Using Recursive Bayesian Estimation for Matching GPS Measurements

to Imperfect Road Network Data

Oleksiy Mazhelis

Abstract— Map-matching refers to the process of projectingpositioning measurements to a location on a digital road net-work map. It is an important element of intelligent transporta-tion systems (ITS) focusing on driver assistance applications,on emergency and incident management, arterial and freewaymanagement, and other applications. This paper addresses theproblem of map-matching in the applications characterized byimperfect map quality and restricted computational resources- e.g. in the context of community-based ITS applications.Whereas a number of map-matching methods are available,often these methods rely on topological analysis, thereby makingthem sensitive to the map inaccuracies. In the paper, a newmap-matching method based on the probabilistic approach isintroduced. In the method, the probabilities of alternative roadlinks are estimated with recursive Bayesian estimation, and theroad link is identified using maximum a posteriori probabilityprinciple. The topological analysis is not used; instead, thedistance between projections on road links is used to assignroad link switching probability. The accuracy of the methodis empirically evaluated, and the link identification accuracy isfound to be similar to that of alternative approaches relying ontopological analysis.

I. INTRODUCTION

The functionality of intelligent transportation systems

(ITS) often includes the so-called map-matching, i.e. the

process of finding the location of an object on a road,

whereby the positioning information is fused with a (digital)

road network map [1]. The process of map-matching usually

consists of identifying the road link and defining the position

of the object on this link. The result of map-matching can

be used both to determine physical location of the object,

and to improve the accuracy of positioning by correcting

positioning errors.

The correctness of the map-matching greatly depends on

the accuracy of positioning and the quality of the map

used [2]. Positioning may rely on a global navigation satellite

system such as Global Positioning System (GPS) or Galileo,

inertial navigation systems (INS) based on accelerometers

and gyro, or on another navigation approach, such as radio

and radar navigation. Nowadays, GPS receivers are available

as inexpensive consumer-grade electronic devices, including

the receivers embedded in numerous smartphone models.

The accuracy of these consumer-grade receivers yields to

the accuracy of high-end devices, and may be as low as over

70m for the first fix, eventually improving to circa 20 m [3].

This research reported in this paper was carried out in Sensor DataFusion and Applications project as a part of the Cooperative Traffic researchprogram of the Strategic Center for Science, Technology and Innovation inthe Field of ICT, funded by the National Technology Agency of Finland.

O. Mazhelis is with the Department of Computer Science and InformationSystems, University of Jyvaskyla, P.O. Box35, FIN-40014, Jyvaskyla,Finland (email: mazhelis@jyu.fi)

Road maps often also contain omissions and inaccuracies

in a form of road curves interpolated as linear segments,

missing links, missing information about maintenance works

or new roads [2], [4], [5]. These inaccuracies may make the

map-mapping based on topology problematic. Besides, an

implicit assumption often exists that the object stays on the

road, therefore excluding off-road motions altogether.

Map-matching is often used in cooperative ITS applica-

tions; an example of such application is pothole detection

based on the acceleration measurements from a fleet of ve-

hicles [6]. These applications may rely on open community-

based map providers such as OpenStreetMap and utilize the

GPS receivers embedded into Nokia N95 phones [7]. In this

case, the task of map-matching is challenging both due to the

positioning inaccuracies of consumer-grade GPS receivers,

and due to the inaccuracy of the map used.

This paper focuses on the problem of map-matching in the

application domains characterized by imperfect map quality

and restricted computational resources, such as the coop-

erative ITS applications exemplified above. It is therefore

assumed that a relatively cheap GPS receivers are used, and

the road network map is assumed to contain omissions and

inaccuracies. The matching is assumed to be done on-line,

and therefore, post-processing is to be avoided. Furthermore,

it is implied that the matching software will be deployed

as a part of a distributed solution, where the concurring

requests from multiple traffic participants need to be served;

in such environment, the computational overhead of the map-

matching method should be conservative to make the solution

scalable.

Whereas a number of map-matching methods are avail-

able, often these methods rely on topological analysis,

thereby making them sensitive to the map inaccuracies.

In this paper, a new map-matching method based on the

probabilistic approach is introduced. In the method, the

probabilities of alternative road links are estimated with

recursive Bayesian estimation, and the correct road link is

identified using maximum a posteriori probability principle.

The topological analysis is not used; instead, the distance

between projections on road links is used to assign road

link switching probability. The accuracy of the method is

empirically evaluated; according to the results, the estimated

probability of correctly identifying road links is similar to

that of alternative approaches relying on topological analysis.

The remainder of the paper is organized as follows.

In the next Section, the related map-matching approaches

are reviewed. In Section III, the map-matching method

based on recursive Bayesian estimation is described. The

2010 13th International IEEEAnnual Conference on Intelligent Transportation SystemsMadeira Island, Portugal, September 19-22, 2010

TC8.3

978-1-4244-7659-6/10/$26.00 ©2010 IEEE 1492

results of performance evaluation experiments are reported

in Section IV. Finally, in Section V, the advantages and

shortcomings of the method are discussed, and the directions

for future work are outlined.

II. RELATED WORKS

A number of map-matching approaches and algorithms

have been developed over last decade varying from geometric

and topological analysis to probabilistic and other advanced

approaches [1]. The geometric approaches rely on searching

for the map node closest to the position fix (point-to-point

matching), on searching the map curve closest to the fix

(point-to-curve matching), or on assessing the similarity

between measured trajectory and the road network (curve-

to-curve matching) [8]. These methods are rather sensitive

to outliers in the positioning measurements, and they were

also found to produce unstable results in dense urban envi-

ronments [1].

The topological approaches, in addition to the geometric

analysis, take into account the connectivity among the road

links [9], [10]. Probabilistic approaches construct an error

region around position measurement, and the likely road link

in this region is identified based on geometry and topological

information [2], [11]. Bayesian inference [12] and particle

filters [13] can be employed in order to estimate the road

link probability.

Besides probabilistic reasoning, the likelihood of road

links can be assessed using Dempster-Shafer evidential

reasoning [14], [5] or fuzzy logic [15]. Furthermore, the

map-matching process is often augmented with (Extended)

Kalman Filter, whereby the fused positioning and motion-

related information from multiple sensors is corrected by

using the map matching results [16], [17], [18], [5].

Majority of map-matching methods, in addition to the po-

sitioning information, also take into account the information

about the heading of the object, e.g. inferred from changes

in gyroscope readings [18] or from sequential positioning

measurements [5]. This information, derived from GPS mea-

surements, is utilized in the proposed method as well.

In many methods, the matching does not take into account

the preceding measurements. Yang et al. [14] take into

account the distance to the closest road at the present point

in time only. Similarly, Greenfeld et al. [9] and Velaga et

al. [10], when computing the total weighted score for the

heading, proximity, connectivity, and other measurements,

ignore the prior measurements. This reliance on the present

measurements makes the methods sensitive to the outliers.

In the proposed method, in order to benefit from the ac-

cumulated information, the recursive Bayesian inference is

applied.

Noteworthy, the road link connectivity information is used

in many approaches. For instance, the multiple hypothesis

technique [12], the “probability of connectivity” is estimated

based on the number of bypassing links between prior

and current mapped positions. Such connectivity analysis,

however, would make the method sensitive to the omissions

and inaccuracies of the digital road maps. Besides, it would

increase the computational complexity of the method, as

the number of bypassing links between prior and current

projections needs to be retrieved for each pair of projections.

Therefore, the analysis of road link connectivity is avoided

in the proposed method.

Arguably, the method closest to the proposed one is

the multiple hypothesis technique (MHT) [12]. Similarly

to the MHT, a set of candidate road links are identified,

and the candidate probabilities are estimated recursively.

However, to tolerate road map omissions and inaccuracies,

in the proposed method, instead of the road link connectivity

analysis, the link change probability is estimated based on

the distance between the position fix projections.

III. MAP MATCHING USING RECURSIVE BAYESIAN

ESTIMATION

We assume that a sequence of positioning measurements

are available, and the measurement vector at time t takes the

form zt = {PN, PE}, where PN and PE are north and east

positions of the object, respectively. The map-matching prob-

lem is formulated in the paper as follows: given a sequence

of positioning (GPS) measurements z0:t = {z0, z1, . . . , zt},

accumulated by time t, find the most likely road link st and

location on the links xt.

In the method, the probabilistic Bayesian theory is applied.

Namely, the a posteriori probability of road links P (st|z0:t)is approximated, and the maximum a posteriori probability

(MAP) principle is used to determine the appropriate road

link. The process of map-matching is recursive; on each

iteration, a new measurement zt is used to update P (st|z0:t).A single iteration consists of i) hypothesis generation, ii) hy-

pothesis evaluation, and iii) hypothesis selection phases,

which are described in detail below.

Hypothesis generation. Given a measurement, a set

of candidate road links is generated. For the initial map-

matching, an error ellipse is constructed around the initial

GPS measurement, and the candidate road links are selected

as the links crossing the error ellipse.

For each consequent measurement, first, the set of candi-

date links from the preceding step is extended with the road

links crossing the error ellipse constructed around the new

measurement. After that, the links in the set, whose distance

to the latest measurement exceeds a pre-defined threshold,

are pruned.

The candidate road links are employed to construct the

set of Nt hypotheses St ≡ {Sit, i = 1, . . . , Nt}. Individual

hypothesis Sit is defined as a vector Si

t = {sit,y

it, θ

it}, where

sit is the hypothesized road link, y

it is the projection of zt

on sit, and θi

t is the heading of the road link at the point of

projection.

Hypothesis evaluation. From Bayes rule, the conditional

probability P (sit|z0:t) can be expressed as:

P (sit|z0:t) ∝ P (z0:t, s

it) = P (zt|s

it)P (si

t|z0:t−1). (1)

Using the complete probability formula, the second term

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in the right-hand side of Eq. 1 can be rewritten as:

P (sit|z0:t−1) =

∑

sj

t−1∈St−1

P (sit|s

jt−1)P (sj

t−1|z0:t−1). (2)

Thus,

P (sit|z0:t) =

1

CP (zt|s

it)

∑

sj

t−1∈St−1

P (sit|s

jt−1)P (sj

t−1|z0:t−1),

(3)

where C represents the normalization coefficient.

The term P (sjt−1|z0:t−1) represents a recursive element.

The other terms in the right-hand side of Eq. 3 are estimated

as follows.

The probability of a measurement given a road link

P (zt|sit) is assumed inversely proportional to the distance

and the heading discrepancy, namely:

P (zt|sit) = Pproximity(zt|s

it)Pheading(zt|s

it). (4)

The proximity probability Pproximity(zt, sit) is inversely

proportional to the distance between zt and sit:

Pproximity(zt|sit) =

1

d(zt,yit) + δ

, (5)

where d(zt,yit) is the distance between zt and y

it, and δ

represents a small positive real number to limit the proximity

probability value.

Similarly, the heading probability Pheading(zt, sit) is

inversely proportional to the discrepancy between the

measurements-derived heading and the road link heading θit:

Pheading(zt|sit) = 1 − 2k

h(θ, ψ)

π, (6)

where ψ is bearing from zt−1 to zt estimated using the flat

earth approximation:

ψ = arctancosPNt−1(PEt − PEt−1)

(PNt − PNt−1)(mod 2π), (7)

h(θ, ψ) ≤ π/2 is the heading deviation between θ and ψ,

and 0 < k ≤ 1 is a regularization coefficient specifying

how sensitive the estimation of the heading discrepancy

probability is to the heading deviation. Note that the heading

deviation is calculated as the smallest angle between the lines

going in the directions θ and ψ. Thus, the heading deviation

ignores the information about one-way directions.

As mentioned above, the link switching probability esti-

mation usually takes into account the road network topology,

e.g. in terms of the road links bypassed [12]. However, this is

sometimes problematic: i) if preceding road link is wrongly

estimated and is not connected to the correct one, the proba-

bility will be close to zero; ii) it will take extra computational

time to retrieve and process the road connectivity from road

network map database; iii) in case a road link connecting the

preceding and the current links is missing in the road network

map, the connectivity information will contain a significant

error.

Therefore, the road link switching probability P (sit|s

jt−1)

is assumed inversely proportional to the square of the dis-

tance from the projection (of measurement zt−1 at time t−1)

onto road link sjt−1 to the projection (of measurement zt at

time t) onto road link sit:

P (sit|s

jt−1) =

{

ci1

[d(yit−1

,yjt)+ξi]2

, if i 6= j

ci1

[d(zt−1

,zt)]2 , if i = j.

(8)

where ci are normalization coefficients. Note that the no-link-

switching probability (i.e. the case of i = j) is estimated

based on the object’s measured displacement d(zt−1, zt).That is, as soon as the vehicle approaches a crossroad (see

Fig. 1), the distance between projections on the crossing road

links, as compared to the displacement, decreases, thereby

increasing the road link switching probability.

z0

z1

i0y

sj

z2

i1y

j2y

j1y

!jid 10 ,yy

!10 ,zzd

!jid 21,yy

!10 ,zzd

si

Fig. 1. The distances between projections d(yit−1

,yjt ) and measurement

displacements d(zt−1, zt). Their values are utilized to estimate the road

link switching probability P (sit|s

jt−1

): closer to a crossroad, the distancebetween projections on the crossing road links, as compared to the displace-ment, decreases, thereby increasing the road link switching probability

The smaller the distance between projections on two

road links, the higher the probability of switching the

links. This may result in erroneous switching between two

parallel roads. Therefore, the auxiliary non-negative term

ξi = d(zt−1, zt) is used in Eq. 8: it assigns greater values

to no-link-switching probability, and therefore increases the

threshold of switching the road links.

Hypothesis selection. The most likely road link is

identified by following MAP principle:

st = arg maxsi

t

P (sit|z0:t), (9)

where P (sit|z0:t) is estimated based on Eq. 3 for all hypothe-

ses in St.

The position of the object on the road link is assumed to

be xt = yt, where yt is the point on road link st closest

to zt. Such simple position determination does not take

into account the dynamics of object movements; in order to

improve the accuracy, the positioning can be smoothed using

Kalman filter (applied to measurements zt or to mapped

positions xt).

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At present, the method always outputs a decision (i.e. st

and xt, unless no road links in the available network map

cross the area used for hypothesis generation. In order to

improve the mapping accuracy, ambiguous decisions can be

filtered by imposing a minimum probability threshold and/or

a minimum ratio between the two largest probabilities; in

case the thresholds are not exceeded, a “no decision” would

be produced as an output.

IV. PERFORMANCE EVALUATION

In order to empirically evaluate the performance of the

proposed map-matching method, it has been applied to sev-

eral data sets. The datasets and the results of experimentation

are described below.

The positioning data used in the experiments was gathered

by using a Nokia N95 phone, which receives GPS readings

from embedded GPS receiver at the frequency of 1 Hz. The

data were stored on the phone’s memory card, and were then

processed offline.

The data were collected during summer and autumn 2009

in the course of 18 drives, all of which took place in the

region of Central Finland. The description of the gathered

datasets is provided in Table I. As could be seen, both

urban, suburban, and rural areas are represented. The urban

characteristics include buildings (though, very tall buildings

were not present due to the specifics of the area), dense

road networks, bridges and flyovers. The length of the drives

varied from 1.5 km for the shortest urban drive to over 70 km

for the longest (largely rural) drive.

In order to test the accuracy of the proposed map-mapping

method, the OpenStreetMap1 was used as a digital road

network map. Since this is a community project, the map

relies on users uploading their GPS track logs and editing the

vector data; as a result, the map is likely to have omissions

and inaccuracies.

1http://www.openstreetmap.org/

TABLE I

POSITIONING DATASETS

Dataset Environment Data points

1 Urban 3192 Urban 1643 Urban 1404 Urban 1595 Urban and suburban 4256 Urban and suburban 4337 Urban and suburban 2798 Urban and suburban 1209 Urban and suburban 42110 Urban and suburban 57911 Urban and suburban 46012 Urban and suburban 45513 Urban and suburban 43014 Urban and suburban 44315 Urban, suburban and rural 294716 Urban, suburban and rural 316317 Urban, suburban and rural 249618 Suburban and rural 2225

The software implementing the proposed map-matching

method is written in Java and is utilizing LibOsm library2.

For practical reasons, the error square bound was employed

instead of error ellipse in hypothesis generation phase; the

square with side of 50 m was used. Whenever a break in

measurements exceeded the threshold of 20 s, the measure-

ments were treated as discontinued and the map-matcher was

reinitialized. The map-matching was carried out in a batch

mode, and the results were processed off-line.

An example of the map-matching result is shown in Fig. 2.

As could be seen, the GPS positions are correctly mapped

onto the appropriate road links. The mapping accuracy was

evaluated by manually comparing the results of matching

with the known routes taken in the data gathering drives.

Only the accuracy of link identification was assessed; the

evaluation of the horizontal accuracy was not possible, since

the true position on the links was not known. Given position

mapped on a link, the mapping was considered correct, if

the corresponding link was driven on and if the order of the

links matched with the sequence of the link within the route

taken; otherwise, the mapping was considered erroneous.

Fig. 2. Example: raw measurements (red circles) and their mappedcounterparts (blue triangles)

It should be noted that the current method implementation

does not take into account the existence of parking lots,

neither does it distinct the opposite lanes. Therefore, neither

the erroneous mapping onto the neighboring road links while

maneuvering on a parking lot nor the mapping onto the

opposite lane were considered as a mapping error.

The results of accuracy evaluation are provided in Table II,

where both the correctly identified links and the link identifi-

cation errors are reported. As can be seen from the table, for

urban datasets, the link identification accuracy varies in the

2http://sourceforge.net/apps/mediawiki/

travelingsales/index.php?title=LibOSM

1495

range 95.7–100%, and for the mixed datasets in the range

87.5–99.9%. The link identification accuracy of the method is

therefore comparable to the results achieved with alternative

approaches utilizing topological data: as observed in [1], the

accuracy achieved with topological approaches varies from

85.8% [19] (suburban) to 99.2% [15] (urban and suburban).

Meanwhile, the proposed method is expected to have some

advantage as compared with the approaches relying on

topology. Namely, as link connectivity is not taken into

account, omissions and inaccuracies in the digital road map

are tolerated. Besides, the topological analysis, if used, would

add to the computational overhead of the map-matching

method, and therefore would make the implementation of

the map-matching software less scalable.

For urban and mixed environments, the obtained link

identification accuracy is summarized in Table III, and Fig. 3

shows the link identification errors while categorizing them

according to the environment. As could be seen, for the

mixed datasets with prevailing suburban and rural data,

the link identification accuracy is slightly better. The more

accurate mapping in suburban and rural areas can be ex-

plained by the scarcity of buildings and less dense and

simpler road network in these environments. It should be

noted that, as shown in the figure, for one of the datasets

representing mixed suburban and urban data (dataset 7), the

link identification errors exceed 12%, which is significantly

worse than the errors observed with the urban datasets. A

further inspection of the dataset has revealed that such an

exceptionally large percentage of errors was caused by a bias

in the positioning measurements.

V. DISCUSSION AND CONCLUDING REMARKS

In the previous sections, the map-matching approach based

on recursive Bayesian estimation was described, and the re-

sults of empirical evaluation of the approach were presented.

The achieved link identification accuracy is comparable to

the accuracy of alternative map-matching approaches. Since

TABLE II

ROAD LINK IDENTIFICATION ERRORS

Dataset Link Link Correctly Correctidentification identification identified link

errors errors (%) links identification (%)

1 0 0.0 319 100.02 6 3.7 158 96.33 6 4.3 134 95.74 2 1.3 157 98.75 9 2.1 416 97.96 9 2.1 424 97.97 35 12.5 244 87.58 1 0.8 119 99.29 19 4.5 402 95.510 12 2.1 567 97.911 12 2.6 448 97.412 2 0.4 453 99.613 1 0.2 429 99.814 2 0.5 441 99.515 27 0.9 2920 99.116 16 0.5 3147 99.517 16 0.6 2480 99.418 2 0.1 2223 99.9

14

8

10

12

14

onerrors, %

2

4

6

Link

identificatio

0

0 2 4 6 8 10 12 14 16 18

Urban Urban and suburban

Urban, suburban and rural Suburban and rural

Fig. 3. Road link identification errors in different environments

TABLE III

SUMMARY OF LINK IDENTIFICATION ACCURACY ESTIMATION

Environment Correct link 95% confidenceidentification (%) interval

Mixed: urban, suburban, rural 97.9 0.9Urban 97.7 2.7Overall 97.8 0.9

the road link connectivity analysis is not used in the method,

and since no post-processing is involved, the method is

deemed useful in the situations when:

• digital road network map contains inaccuracies, such

as road curves interpolated as linear segments, missing

links, links outdated due to maintenance works or new

roads constructed;

• the matching needs to be done on-line and conserva-

tive computational overhead is important, e.g. in large-

scale solutions concurrently processing map-matching

requests from multiple traffic participants.

It should be noted that, since presumably inaccurate map is

used for mapping, the result of matching could hardly be

used for correcting positioning errors.

Based on the analysis of the results of map-matching, the

observed link identification errors can be categorized into the

following groups:

a) Missing a turn at a crossroad: Given equal distances

to the previous and the new road link, the method, due to

its Bayesian nature, will favor the previous road link. If

due to positioning errors, the estimated heading is closer

to the previous road link, the error of missing a turn is

likely. However, as soon as the distance to the previous link

increases, the correct new link is identified.

b) Errors at Y-junctions: At or near Y-junctions, the

heading of the road links differs insignificantly. If, due to

positioning errors, the estimated distance to an incorrect

link is smaller, the link identification error is likely. This

is sometimes observed near exit or entrance ramps until the

distance between road links becomes sufficient.

1496

c) Failing to recognize parking lots and correct lanes:

As mentioned above, the implementation ignores parking

areas and the directions of one-way lanes; as a result,

incorrect link identification is likely.

Many of these errors are caused either by the bias or

noise in the GPS positioning measurements. The results

of the experiments indicate that the method tolerates noise

in the positioning information well: the impact of random

deviations from the real position is smoothed during the

recursive Bayesian estimation process. However, the bias in

the measurements may reduce the link identification accuracy

dramatically: if the bias is of the same order as the distance

between closest links (with similar heading), the method will

eventually assign the measurements to incorrect link.

In further work, the method needs to be equipped with the

possibility to tolerate the bias in positioning measurements,

so that the above errors would be reduced. For instance,

Kalman filter can be used to estimate and correct the bias.

However, when positioning bias is too high (in some tests,

the bias exceeding 50 m was observed), the use of Kalman

filter will unlikely be able to compensate it.

Some of the errors may be avoided by delaying the map-

matching decision. For instance, if the identified road link

a (e.g. highway) changes for a second to b (e.g. exit ramp)

and then again returns to a, then the road link b is likely

to be identified incorrectly and can be filtered. However,

such delay would represent a form of post-processing, and

hence would limit the applicability of the method in online

applications.

In future work, some elements of topological analysis can

be used to assign the road link switching probabilities. In par-

ticular, near the end of a link higher switching probabilities

can be assigned to the adjacent links. If the information about

adjacent links is easily retrieved from the map database, the

computational overhead should be minimal. This should be

applied with care, however, since several road links may be

passed in the interval between consequent positioning mea-

surements (e.g. an approach to a roundabout, the roundabout,

and an exit from the roundabout), and analyzing adjacent

roads only may therefore be insufficient. Also, the benefit

of such connectivity analysis depends on the map accuracy,

and hence the influence of the connectivity on probability

assignment should be limited to tolerate inaccuracies in the

map.

Provisions should be made to accommodate the boundaries

of parking lots and other suitable for driving areas into the

analysis, and to equip the implementation with the possibility

to distinguish among opposite lanes in the maps.

VI. ACKNOWLEDGMENTS

The author would like to thank anonymous reviewers, as

well as colleagues from the Sensor Data Fusion and Appli-

cations project for their valuable comments and suggestions.

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