Floating Car and Camera Data Fusion for Non-Parametric RouteTravel Time Estimation

Mahmood Rahmani1, Erik Jenelius2, and Haris N. Koutsopoulos3

Abstract— The paper proposes a non-parametric route traveltime estimation method based on fusion of floating car data(FCD) and automated number plate recognition (ANPR) data.Today’s traffic management utilizes heterogeneous data collec-tion systems which can be stationary or mobile. Each datacollection system has its own advantages and disadvantages.Stationary sensors usually have less measurement noise thanmobile sensors but their network coverage is limited. On theother hand, mobile sensors, commonly installed in fleet vehicles,cover relatively wider areas of the network but they sufferfrom low penetration rate and low sampling frequency. Trafficstate estimations can benefit from fusion of data collected byvarious sources as they complement each other. The proposedestimation method is implemented using FCD from taxis andthe ANPR data from Stockholm, Sweden. The results suggestthat the fusion increases the robustness of the estimation,meaning that the fused estimates are always better than theworst of the two (FCD or ANPR), and it sometimes outperformsthe two single sources.

I. INTRODUCTION

In light of increasing congestion in urban areas, moni-toring and providing information about traffic conditions iscritical for traffic management and effective transport policy.Travel time data may be collected from stationary automaticvehicle identification (AVI) sensors (automatic number platerecognition (ANPR) cameras, Bluetooth devices, etc.). AVIsystems provide direct measurements of route travel times,but the spatial coverage is typically small and may not berepresentative of the network as a whole. Meanwhile, floatingcar data (FCD) collected from GPS devices installed invehicle fleets or smart phones provide information from theentire network. Travel time estimation from FCD is oftenchallenging because of low penetration rate, which meansthat the number of available FCD observations from vehiclestraveling along the route of interest may be low if it is nota common one.

AVI and FCD have complementary strengths as FCDprovides network coverage while AVI provides accurate mea-surements on specific route segments (larger sample size).The combination of AVI data and FCD has not been studiedmuch in the literature, however. A data fusion methodologyfor estimation of freeway space-time speed diagrams based

1M. Rahmani, Department of Transport Science, KTH Royal Instituteof Technology. Teknikringen 72, SE-100 44 Stockholm, SWEDEN, phone:+46-8-790-8301; fax: +46-8-21-2899; mahmoodr@kth.se

2E. Jenelius, Department of Transport Science, KTH Royal Insti-tute of Technology. Teknikringen 72, SE-100 44 Stockholm, SWEDENjenelius@kth.se

3H. N. Koutsopoulos, Department of Transport Science, KTH RoyalInstitute of Technology. Teknikringen 72, SE-100 44 Stockholm, SWEDENhnk@kth.se

on loop detector data, AVI and FCD has been proposed [1].For the arterial network, research on travel time estimationbased on FCD has largely focused on links [2], [3]. As faras we are aware, no studies have combined stationary andmobile sensors to estimate travel time distributions on arterialnetwork routes.

The aim of this paper is to utilize the complementarybenefits of ANPR and FCD by integrating the two datasources in the estimation of arterial route travel times, wherea route may be fully or partially covered by the two sourcesof data. The paper proposes a computationally efficient, non-parametric method for route travel time estimation using bothANPR data and low-frequency FCD. The approach estimatesroute travel time distributions directly from ANPR and FCDmeasurements partially covering the route, incorporating allinformation available from the data. The methodology ex-tends ideas from kernel-based estimation [4] and is developedconsidering the particular features of network routes andANPR and FCD observations. No assumptions are maderegarding the form of the distribution. This flexibility ishighly valuable whenever the variability of travel times isof interest, e.g., for monitoring of travel time reliability.

The paper is organized as follows: Section 2 describes themethodology, Section 3 presents a case study for Stockholm,Sweden, and Section 4 concludes the paper.

II. METHODOLOGY

A. Preliminaries

A network route is defined as an acyclic path ⇡ =(ks, k⇤, ke) connecting the beginning and end links ks andke, and two distances os and oe marking the two offsets onks and ke respectively. k⇤ denotes 0 or more links betweenks and ke. In a special case a route can consist of only onelink, i.e., ks = ke, k⇤ = ;, and os < oe. The fraction of linkk covered by the network route, denoted ↵k, is the length ofoverlap between the route and the link divided by the linklength. The route travel time is denoted by T = T (s) andvaries stochastically between trips and as a function of theroute entry time s. The aim of this research is to estimate thedistribution of T (s) from ANPR and FCD measurements.

a) Automatic number plate recognition (ANPR) data:ANPR data are collected from ordered pairs of cameraswhich identify vehicles based on optical recognition oflicense numbers. An ANPR route is defined as the pathbetween the locations of the first and the second camera(more precisely, the locations where vehicles are detected);it is assumed that there is a unique reasonable route betweenthe two locations. A data record is created whenever the

2014 IEEE 17th International Conference onIntelligent Transportation Systems (ITSC)October 8-11, 2014. Qingdao, China

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Network route

FCD route

ANPR route

Fig. 1: An example of a network route and a number ofANPR and FCD observations partially overlapping the route.

same vehicle is identified sequentially by both cameras. Arecord is a triplet (h, s, e), where h is a unique ANPR routeidentifier, and s and e are the timestamps of the detection ofthe vehicle at the first and the second camera, respectively.

b) Floating car data (FCD): FCD consist of sequencesof reports, or probes, from vehicles traveling on the network.Each probe is a triplet (◆,�, hx, yi), where ◆ is a uniquevehicle identifier, � is a timestamp and hx, yi are the GPScoordinates of the vehicle location at that time. In practice thetime gap between consecutive reports from the same vehiclevaries from a few seconds up to minutes. The focus in thisresearch is on FCD with gaps longer than a minute, usuallyreferred to by Low-frequency FCD. Low-frequency FCDrequire preprocessing to be useful for travel time estimation.Most importantly, reported positions must be matched to themodel of the road network and the paths taken by the vehiclesbetween probes must be inferred [5], [6].

B. Travel time estimation

A non-parametric method for route travel time estimationfrom FCD has recently been developed [7]. The computa-tional efficiency allows the method to be applied on-demandfor any network route. This paper extends the method tocombine FCD with available ANPR data overlapping theroute. A common observation model, consisting of a routeand a travel time measurement, is used to represent bothANPR data and FCD. For ANPR observations the route isgiven by the fixed camera locations and the intermediateroute, and the travel time measurement ⌧ = e�s is obtainedfrom the difference between the detection timestamps. ForFCD observations the route is given by the inferred pathbetween two consecutive probes from the same vehicle, andthe travel time measurement ⌧ = �2 � �1 is obtained fromthe difference between the corresponding timestamps. Theframework is illustrated in Figure 1.

In general, observation i from either ANPR or FCD isrepresented by a travel time ⌧i, a path pi = (ki,1, k⇤, ki,2)and two distances oi,1 and oi,2 marking the two offsets onki,1 and ki,2 respectively. The fraction of link k traversed byobservation i is denoted by ⇢ik. The part of the observationroute overlapping with the network route is referred to asthe overlap route for short. The fraction of the overlap inrelation to the length of the link is denoted by �ik.

⇢1 = e1`1

↵1 = 0 �1 = 0⇢2 = 1 ↵2 = r1

`2�2 = r1

`2⇢3 = 1 ↵3 = r2

`3�3 = e3

`3⇢4 = e4

`4↵4 = r3

`4�4 = e4

`4

Fig. 2: Notation example.

The notation used in the paper is summarized below; anillustrative example is given in Figure 2.

⌧i travel time observation i⇢ik fraction of link k covered by observation i↵k fraction of link k included in definition of the network route�ik fraction of link k covered by both observation i and network route`k length of link kt0k prior travel time of link k

ANPR and FCD observations are processed together inthree steps: transformation, weighting, and aggregation.

1) Transformation: Each observation partially coveringthe network route is transformed into an observation ofthe actual route travel time. The step consists of four sub-parts: concatenation, allocation, scaling, and route entry timeestimation. Concatenation applies to FCD and sequences ofANPR cameras, where a vehicle may generate multiple datarecords along the route. It is reasonable, however, to considerone passage of a vehicle on the route as one travel timeobservation. Consecutive observations from the same vehicleare thus concatenated into a single travel time observation.

For each observation i, the observed travel time ⌧i isthen allocated between the network route and the adjacentnetwork. The allocation is based on prior knowledge of linktravel times t

0k and the distance traversed on each link. Prior

link travel times can be estimated using historical data andbe categorized based on time of day, day of week, season,weather condition, etc. and become updated on a rollinghorizon manner so that estimated link travel times of previoustime interval have impact on allocation of the observationsin the next time interval. In cases prior link travel times areunavailable or cannot be estimated, free-flow travel timescan be used. In general, the assumption here is that thefraction of time spent on the overlap route in relation tothe whole FCD route, �i, is the same as for the prior traveltimes on the same sections. The travel time allocated to thenetwork route is then ⌧

0i = �i⌧i, where the allocation factor

�i is �i =P

k �ikt0k/

Pk ⇢ikt

0k. The allocation factor is

1 for observations traversing only the network route andapproaches 0 as the distance traversed on adjacent linksincreases.

The travel time observations are then scaled up to the en-tire network route. Similar to the allocation, the assumptionis that the ratio between the travel time on the overlap routeand on the network route is the same as for the prior traveltime estimates on the same sections. The scaled route travel

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time observation is then Ti = ⌧

0i/⌘i, where ⌘i is the scaling

factor ⌘i =P

k �ikt0k/

Pk ↵kt

0k.

The time that each observed vehicle passes the beginningof the network route is the basis for grouping observationsto time intervals and aggregating, but is in general notobserved. For each observation the route entry time s

0, realor hypothetical, is estimated based on the prior travel timesalong the same lines as the allocation and the scaling.

2) Weighting: Each observation Ti is assigned a weight!i that determines its influence in the estimation of routetravel time statistics. Observations are weighted for threedistinct reasons: to reflect the representativeness in relation tothe network route; to correct for sampling bias due to unevenroute coverage; and to reflect the relative reliability of FCDand ANPR measurements. The final weight is the product ofthe representativeness weight ⌫i, the sampling bias weight �i

and the source reliability weight �i, i.e., !i = ⌫i�i�i. In thispaper �i is set to 1 for both ANPR and FCD observations.

Less overlap with the network route means that the rep-resentativeness as a network route observation is lower andthat the potential for error in allocation and scaling is higher.Observations are thus weighted based on the allocation andscaling factors, ⌫i = �

1/✓1i ⌘

1/✓2i . The parameters ✓1 and ✓2

control how fast the weight function decays as the overlapwith the adjacent networks increases, and the overlap withthe network route decreases, respectively.

Route coverage is evaluated at the link level. Let Nk bethe number of observations covering (partially or fully) linkk, or Nk =

Pid�ike. The weight �i is then the inverse of

the weighted average coverage for the traversed part of theroute, i.e. �i =

Pk �ikt

0k/

Pk �ikt

0kNk.

3) Aggregation: Statistics of the route travel time dis-tribution are calculated from the observations Ti and theassociated weights !i. The statistics are aggregated based onthe route entry time of each observation. For example, themean route travel time estimator is µ̂T =

Pi !iTi/

Pi !i.

Other statistics of the travel time distribution such as varianceand percentiles are also straightforward to calculate [7].

III. APPLICATION

The proposed travel time estimation method is applied ontwo routes in the arterial network of Stockholm, Sweden.FCD are collected by a GPS-based taxi fleet managementsystem covering about 1500 taxis. Each taxi broadcasts itslocation, timestamp, id number, and status (free/hired) onceevery two minutes on average [8]. A map-matching and pathinference algorithm [6] is performed on the raw FCD. TheANPR system in Stockholm measures direct travel time ofmany major routes. ANPR data typically have significantamounts of noise and need to be filtered before travel timestatistics are calculated. The method introduced by Kazagliet al. [9] is used for ANPR filtering.

For both FCD and ANPR, data from Mondays throughThursdays between 6 a.m. and 10 p.m. are used, collectedfrom September 15, 2012 to September 15, 2013. After pathinference, only observations with hired status are utilized fortravel time estimation. The prior link travel times t

0k for the

34# 51#

52#

54#68#

70#

111#

112#

34# 51#

52#

54#68#

70#

111#

112#

Fig. 3: The study area with 4 ANPR routes (51, 34, 52, and54), and 2 combined routes, 111 and 112.

network were estimated from FCD by applying the proposedmethod on each individual link (i.e. similar to the way µ̂T

is calculated but at the link level). The allocation, scalingand weighting of FCD in this step (estimation of prior linktravel times) are performed based on the length and free-flow speed (posted speed limit) of each link. The reason thatFCD is used for prior link travel time estimation is that ithas a greater spatial coverage compared to ANPR data whichcovers a limited number of links. In general, however, thefusion methodology proposed here can be used also for theprior link travel times.

Parameters �i, ✓1 and ✓2 are set to 1 in this paper. Ifground-truth travel time data were available, they can beselected using cross-validation techniques.

A. Experimental setup

Two network routes are defined for the experiment, de-noted as routes 111 and 112 in Figure 3. Route 111 (112)starts from the beginning of ANPR route 51 (52) and ends atthe end of ANPR route 34 (54). The network routes are inten-tionally defined as the combination of two consecutive ANPRroutes for evaluation purposes. Since consecutive ANPRroutes r1 and r2 share the same camera at their connectionpoint, direct travel time observations for the combined routeR can be calculated by matching the exit timestamp of r1

with the entry timestamp of r2. In other words, travel timesof routes 111 and 112 are not reported by the ANPR system,but calculated afterward by matching ANPR timestamps andsumming up the ravel times of corresponding sub-routes. Thetravel times of the matched ANPR observations are usedas references for evaluating the estimated travel time usingdifferent combinations of data sources.

The mean and the 25th, 50th (median) and 75th percentilesof the travel time distribution of route R is estimated usingFCD and ANPR data considering the following scenarios:

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i) Only FCD that fully or partially overlap the route R

ii) Only ANPR of r1iii) Only ANPR of r2iv) ANPR of r1 and FCDv) ANPR of r2 and FCDTravel time observations are grouped by route entry time-

stamp into 15-minute intervals, and the travel time statisticsare calculated for each time interval (N = 64 intervals from6 a.m. to 10 p.m.). The similarity between the estimatedtravel time statistic and the reference is evaluated using theroot-mean-square error (RMSE) across all time intervals.

B. Results

Figure 4 shows the estimated travel time of the two routes,111 and 112, under the data availability scenarios mentionedabove. In general, the estimation method captures the trendacross the day reasonably well in all scenarios, in particularfor the mean and median travel time.

The RMSE relative to the matched ANPR measurements,as well as the number of observations available for theestimation, are shown in Tables I and II. It can be seenthat “only FCD” performs better than “only ANPR” in somecases but worse in others, and the results of “only ANPR”differ significantly depending on which ANPR route is used.The estimator fusing ANPR and FCD is always better thanthe worst of “only ANPR” and “only FCD”, and in somecases is better than the best of the two. The results suggestthat the fusion of ANPR and FCD increases the robustnessof the estimation.

A network route may have multiple sections with differenttraffic characteristics. Because of such biases, extrapolatingthe travel times of a section may or may not result in goodestimates of the total travel time of the entire route dependingon how similar the selected sub-route is to the entire route.In the two examples, the sub-routes covered by ANPR arenot similar in terms of traffic characteristics, meaning thatone of them is better in estimating the travel time of thecombined route than the other one. The RMSE errors implythat the estimates using only FCD (scenario i) are in betweenthe estimates based on the two ANPR sub-routes eitherseparately or combined with FCD (i.e., between scenarios(ii, iv) and scenarios (iii, v)). Thus, if the ANPR data coverthe sub-route with characteristics most dissimilar to the fullroute, then fusion with FCD improves the estimates. On theother hand, fusion of FCD with an ANPR sub-route that issimilar to the full route results, in most cases, in only slightchanges in the estimates.

In general, some reasons for the differences between theestimated travel times in the various scenarios are as follows:

� ANPR observations come from the entire population ofvehicles while the FCD are generated by taxis. Taxismay not be a representative of the entire populationin terms of driving behavior, route choice, etc., whichresults in different reported travel times. Some of thesebiases can be corrected for as demonstrated in [7].

� The filtering method used for ANPR may classify someof the longer observations as outliers and exclude them,

resulting in a distribution with shorter right tail.� The method of pairing ANPR observations of two

consecutive routes may introduce errors where there ismore than one matching timestamp.

� Map matching and path inference of sparse FCD areother sources of error. Errors in path inference result inwrong assignment of travel time to network links.

IV. CONCLUSION

The paper proposes a non-parametric route travel timeestimation method based on fusion of FCD and ANPR data.The approach combines the network coverage of FCD withthe accurate measurements on specific route segments ofANPR. A common observation model for both sources ofdata is used to estimate travel time through a sequenceof transformation, weighting and aggregation. Applicationresults suggest that the fusion increases the robustness of theestimation, meaning that the fused estimate is always betterthan the worst of the two (FCD or ANPR), and sometimesbetter than the best of them. Further research is needed toevaluate the method on a varied set of network routes anddata sources, and to calibrate the parameters of the methodto optimize the performance.

REFERENCES

[1] J. W. C. van Lint and S. P. Hoogendoorn, “A robust and efficientmethod for fusing heterogeneous data from traffic sensors on freeways,”Computer-Aided Civil and Infrastructure Engineering, vol. 25, pp. 596–612, 2010.

[2] A. Hofleitner, R. Herring, P. Abbeel, and A. Bayen, “Learning thedynamics of arterial traffic from probe data using a dynamic Bayesiannetwork,” IEEE Transactions on Intelligent Transportation Systems,vol. 13, pp. 1679–1693, 2012.

[3] F. Zheng and H. van Zuylen, “Urban link travel time estimation basedon sparse probe data,” Transportation Research Part C, vol. 31, pp. 145–157, 2012.

[4] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of StatisticalLearning. Springer, 2nd ed., 2009.

[5] T. Miwa, D. Kiuchi, T. Yamamoto, and T. Morikawa, “Development ofmap matching algorithm for low frequency probe data,” TransportationResearch Part C, vol. 22, pp. 132–145, 2012.

[6] M. Rahmani and H. N. Koutsopoulos, “Path inference of sparse GPSprobes for urban networks,” Transportation Research Part C, vol. 30,pp. 41–54, 2013.

[7] M. Rahmani, E. Jenelius, and H. N. Koutsopoulos, “Non-parametricestimation of route travel time distributions based on low-frequencyfloating car data,” tech. rep., KTH Royal Institute of Technology, Dept.of Transport Science, 2014.

[8] M. Rahmani, H. Koutsopoulos, and A. Ranganathan, “Requirementsand potential of GPS-based floating car data for traffic management:Stockholm case study,” in Intelligent Transportation Systems (ITSC),2010 13th International IEEE Conference on, pp. 730–735, IEEE, 2010.

[9] E. Kazagli and H. N. Koutsopoulos, “Arterial travel time estimationfrom automatic number plate recognition data.” Proceedings of the 92ndAnnual Transportation Research Board Meeting, 2013.

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6 8 10 12 14 16 18 20 223

4

5

6

7

8

9

Trav

el ti

me

(min

)Route 111, Mean

6 8 10 12 14 16 18 20 22

Route 111, 25th Percentile

6 8 10 12 14 16 18 20 223

4

5

6

7

8

9

Route 111, 50th Percentile

Trav

el ti

me

(min

)

6 8 10 12 14 16 18 20 22

Route 111, 75th Percentile

6 8 10 12 14 16 18 20 22

3

4

5

6

7

Trav

el ti

me

(min

)

Route 112, Mean

6 8 10 12 14 16 18 20 22

Route 112, 25th Percentile

6 8 10 12 14 16 18 20 22

3

4

5

6

7

Hour of day

Route 112, 50th Percentile

Trav

el ti

me

(min

)

6 8 10 12 14 16 18 20 22Hour of day

Route 112, 75th Percentile

ANPR(R)FCD(R)ANPR(r1)

ANPR(r2)

ANPR(r1) and FCD(R)

ANPR(r2) and FCD(R)

ANPR(r_1,r_2) \& FCD(R)

Fig. 4: Comparison of estimated mean and percentiles of the travel time of routes 111 and 112 by various data availabilityscenarios against direct ANPR observations.

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TABLE I: Error of estimated travel time of route 111 by various scenarios against the ”Only ANPR” scenario.

Only FCD Only ANPR51 Only ANPR34 Fusion of ANPR51 and FCD Fusion of ANPR34 and FCDmean 0.28 0.46 0.26 0.34 0.2325th percentile 0.84 0.72 0.73 0.74 0.7750th percentile 0.49 0.50 0.33 0.46 0.3475th percentile 0.26 0.29 0.53 0.22 0.45Total number of observations 84,590 103,423 1,001,696 188,013 1,086,286

TABLE II: Error of estimated travel time of route 112 by various scenarios against the ”Only ANPR” scenario.

Only FCD Only ANPR52 Only ANPR54 Fusion of ANPR52 and FCD Fusion of ANPR54 and FCDmean 0.30 0.16 0.53 0.16 0.4425th percentile 0.33 0.22 0.68 0.23 0.6050th percentile 0.18 0.16 0.28 0.14 0.1975th percentile 0.37 0.25 0.89 0.25 0.71Total number of observations 95,944 305,227 768,577 401,171 864,521

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