acceleratio with calibrated GM model differ quite a lot from that by GNSS data. Eve though, further study idicates that the low precisio of cell phoe data may ot have obvious ifluece o accuracy of model calibratio. Data aalysis results show as follows, (1) The GM model parameters calibrated by cell phoe data ad GNSS data differs ot too much, ad the errors are withi reasoable rage; (2) Whe radomly separate both GNSS data ad cell phoe data each to two groups ad use oe group of data for model calibratio ad the other group of data for model verificatio, the results fit well; (3) Calculated results with GM model that is calibrated by cell phoe data fit satisfactorily with the directly collected data by GNSS devices i experimet. The results of this paper idicate possibility of rapid modelig usig cell phoe data ad proved the feasibility of real-time modelig. For future study, research will be focused o more precise approaches i data aalysis, ad usig more other carfollowig models to verify ability of model calibratio. ACKNOWLEDGMENTS This work is fuded by Natioal ad Natural Sciece Foudatio of Chia (No , No , No , ad No ) ad Project of Natioal Key Techologies R&D Program of Chia (No.2015BAK2B01). [2] Tu H, Tammiga G, Drolega H, et al. Evacuatio pla of the city of almere: simulatig the impact of drivig behavior o evacuatio clearace time[j]. Procedia Egieerig, 2010, 3: [3] Li X, Bai R, Siebers P O, et al. Modelig urba road risky drivig behaviors i Chia with multi-aget microscopic traffic simulatio[c]// IEEE, Iteratioal Coferece o Itelliget Trasportatio Systems. 2014: [4] Pel A J, Bliemer M C J, Hoogedoor S P. A review o travel behaviour modellig i dyamic traffic simulatio models for evacuatios[j]. Trasportatio, 2012, 39(1): [5] Gipps P G. A behavioural car-followig model for computer simulatio[j]. Trasportatio Research Part B: Methodological, 1981, 15(2): [6] Gazis D C, Rothery R W. Noliear follow-the-leader models of traffic flow[j]. Operatios Research, 1961, 9(4): [7] Murray-Tuite P, Wolsho B. Evacuatio trasportatio modelig: A overview of research, developmet, ad practice[j]. Trasportatio Research Part C Emergig Techologies, 2013, 27(2): [8] Pel A J, Bliemer M C J, Hoogedoor S P. A review o travel behaviour modellig i dyamic traffic simulatio models for evacuatios[j]. Trasportatio, 2012, 39(1): [9] Yua S, Liu Y, Wag G, et al. A dyamic-data-drive drivig variability modelig ad simulatio for emergecy evacuatio[j]. [10] Kestig A, Treiber M. Calibratig Car-Followig Models usig Trajectory Data: Methodological Study[J]. Trasportatio Research Record Joural of the Trasportatio Research Board, 2008, 2088(2088): [11] Puzo V, Ciuffo B, Motaio M. Ca Results of Car- Followig Model Calibratio Based o Trajectory Data Be Trusted?[J]. Trasportatio Research Record Joural of the Trasportatio Research Board, 2012, 2315(2315): [12] Kometai E, Sasaki T. Dyamic behaviour of traffic with a oliear spacig-speed relatioship[j]. Symp Theory Traffic Flow Research Laboratories Geeral Motors, [13] Leutzbach W, Wiedema R. Developmet ad applicatios of traffic simulatio models at the Karlsruhe Istitut für Verkehrswese[J]. Traffic egieerig & cotrol, 1986, 27(5): [14] Azimirad E, Pariz N, Sistai M B N. A ovel fuzzy model ad cotrol of sigle itersectio at urba traffic etwork[j]. IEEE Systems Joural, 2010, 4(1): REFERENCES [1] Osse S, Hoogedoor S P. Heterogeeity i car-followig behavior: Theory ad empirics[j]. Trasportatio research part C: emergig techologies, 2011, 19(2):

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