6
Azimuth Based Localization for Mobile Phones Anish Thomas, Jan Geldmacher, J¨ urgen G¨ otze Information Processing Lab TU Dortmund University Otto-Hahn-Str. 4, 44227 Dortmund, Germany. Correspondence: [email protected] Edmund Coersmeier Task9 GmbH Universit¨ atsstr. 142 44799 Bochum, Germany. Abstract— Based on measured acceleration and compass data of smartphones a concept for GPS-free localization and traveling route estimation is presented. The built-in compass is used to measure the relative direction changes of the traveling user. The resulting azimuth trajectories are then successively matched to a vectorized street map. In order to relate the measured trajectory to the street map data, it has to be scaled correctly by the current user velocity. To estimate the current velocity, pattern matching is applied to the acceleration sensor data to detect the current means of transportation (MOT). By associating typical velocities with each MOT, a set of possible scaled azimuth trajectories can be found. I. I NTRODUCTION The evolution of personal mobile communications estab- lishes new features and applications for mobile phones. Re- cently it can be observed that phones are equipped not only with communication technologies like bluetooth and wireless LAN, but also with multiple sensors for measuring the en- vironment. Prominent examples are acceleration sensor and digital compass. These sensors can be used for improving the usability of the user interface, for example by turning the screen according to the geographical direction or angle of the device. However, these sensors also reveal information about their physical environment, which may be used to assist or improve localization technologies. As an example, the acceleration sensor of a mobile phone can be used to recognize the current means of transportation (MOT) of a user [1]. Using the fact that every MOT, like car, train, pedestrian, has its own specific movement pattern, a pattern recognition approach can be applied to the acceleration sensor data to estimate the current MOT. This information can be used to assist the implementation of Location Based Services (LBS), like for example advanced traffic information systems [2]. It may also be used to improve localization accuracy in combination with digital map data, because it can be seen as a constraint on possible user positions. Realizing a localization algorithm for mobile phones based on sensor data and GSM/UMTS network measurements [3], [4] and not on the GPS technology can be beneficial for several reasons. Adopting a localization technology for LBS in the field of social or entertainment applications [5], [6], poses different requirements than navigation applications. While the latter requires high accuracy and is actively controlled by the user, the former are often so called pushed services, which rely on continuous, but less accurate position estimates, and which trigger the user on location dependent events. In the latter case, the GPS technology is not necessarily the optimal solution, because of its poor user-time coverage due to the line of sight (LOS) requirement [7], [3] and its increased energy consumption. Alternative approaches, based on sensor or baseband measurements can be more suitable, because they rely on data, that is available continually, and that is less dependent or independent of LOS conditions. In this paper, we consider measurements from a digital compass built into a mobile phone, and its application for localization. The digital compass delivers relative information about the change of moving direction of the mobile user. Based on the observation of the direction changes for a certain time, a movement trajectory can be constructed. We refer to this trajectory, that reflects the directions changes over time, as the azimuth trajectory. The estimated azimuth trajectory can be correlated with digital map data to estimate the route and possibly the position of the user. Thus, the localization approach described in this paper can be seen as azimuth based map matching. While the basic idea seems intuitive on first sight, it poses several problems when it comes to a practical realization: A principle problem is that observing solely the direction changes over time is not sufficient. In fact, to connect the trajectory with digital map data, it has to be linked to the current velocity in order to provide the correct scaling of the trajectory. However, estimating the current velocity in a mobile phone is not straight-forward. A second principle problem is that the measured az- imuth trajectory does not reveal the absolute movement direction, but only relative direction changes. This is due to the fact that while the compass delivers absolute measurements, the relation of the moving direction to the measurement axis of the phone is generally not known. “User interference” can also become a problem: The measured direction changes not only depend on the user movement, but also on turns of the phone that are performed manually by user. Like all measured data, the compass measurements are distorted by noise. The distortion can introduce strong degradation of the measured data, due to the rather poor quality of the involved, built-in magnetic sensor and the interfering magnetic fields often found in vehicles and trains. 978-1-61284-4577-0188-7/11/$26.00 c 2011IEEE71

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Page 1: [IEEE 2011 International Conference on Localization and GNSS (ICL-GNSS) - Tampere, Finland (2011.06.29-2011.06.30)] 2011 International Conference on Localization and GNSS (ICL-GNSS)

Azimuth Based Localization for Mobile Phones

Anish Thomas, Jan Geldmacher, Jurgen Gotze

Information Processing Lab

TU Dortmund University

Otto-Hahn-Str. 4, 44227 Dortmund, Germany.

Correspondence: [email protected]

Edmund Coersmeier

Task9 GmbH

Universitatsstr. 142

44799 Bochum, Germany.

Abstract—Based on measured acceleration and compass dataof smartphones a concept for GPS-free localization and travelingroute estimation is presented. The built-in compass is used tomeasure the relative direction changes of the traveling user. Theresulting azimuth trajectories are then successively matched to avectorized street map. In order to relate the measured trajectoryto the street map data, it has to be scaled correctly by the currentuser velocity. To estimate the current velocity, pattern matchingis applied to the acceleration sensor data to detect the currentmeans of transportation (MOT). By associating typical velocitieswith each MOT, a set of possible scaled azimuth trajectories canbe found.

I. INTRODUCTION

The evolution of personal mobile communications estab-

lishes new features and applications for mobile phones. Re-

cently it can be observed that phones are equipped not only

with communication technologies like bluetooth and wireless

LAN, but also with multiple sensors for measuring the en-

vironment. Prominent examples are acceleration sensor and

digital compass. These sensors can be used for improving

the usability of the user interface, for example by turning the

screen according to the geographical direction or angle of the

device. However, these sensors also reveal information about

their physical environment, which may be used to assist or

improve localization technologies.

As an example, the acceleration sensor of a mobile phone

can be used to recognize the current means of transportation

(MOT) of a user [1]. Using the fact that every MOT, like

car, train, pedestrian, has its own specific movement pattern, a

pattern recognition approach can be applied to the acceleration

sensor data to estimate the current MOT. This information

can be used to assist the implementation of Location Based

Services (LBS), like for example advanced traffic information

systems [2]. It may also be used to improve localization

accuracy in combination with digital map data, because it can

be seen as a constraint on possible user positions.

Realizing a localization algorithm for mobile phones based

on sensor data and GSM/UMTS network measurements [3],

[4] and not on the GPS technology can be beneficial for several

reasons. Adopting a localization technology for LBS in the

field of social or entertainment applications [5], [6], poses

different requirements than navigation applications. While the

latter requires high accuracy and is actively controlled by the

user, the former are often so called pushed services, which

rely on continuous, but less accurate position estimates, and

which trigger the user on location dependent events. In the

latter case, the GPS technology is not necessarily the optimal

solution, because of its poor user-time coverage due to the

line of sight (LOS) requirement [7], [3] and its increased

energy consumption. Alternative approaches, based on sensor

or baseband measurements can be more suitable, because they

rely on data, that is available continually, and that is less

dependent or independent of LOS conditions.

In this paper, we consider measurements from a digital

compass built into a mobile phone, and its application for

localization. The digital compass delivers relative information

about the change of moving direction of the mobile user.

Based on the observation of the direction changes for a certain

time, a movement trajectory can be constructed. We refer to

this trajectory, that reflects the directions changes over time,

as the azimuth trajectory. The estimated azimuth trajectory

can be correlated with digital map data to estimate the route

and possibly the position of the user. Thus, the localization

approach described in this paper can be seen as azimuth based

map matching.

While the basic idea seems intuitive on first sight, it poses

several problems when it comes to a practical realization:

• A principle problem is that observing solely the direction

changes over time is not sufficient. In fact, to connect the

trajectory with digital map data, it has to be linked to the

current velocity in order to provide the correct scaling of

the trajectory. However, estimating the current velocity in

a mobile phone is not straight-forward.

• A second principle problem is that the measured az-

imuth trajectory does not reveal the absolute movement

direction, but only relative direction changes. This is

due to the fact that while the compass delivers absolute

measurements, the relation of the moving direction to the

measurement axis of the phone is generally not known.

• “User interference” can also become a problem: The

measured direction changes not only depend on the

user movement, but also on turns of the phone that are

performed manually by user.

• Like all measured data, the compass measurements are

distorted by noise. The distortion can introduce strong

degradation of the measured data, due to the rather poor

quality of the involved, built-in magnetic sensor and the

interfering magnetic fields often found in vehicles and

trains.

978-1-61284-4577-0188-7/11/$26.00 c©2011 IEEE71

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Acceleration

Sensor Compass

Digital

ClassificationAzimuth

Generation

Cell-ID

Measurement

Previous

Results

Vectorized

Map Data

Candidate

Correlation

Selection

Set of Possible Routes and Metrics

Set of Azimuth Trajectories Set of Candidate Azimuths

Generation

aj(i) ∈ A(i) ck(i) ∈ C(i)

Fig. 1: Azimuth based map matching.

This paper is organized as follows: The proposed azimuth

based map matching concept is described in Sec. II: Subsec.

II-A describes pre-processing of the measured data, Subsec.

II-B explains the involved MOT classification and Subsecs.

II-C and II-D describe the generation of candidate routes

and matching of the measured azimuth trajectories to the

map. Experimental results are used to illustrate the proposed

approach in Section III. Finally, conclusions are drawn in

Section IV.

II. AZIMUTH BASED MAP MATCHING

An overview of the azimuth based map matching approach

and the involved measurements is given in Fig. 1. As explained

before, the underlying principle is to measure the temporal

azimuth changes, while the user is moving, and periodically

correlate the resulting estimated azimuth trajectories with

candidate azimuth trajectories generated from a vectorized

digital map. The result is an estimate of the route that the user

has travelled and an estimate of possible current locations.

The involved computations and measurements mentioned in

Fig. 1 are described in detail in the following subsections.

A. Azimuth Measurement and Pre-Processing

The azimuth trajectory is constructed from the measure-

ments obtained from a digital compass built into the mobile

phone. The digital compass is based on a triaxial magnetome-

ter, which measures the magnetic flux in three dimensions.

In the ideal case, with no magnetic fields except the earth’s

magnetic field, a projection of the 3-D flux vector into a

plane parallel to earth surface delivers the direction of current

magnetic north. The azimuth is the angle between magnetic

north and the arbitrary defined reference axis of the mobile

phone.

Clearly, in a realworld scenario, the measured magnetic flux,

and with it the estimated azimuth, is influenced by multiple,

distorting magnetic fields. Generally, we observed stronger

distortions for measurements in MOTs like trains, buses and

cars, then for pedestrians. This is due to the multiple artificial

electromagnetic fields, which superimpose the earth magnetic

field. However, while there are typically less magnetic distor-

tions for pedestrians, in this case the measured azimuth suffers

from stronger impact of the vibrations due to the walking

motion. This can be seen as a constantly moving reference

axis for the azimuth computation.

0 200 400 600 800 1000 12000

50

100

150

200

250

300

350

400

Samples

Azim

uth

[d

eg

]

Raw Measurement

After Median FilterAfter Median Filter

& Line SimplificationReference

Fig. 2: Pre-processing of measured azimuth trajectory from a

pedestrian (Sampling frequency 1Hz).

Two types of filters are used to reduce the noise impairment:

• First a median filter is used to remove outliers, while pre-

serving direction changes, in the measured raw azimuth

values ϕt. Assume a sliding window of sorted samples

ϕt+n of length N (n = 1 . . . N ), then the median ϕ′t for

this window is computed by

ϕ′t =

{

ϕt+ν+1 if N = 2ν + 1,

0.5(ϕt+ν + ϕt+ν+1) if N = 2ν.(1)

• In order to further reduce the complexity of the measured

azimuth trajectory and to extract only stronger direction

changes, a line simplification [8] is applied to the median

filtered signal ϕ′t. The line simplification is an iterative

method, which iterates until a specified tolerance ∆threshold is fulfilled, i.e. it removes direction changes

≤ ∆.

To illustrate the effect of both filters, Fig. 2 shows a raw

azimuth measurement in degrees sampled with 1Hz, along

with a reference azimuth constructed from a combination of

the tracked GPS path and map data. The median filter window

length is set to N = 40 samples and the tolerance threshold

for line simplification is set to ∆ = 5◦. The result of both

filters can be clearly observed, i.e. outliers are removed by

the median filter, while consecutive application of the line

simplification removes direction changes smaller than ∆.

B. State Classification

In order to link the measured azimuth trajectory to a

physical movement and thus use it for map matching, it

has to be scaled with the current velocity of the user. More

specifically, we first have to decide,

• if an azimuth change stems from a real physical move-

ment of the user, or

• if it just stems from manual movements of the phone,

while the user stays at the same place.

72

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0 200 400 600 800 1000 120050

100

150

200

250

300

350

400

Samples

Sca

led

Azim

uth

[d

eg

]

Measurement scaled by v=1.0 m/s

Measurement scaled by v=1.4 m/s

Measurement scaled by v=1.8 m/s

Reference (v=1.4 m/s)

Fig. 3: Measured, filtered azimuth trajectory, scaled with

different pedestrian velocities.

In the second case, the azimuth bears no information that can

be used for localization, such that the measured data cannot

be further processed. If we decide for the first case, then the

azimuth changes reflect the movements of the user and the

measured data can be further utilized. We refer to the first

case as traveling-state and to the second as halt-state.

If deciding for the traveling-state, the next step is to scale

a length L window ϕ′(i) of the time dependent data with the

current velocity, i.e. make ϕ′(i) a function of distance instead

of time. The resulting scaled azimuth trajectory a(i) can then

be correlated with candidate trajectories generated from the

map data in order to find a possible matching route.

However, like the information about traveling- or halt-state,

the moving velocity is generally not known inside the mobile

phone. Therefore, we further differentiate the traveling-state

by also considering the current MOT. By associating each class

of MOT with a set of J typical velocities v(j)(i) ∈ V(i), a

set A(i) of possible distance dependent azimuth trajectories

a(j)(i) ∈ A(i) is generated by scaling ϕ

′(i) with all possible

velocities of the corresponding MOT. Note that the velocity

is assumed to be constant inside a window. Thus the number

L of samples per window has to be selected small enough so

that the assumption of a constant velocity is reasonable.

To differentiate between halt- or traveling-state, and further

classify the latter into different MOT, data from an additional

sensor is used. This sensor is the built-in acceleration sensor:

As described in detail in [1], the measured acceleration data

can be used to classify the current MOT of the user by

exploiting the characteristic acceleration patterns that emerge

from different MOTs. At the same time the approach reveals if

the user is in traveling- or halt-state by comparing acceleration

measurements against predefined thresholds.

In the current realization, the MOT classification is based on

the following three classes: car, train and pedestrian. Reason-

able velocities are associated with each class. For example, for

the pedestrian class, reasonable velocity values could be 1m/s,

1.4m/s, and 1.8m/s. Fig. 3 shows the candidate trajectories

Fig. 4: Street map data and corresponding tree representation.

a(1)(i), a

(2)(i), a(3)(i), which result from scaling a measured

azimuth trajectory ϕ′(i) with these three scaling factors. The

reference velocity is 1.4m/s in this case, such that a strong

correlation of a(2)(i) with the reference can be observed.

It might seem odd that instead of directly using the accel-

eration sensor for estimating the velocity, we suggest to use

the described pattern matching approach. It however turns out

that the acceleration measurements from the built-in sensor are

very coarse, and much more affected by ”local“ movements

(vibrations and manual turns) than by ”global“ movements

(movements related to the traveling route). Given this point of

view, the resulting data cannot be treated like data stemming

from a classical inertial measurement unit.

C. Candidate Generation

In order to determine a possible location and route, the

scaled trajectories a(j)(i) have to be correlated with candidate

trajectories c(m)(i) generated from vectorized street map data.

A very simple representation of street map data is shown

in Fig. 4 on the right: The representation is basically an

undirected graph, consisting of vertices, which are connected

by edges. Vertices can either be shape vertices or junction

vertices and edges represent linear street segments. Shape

vertices determine the shape of a sequence of street segments,

junction vertices define the topological relation of the street

network. In this work, the OpenStreetMap project [9] has been

used as digital map provider – a subset of its data structure,

consisting of nodes and ways, directly relates to the structure

shown in Fig. 4.

To extract candidate trajectories c(m)(i), a tree represen-

tation is used, as illustrated in Fig. 4 on the left. A tree is

constructed by first selecting a starting vertex as root, which

may be a shape or a junction vertex in the map representation.

This vertex is supposed to be the geographical starting point of

the current measurement window (cf. Sec. II-D). Starting from

the root vertex, all possible street segments are parsed until

the respective next junction vertex. These junction vertices

73

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Fig. 5: Successive construction of search tree.

become the children of the root vertex. Starting from each of

the children, the map is further parsed for the respective next

junction vertices, which then form the next set of children.

The process is repeated for each of the children, while its

geographical distance to the root is smaller than a value

ℓmax(i). The value ℓmax(i) is defined as

ℓmax(i) = L · ∆t · maxj

v(j)(i), (2)

where ∆t is the sampling time. Thus ℓmax(i) describes the

maximum geographical length of the azimuth trajectories

a(j)(i). Note that the sequence of street segments between

two consecutive junction vertices transforms into one edge in

the tree representation.

After the tree has been constructed, every path from root

to each of the leafs represents a possible sequence of shape

vertices, i.e. a possible sequence of street segments with

length greater or equal ℓmax(i). Thus the candidate trajectories

c(m)(i) can be generated by parsing from root to each leaf and

by computing the azimuth changes based on the shape vertices,

that lie on this path.

Depending on ℓmax(i) and the density of the street network

in the considered region, the tree can become quite complex,

producing a large set of candidate trajectories c(m)(i). To

reduce the complexity the following constraints are employed

during the tree construction:

• Cycles The tree is constructed cycle-free, such that each

junction vertex can only appear once if tracing from root

to a leaf.

• Cell-ID The geographical expansion of the graph is

restricted to the coverage of the Base Transceiver Stations

(BTSs) the phone is connected to during the current

measurement window. The currently connected BTS is

easily identified by reading the current Cell-ID from the

GSM/UMTS baseband.

D. Correlation and Selection

The map matching process consists of successively gener-

ating candidate sets C(i) at each instant i, by constructing

consecutive tree representations based on the considered part

of the street network. As described in the previous section,

each tree is constructed by selecting a starting vertex as the

root. The root vertices at time instant i are determined by those

tree leafs from the previous instant i − 1, that correspond to

the B best candidate trajectories of C(i − 1).In the initial run (i = 0) of the algorithm, the correct starting

node is not known, such that a set of potential starting nodes

has to be selected in a different way. This could be realized

based on the combination of Cell-ID observations and other

reasoning (typical places visited by the user, e.g. home or

work place). Each of the potential starting nodes forms the

root vertex of a separate tree.

To clarify the procedure, it is illustrated in Fig. 5 in a

simplified manner: At instant i = 0, a root vertex is selected

and a tree is constructed. The root vertex has two children,

which again have two children each and form the leafs of

the tree. The distance from the four leafs to the root vertex

is therefore ≥ ℓmax(0). From the resulting four candidates

c(m)(0), in this example the B = 2 best ones are selected.

The leafs of these two candidates, marked in green in Fig.

5, are the root vertices of the two trees at i = 1. These trees

are constructed, resulting in 8 possible candidates c(m)(1) and

again the B = 2 best candidates are selected, which then form

the root vertices in the next step i = 2.

In order to select the B best candidates out of C(i), each

c(m)(i) ∈ C(i) has to be correlated with each a

(j)(i) ∈ A(i).At instant i, we use the correlation coefficient r(m,j)(i) to

define the similarity between a pair (c(m)(i),a(j)(i)):

r(m,j)(i) = Corr(

c(m)(i) − c(m)(i),a(j)(i) − a(j)(i)

)

, (3)

where a(j)(i) and c(m)(i) denote the mean of a(j)(i) and

c(m)(i), respectively. Thus, by actually correlating zero-mean

trajectories, the correlation becomes independent of the di-

rection of the measurement axis of the mobile phone. As

noted in Sec. I, this is important because the angle between

moving direction and direction of compass measurement axis

is generally not known and therefore no absolute, but only

a relative azimuth measurement is given. The scalar valued

function Corr(x,y) is defined as the maximum of the cross-

correlation of x and y, i.e.

Corr(x,y) = maxκ

1

K

K−1−|κ|∑

k=0

xkyk+κ, (4)

with K = min {length(x), length(y)}.

The value r(m,j)(i) represents the degree of similarity

between each of the M candidate trajectories c(m)(i) and

the azimuth measurement scaled with the J different velocity

components v(j)(i). The index j(m)best(i) of the most likely

velocity for each c(m)(i) can be found as

j(m)best(i) = arg max

jr(m,j)(i) for ∀m, (5)

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51.44

51.442

51.444

51.446

51.448

51.45

7.25 7.252 7.254 7.256 7.258 7.26 7.262 7.264

(a) Map representation i = 0. (b) Tree representation i = 0.

(c) Map representation i = 4. (d) Tree representation i = 4.

Fig. 6: Experimental result for azimuth based localization of a pedestrian at different instants i. Left column: Map representation

(magenta) and reference route (red dotted, only in Fig. a)). Right column: Tree representation. Blue and green segments denote

candidates c(m)(i) and the best candidate, respectively.

and the B best candidates c(m)best(i) are found by selecting the

B largest correlation values from

r(m,j)(i) s.t. j = j(m)best(i). (6)

As a result, there is a set of best candidates c(m)best(i) at

each instant i, and by selecting one of the c(m)best(i) and tracing

the tree up to i = 0, we get an estimate of a possible route

the user has taken. The parameter B is a design parameter,

which controls a trade-off between computational effort and

possibility of loosing the correct path. Detecting of the latter

is crucial, and can be realized during the tree expansion by

validating the locations of candidates with the current Cell-ID

measurement, as mentioned in the previous section.

III. EXPERIMENTAL RESULTS

In this section results of the localization approach based on

experimental data are presented. The azimuth measurements

have been collected by a pedestrian using a Nokia N97

smartphone and walking a route of about 1100m. Fig. 6

illustrates the tree construction and selection procedure by

showing the candidates trajectories (blue) in the tree (right)

and map (left) representation at different instants i of the

algorithm. The route taken by the person is marked by red

dots in the map representation in Fig. 6(a).

Note that in this example, we assume that the starting node

is known, such that there is only one tree constructed at

i = 0 with the root vertex matching the geographical starting

point of the route. In Fig. 6(a) and Fig. 6(b), the first instant

of the algorithm is shown. The tree is extended into three

possible directions from the starting node, which again divide

into multiple branches at the subsequent junctions. In the first

measurement period, the path is straight, such that a(j)(0) does

not contain any azimuth changes and the information is not

yet sufficient for a successful localization. Consequently, the

75

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(e) Map representation i = 9. (f) Tree representation i = 9.

Fig. 6: Experimental result for azimuth based localization of a pedestrian at different instants i (continued).

best candidate (green) does not match with the actual route.

At instant i = 4, the measured data contains a 90◦ azimuth

change, and the best of the candidates can be seen to match the

real route in Fig. 6(c). For the corresponding tree in Fig. 6(d),

it can be seen that due to the selection of the best candidates,

the number of branches in the upper part have been reduced.

This becomes more clear at instant i = 9, shown in Fig. 6(f),

where the upper part of the tree and with it the beginning part

of possible street segments in Fig. 6(e), has reduced to only

one branch. At both instants, the best candidate matches the

true route.

From the map representations in Figs. 6(a), 6(c) and 6(e)

it can also be observed that the candidate paths (blue street

segments) can have a greater physical length than the actual

measurement period. This is due to the fact that the different

velocities are used while scaling the measured azimuth, as

described in Sec. II-B. Scaling ϕ′(i) with a velocity that is

too high can therefore lead to candidates, that are too long.

IV. CONCLUSIONS

In this paper a concept for localization and route estimation

of mobile phones based on measured azimuth values has

been described. The concept is based on generating candi-

date azimuth trajectories from a tree representation of street

map data, and correlating them with scaled versions of the

measured azimuth trajectory. The scaling factors are selected

based on the current MOT, which is estimated by applying

pattern recognition to the data obtained from the acceleration

sensor as described in [1]. To reduce the computational effort

of the tree construction and correlation, instead of applying

the computations to one large growing tree, smaller trees

are successively constructed and appended to each other. The

approach essentially resembles the well known M -algorithm

[10] for breadth-first tree search.

In practical tests, the concept can successfully deliver route

estimates, if there is sufficient knowledge of the starting

point or region of the measurement and if proper azimuth

measurements are given. Especially the latter turned out as a

critical part in practice: Depending on the MOT, the quality

of the azimuth measurement can be heavily degraded – while

azimuth measurements carried out by pedestrians can deliver

good quality in many cases, measurements carried out in

vehicles often turn out as strongly distorted due to the presence

of various superimposed magnetic fields.

Rather than considering the proposed concept as a stan-

dalone localization technology, it could also be analyzed as

a supporting technology for localization approaches based on

cellular measurements.

ACKNOWLEDGMENT

Copyright of the underlying street map data for Figs. 6(a),

6(c), and 6(e) is by OpenStreetMap contributors, CC-BY-SA.

REFERENCES

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[3] J. Geldmacher, J. Gotze, and E. Coersmeier, “Application and perfor-mance of joint cooperative cell-id localization and robust map matching,”in EUSIPCO-2010, Aalborg, Denmark, 2010.

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