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VEHICLE REIDENTIFICATION USING INDUCTIVE LOOPS IN

URBAN AREASR.J. Blokpoel

Peek Traffic BV, Department of Traffic Engineering, Basicweg 16, P.O. Box 2542, 3800 GB

Amersfoort. Telephone: +31 334541731 Email: [email protected]

ABSTRACT

Travel time information is of vital importance for traffic management and monitoring purposes.This information can be acquired by using reidentification on inductive loop profiles, which is

cheaper than expensive cameras registering the license plate numbers. Until now, most research

has focused on the motorways where double loops are mostly present. This paper presents analgorithm suitable for urban areas with various sizes of single loops. Validation tests showed

reidentification rates up to 100% when matching loops of the same type and 88% when matching

between different types. Introducing a likelihood border reduced the amount of false positivesbelow 2%.

KEYWORDS

Travel time measurement, data collection, inductive loops, vehicle reidentification.

INTRODUCTION

With the current increasing traffic densities and the focus on more environmentally friendlyIntelligent Traffic Systems (ITS) there is more demand for travel time information. This

information can be used for traffic management and monitoring purposes, which will result in

better infrastructural planning. ITS solutions will also perform more effectively when they are

able to access this information. Both advantages will result in a higher network throughput, lesstraffic jams and thus less environmental pollution.

Currently a well-known solution for travel time evaluation is the use of cameras which register

license plates. However, this solution is quite expensive and therefore local and state

governments are rarely willing to invest in those systems. Registering license plates also

introduces privacy issues. Another solution is using inductive loops which are cut in the roadsurface for the detection of vehicles. From those loops a fingerprint can be captured for every car

passing by. The travel times can be determined when those fingerprints or certain aspects of

them coming from different locations are compared with each other for reidentification. Current

research mainly focuses on motorway application of the concept [1-3]. Matching rates between

55% and 89% were achieved while no special attention to false positives was given.

However, the need for travel time information is even higher in the urban area. This is due to thenext generation of ITS solutions using cooperative systems with car-to-infrastructure [4] and car-

to-car-communication [5]. At low degrees of penetration detailed information about vehicles not

equipped with the new communication hardware is vital for the systems to work properly.

Therefore research for using the inductive loops in the urban area was carried out.

This paper first discusses the theoretical aspects of the matching algorithm used. These include

the algorithm used for comparison of the signatures, a post-processing algorithm and an extra


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pre-processing step for matching signatures from different loop types. Then the setup for the

validation test runs will be described together with the results.

THEORY

Comparison algorithm

The basis for reidentification of the vehicle profiles is a comparison algorithm to evaluate with

which previously-acquired signature a passing vehicle matches. Together with timestamps the

travel times can then be calculated easily. First a short description of literature solutions will begiven before the new algorithm is explained.

In [1] only a length estimation based on the inductive loop profiles is used. That method is notvery accurate and results in many possible matches in the matching matrix. Because many

vehicles pass on motorways it is still possible to calculate an average travel time by trying to

identify consecutive sequences of possible matches. It is, however, not suitable for urban areas

since travel times can change rapidly and the generally smaller platoons can change atintersections. Also, dual loops were used in [1] to get an estimate of the lenght, while dual loops

are not present everywhere in urban areas.

The lexicographic optimization method of [2] also uses double loops. The concept, however, is

more accurate than the previous one based on the length only since the lexicographic method

uses many aspects from the signature. Therefore, higher matching rates were achieved. The main

problem was the accuracy of the speed estimation from the double loops. With perfect speedestimations the performance was 73%, while a variance of 6.7 (m/s)2 only resulted in 33%

matching rate. This dependency on double loops and accurate speed estimates makes this method

also unsuitable for the urban area. The method did not pay attention to reducing false positive

matches either. Therefore the false positive rate in case of 73% percent correct matches was27%.

0

20000

40000

60000

80000

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81

Sample number

Loop

output

Figure 1: Raw signature from a 1.5 meter wide inductive loop from a normal hatchback car


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From these existing solutions it can be concluded that a comparative method is needed which

does not require double loops and the speed estimations. Therefore the algorithm proposed in

this paper will only use the raw signature from a single loop as input. A raw signature of a car is

presented in Figure 1. The unit on the Y-axis is an arbitrary unit which increases with the amountof material with a high permeability that is present above the loop. The value also increases

when the material is closer to the loop, i.e. closer to the road surface. On the X-axis the samples

are shown, which were taken every 6 ms.

The first step in the algorithm is the pre-processing, which includes the removal of the beginning

and end of the fingerprint, because at such low output levels the system is more susceptible to

noise. Then the fingerprint can be compared with another one resulting in a metric according tothe following formula:

=i

ii gf (1)

in which fi and gi are the points of the fingerprints which are compared with each other. Themetric is thus the total distance between the fingerprints. A matching matrix can be defined asfollows when at a travel time section multiple fingerprints are acquired at both the entry and the

exit of the section:

=

JIII

J

J

,2,1,

,21,2

,12,11,1

.

....

..

.

(2)

in whichI is the number of entry fingerprints and Jthe number of exit fingerprints. From every

column the most likely match can then be selected to re-identify the exiting vehicle. Then thefinal step of determining the travel time is just subtracting the time stamps.

Post-processing algorithm

The resulting matches from selecting the best match in every column of matrixMfrom equation

(2) might still contain a few errors. Therefore, it is interesting to evaluate that matrix by looking

not only at the columns but also at the rows. This is because a vehicle which enters the travel

time section cannot exit it twice. To get more insight in this consider the followingM-matrix:

Table 1: An example of an erroneous Mmatrix which can be corrected with post-processing

i \ j 1 2 3 4

1 2 10 11 92 7 4 8 12

3 12 6 3 11

4 9 3 13 2

The grey areas indicate the minimal values of every column, however, when considering the

complete matrix one can also look at the rows. Then the fourth row turns out to have two

matches, while the second row has no matches. Since the square in [2,2] has a value of 4 whichis only slightly larger than the 3 of [2,4], it is intuitively a good solution to correct the match of

the second column to [2,2].


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This basic thought can be generalized to an algorithm finding those solutions automatically. The

correction applied to the matrix of Table 1 can be checked by minimizing the sum of all selected

values under the constraint that only one value is selected per column and only one per row.When using Non-Linear Programming (NLP) techniques [6] that sum can be used as objective

function, while the row and column selection are used as constraints. This results in the

following formula:

[ ]

[ ] [ ]

)1,0(

1..11..1

1

..

1

1

..

1

..

)

1

..

1

)(1..1min(

,

=

=

jix

X

X

ts

X

(3)

in which X is the selection matrix and the x indicates an element wise multiplication. So theobjective function is the sum of all selected values in the matrix M. The first constraint makes

sure that exactly one value in each row will be selected and the second does the same for the

columns. Note that the row vector with all 1s should be J long and the column vector should

have lengthI. The last constraint makes sure that all the values ofXare either 0 or 1. Since NLPsolvers are quite computationally complex it might be better to convert the problem into a Semi-

Definite Programming (SDP) problem, which are more computationally efficient according to

[7]. This can be done by converting both Xand into concatenated vector format and adaptingthe constraints into that form as well.

An alternative would be to delete the entry profiles once they have been matched to an exit

profile. That way two matches on one row in an Mmatrix cannot occur either. However, such amethod makes it impossible to correct previously made mistakes.

Matching different loop types

Not all loops in the road surface have exactly the same size, resulting in different signatures for

the same vehicle. In [3] a method was presented using blind deconvolution to acquire the

impulse response of the car. However, those results seemed quite unstable since sometimes thedeconvolved matching was worse than without deconvolution. Therefore, a new way is presented

here. Most detectors have a rectangular shape and cover almost the whole width of a lane. Their

width in the driving direction can vary from 1 meter to 30 meters. From a theoretic point of viewone would expect that the narrower the loop is the more detailed the signature will be when

combined with a high sampling frequency. Smaller loops, however, also have a less high reach

which is illustrated in Figure 2.


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The bold line in the figure indicates the

effective range of the loop. A perfect

conversion from one profile to another is

not possible, because the heights of thescanning ranges differ and the

information from the upper part cannot

be acquired or separated and removed

afterwards. Converting from the largeloop to the smaller one isnt possible

either, because the extra

detail cannot be acquired afterwardseither.

Figure 2: Approximation of the magnetic field around an inductive loop

Therefore, the best possibility is to convert the profile of a small loop into a large loop profile,with the notion that the information of the upper part wont be present in it. The conversion to a

more stretched profile can be carried out by using a Finite Impulse Response (FIR) filter, which

has the form:

( ) ( )=

=

+=

bi

aii inxcny (4)

in whichyis the output andxis the input function. The start (a) and stop (b) of the index iare

free to choose. Suppose the average car length is 4 meters, the loop sizes are 1 and 1.5 meter,

then a vehicle travelling at 10 m/s will be above the 1 meter loop for 0.5 seconds and for 0.55seconds above the 1.5 meter loop. Then the filter coefficients can be trained by solving the NLPproblem defined as:

)for all(with

..

min

50

0

0

55

0

kxcz

UcL

ts

yz

jjiji

ij

K

k ikiki

=

= =

=

(5)

In this equation the index kranges over all vehicles in the training set, jgoes over all samples inthe 1-meter profile and iover all samples in the 1.5-meter profile. The functionyis the original

1.5-meter profile,x the original 1-meter profile and zthe 1-meter profile converted to 1.5-meterformat. The bounds for cij are L and U and they can prevent the solver from converging to

unfeasible solutions. The solution of this problem is the set of FIR filter coefficients included in

the matrix cij. This matrix can contain a lot of information, but logically most values far away

from the diagonal should be zeros.


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False positive identification

For measuring travel times it is not required to have data of every single vehicle. More important

is having a reliable and representative subset of travel times. Therefore, a matching algorithm

that matches 90% of the vehicles correct while having the other 10% wrongly matched is worthless than having an algorithm with 50% correct and the other 50% classified as unknown. The

wrong matches, or false positives, can introduce large errors in travel time measurements. When

a measurement location is chosen where cars can leave the route between the start and endpoint

then false positives will be more common, because it is theoretically impossible to match everyvehicle. Therefore, it is important to introduce a likelihood border for matches. When a match is

below the border it has to be classified as unknown in order to prevent false positives.

Acceleration and deceleration effects can also introduce many false positives, because they

distort the vehicles signature. Consider Figure 3 where an example signature is shown with

constant speed and with a high acceleration to get a good idea what acceleration can do to a

signature.

Figure 3: Example signature under constant speed (left) and acceleration (right)

The speed of the vehicle increases with a factor four from the start to the end of the signature.

This causes a lot of distortion and can very well cause the signature to be matched to a wrong

car. Correcting for these effects is only possible when the acceleration is known, which is onlypossible with a double loop. Therefore, induction loops very close to a stopline at an intersection

are less suitable for inductive fingerprinting techniques than loops at locations where cars pass in

free flow condition.

RESULTS

A validation test was carried out on the Outputweg in Amersfoort at a location where several

loops were placed close after one another. Three types of loops were used in the test, a 1.5 meterwide loop, an eight-shaped loop of two times 0.75 meters and a 1.0 meter loop. Two loops of

each kind were present so that the signatures can be compared and possibly matched by the

algorithms. The signatures of 70 vehicles were captured and tried to match. The eight-shaped

loop was not matched with the other types, because it has a very different signature. The

sampling period of the loop detectors was 6 ms and the average speed of the vehicles 60 km/h.


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The results are presented in Table 2. The matching rates are as high as 100% or close to it and it

can be concluded that the post-processing really improves the results. The matching rate of

signatures of different types is also promising with 80%. However, the learning process of the

filter coefficients needs some more research since it was not very stable with large variationsbetween adjacent coefficients.

Table 2: Matching results of the Outputweg

Loop type Set size Normal matching Post-processed

1.5 meter 50 92% 100%

8-shaped 50 98% 100%

1.0 meter 50 100% 100%

1.5 with 1.0 meter 50 80% 88%

The results in Table 2 do not take false positives into account, so all non-correct matches are

false positives. Therefore another test was carried out to investigate the effects of a likelihoodborder. The test was carried out under more challenging conditions on a motorway with a

sampling period of 12 ms and an average vehicle speed of 110 km/h. The loops were 1.5 meterswide. So there is less detail in the signatures while the sampling rate is too low.

Table 3: Motorway test with different likelihood borders

Set size Likelihood border Correct False Unknown

100 0% 83% 17% 0%

100 25% 72% 6% 22%

100 100% 50% 0% 50%

200 0% 73% 27% 0%

200 25% 62% 7% 31%

200 100% 37,5% 0,5% 62%

500 0% 68% 32% 0%

As a reference the data sets have been subjected to the method without likelihood border (0%) aswell. From those data it can be concluded that higher set sizes are more difficult to match, but

that the performance only degrades 5% when going from a set size of 200 to 500. Likelihood

borders of 25% and 100% have been used. From the results it can be concluded that even under

challenging conditions a border of 100% is very effective.

In the theory section it was mentioned that both acceleration effects and measurement locations

where cars can leave the route between the start and endpoint can lead to more false positives.

Therefore a test was carried out at a 4 km long section of a local road with motorway on and off-ramps between the start and endpoint. The loops at the start and endpoint were positioned at the

stopline of an intersection and therefore many cars have passed the loop while accelerating. The

results of the test where a 100% likelihood border was used are presented in Table 4. A samplingperiod of 12 ms was used and the loops were 1.0 meter wide. As expected from the theory it was

impossible to match vehicles with a high acceleration while passing the loop. Therefore the

results are shown with and without the accelerating vehicles. A vehicle was counted asaccelerating when its speed upon entry of the loop was 10% lower than while leaving the loop.


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Again the likelihood border of 100% showed to be effective since the amount of false positives

was kept very low.Table 4: Test on a longer section with and without acceleration effects

Method Correct matches False positives Set sizeNo acceleration 71,4% 0.85% 117

All vehicles 19.2% 1.27% 157

ConclusionThe matching algorithm combined with post-processing gave promising results. The results werebetter than previously reported in literature and also suitable for urban areas whereas previous

research mainly focused on the highway application. The method to filter out false positives

showed to be effective even under challenging conditions with cars leaving between start and

end point of the route, acceleration effects and too few samples.

Loops at locations where vehicles are often accelerating should be avoided, but long travel time

sections with intersections between the start and endpoint are not a problem. Although different

loops sizes have been used, the preferred loop size is a rectangular loop of 1.0 meters wide. Withthe effective method of reducing false positives the technique would also be suitable for Origin-

Destination (OD) matrix measurement.

Overall this research proved that cheap reidentification by using inductive loops should bepossible in urban areas. It is a low-cost solution because it can be done using existing detection

hardware without the need for expensive cameras. The technique gives access to lots of valuable

information for new emerging ITS solutions like the CVIS micro-routing application. Inductivefingerprinting can play a vital role in the transition phase from traditional traffic systems to

cooperative systems by providing traffic information at low penetration grades.

References[1] B.A. Coifman, Vehicle Reidentification and Travel Time Measurement Using Loop

Detector Speed Traps, Ph.D. thesis, University of California, 1998[2] Stephen Ritchie and Carlos Sun, Section Related Measures of Traffic System

Performance, university of California, November 1998.

[3] T.M. Kwon, Blind Deconvolution of Vehicle Inductance Signatures for Travel-Time

Estimation, University of Minnesota Duluth, 2006.[4] J.D. Vreeswijk and E.C. Koenders, Cooperative Infrastructure, IEEE Intelligent

Vehicles Symposium, 2008.

[5] V. Gradinescu, C. Gorgorin, R. Diaconescu, V. Cristea and L. Iftode, Adaptive

Traffic Lights Using Car-to-Car Communication, IEEE Vehicular TechnologyConference, 2007.

[6] Avriel, Mordecai, Nonlinear Programming: Analysis and Methods, Dover Publishing,

2003.

[7] Jos F. Sturm, Primal-dual interior point approach to semi-definite programming,Ph.D. thesis, Tilburg University, The Netherlands, 1997.

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