AN INDOOR LOCALIZATION ALGORITHM BASED IN WEIBULL

DISTRIBUTION AND BAYESIAN CLASSIFIER

S. Orozco-Ochoa, X. A. Vila-Sobrino, I. G

omez-Conde and M. J. Lado

Escola Superior de Enxe

ner

ıa Inform

atica, Universidade de Vigo, As lagoas S/N, 32004, Ourense, Spain

Keywords:

Bluetooth, Received Signal Strength, Indoor Positioning, Weibull, Bayes, RSS.

Abstract:

The location of objects and people by the use of Global Positioning System (GPS) or Global System for Mobile

Communications (GSM) network is increasingly used to provide location-based services. These technologies

work well outdoors and when the required accuracy is not very high, up to 10 meters. This paper describes

an algorithm for monitoring elderly people at home, by continuously taking its position, which uses the RSS

information exchanged between Bluetooth devices, Weibull distributions and Bayesian classiﬁers. This algo-

rithm has been validated in a real environment, an area of 13 × 12 meters, with several rooms and corridors,

where zones of approximately 6 square meters have been delimited. Our algorithm achieved a rate of correct

detections of 91.875%.

1 INTRODUCTION

Today’s highly technical society is continuously de-

manding more advanced and sophisticated services.

Communication networks are all pervasive: there are

more than 5000 million mobile phones and 2000 mil-

lion Internet connections all over the world. Until re-

cently, these networks essentially acted as ”commu-

nication” networks for voice or text (e-mail), but this

is rapidly changing.

”Location-based services”, that is, applications that

require the user’s current location to provide ser-

vices are also becoming increasingly popular. In fact,

some studies (Vaughan-Nichols, 2009) indicate that

in 2012, a percentage of 20% of the mobile services

will depend on the user’s location.

Nevertheless, how to get the people’s location?

Currently, the most common way is to use the mo-

bile telephone network itself, where the position and

power level from several antennas are known and,

by triangulation, it is possible to calculate the ap-

proximate location of the mobile device. The er-

ror is between 100 and 1000 meters, depending on

the distance among the antennas and the environment

(Nurmi et al., 2010). Recently, most mobile phones

incorporate a Global Positioning System (GPS) re-

ceiver. Appart from this, the scientiﬁc community has

started to publish location algorithms that mix data

from telephone antennas and satellites. Through such

enhancements, the mean error can be reduced to 50

meters (Fritsche and Klein, 2009).

Just as there is a growing trend towards ser-

vices for outdoor location, there is also an increas-

ing trend for indoor location services. These are cur-

rently poorly developed, among other reasons, be-

cause Global System for Mobile Communications

(GSM) and GPS tracking do not work indoors. There-

fore, new technical alternatives are required. The two

solutions most deployed are radiofrequency identiﬁ-

cation tags (RFID tags) and wireless transceivers.

In our group, we are interested in developing sys-

tems for monitoring elderly people at home. In partic-

ular, an important task would be the development of a

system capable of detecting not only alarm conditions

(falls or warnings from the user), but also anoma-

lous behavior or cognitive impairments by continu-

ously monitor the person at home. In order to do so,

we address this issue in two ways: tracking with in-

telligent video analysis (G

omez-Conde et al., 2011)

and localization via Bluetooth (Orozco-Ochoa et al.,

2011). In the current paper, we present an algorithm

which seeks to locate the ”zone” where the user is.

2 STATE OF THE ART

As it has been previously metioned, indoor localiza-

tion is not yet very extended. However, extense re-

search literature can be found. In particular, two re-

view refences can be cited: Liu (Liu et al., 2007), and

338

Orozco-Ochoa S., A. Vila-Sobrino X., Gómez-Conde I. and J. Lado M..

AN INDOOR LOCALIZATION ALGORITHM BASED IN WEIBULL DISTRIBUTION AND BAYESIAN CLASSIFIER.

DOI: 10.5220/0003742203380341

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 338-341

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Gu (Gu et al., 2009). There are other works that em-

ploy the Bluetooth’s RSS (Received Signal Strength)

parameter, and offer experimental data, as well as the

mean error. Some of these works will be now de-

scribed in chronological order.

Forno (Forno et al., 2005) used inquiries with dif-

ferent trasmission power. They experimented in un-

obstructed areas, without indoor walls. Hossain (Hos-

sain et al., 2007) presented a novel method, based on

calculating differences among RSS values. The ex-

perimental values (a mean error of 3.5 m) were again

obtained in a free-of-walls area. In a recent paper,

Aparicio (Aparicio et al., 2008) reached a mean er-

ror of 2.21 meters, employing a hybrid method, based

on wireless LAN and Bluetooth, and a 4-NN classi-

ﬁer. In this work, the experimental area was a com-

plex zone, including walls, rooms and corridors. In

2010, Pei (Pei et al., 2010) obtained a mean error of

5.1 meters by applying a Weibull distribution to the

RSS dataset, and using a Bayesian classiﬁer; however,

it must be taken into consideration that they only em-

ployed 3 access points for a quite extense area. In

fact, the methodology employed in this paper is based

in Pei’s work.

3 METHODOLOGY

3.1 Algorithm

The algorithm proposed in this paper belongs to

the category of the so-called ﬁngerprinting methods

based on the RSS parameter. It has a training phase

in which a set of ”inquiries” are performed at known

positions. The Bluetooth inquiry mechanism consists

of an inquirer that broadcasts inquiry packets to de-

vices in the neighborhood. A radio map is built with

all RSS values from the different Base Stations (BS)

that respond to the inquiry. Then, the radiomap is pro-

cessed in order to obtain a new feature map, where

each zone is identiﬁed with a particular feature vec-

tor. In the localization stage, data from inquiries in

an unknown area are processed for feature extraction

from the RSS values. Such features will be compared

with the feature map to determine which is the area

that best matches and then, infere the target location.

Training Stage

We will call the set of training data tr, and the valida-

tion or test set te. We also assume that the set of RSS

values taken in the training stage is collected in an ar-

ray, called Original Radio Map (ORM), where ORM

[i, j] would be a variable length vector containing all

RSSs surveyed at zone i from BS

Many obstacles in indoor spaces can either pre-

vent or hinder the propagation of waves, as well as

introduce wave reﬂection that cause a noisy signal

from reﬂected waves. These characteristics of in-

door spaces explain why indoor wave propagation is

much more complex than outdoor wave propagation

(Figueiras et al., 2005). In an attempt to mitigate pos-

sible side effects of these reﬂections, we have decided

to ﬁlter the ORM by removing the lowest values. The

resulting Filtered Radio Map (FRM) was built as fol-

lows:

FRM[i, j] =

{

ORM[i, j][l]|

ORM[i, j][l] >= Q

(ORM[i, j])

(1)

being Q

(x) the ﬁrst quartile of vector x.

For feature extraction we assume that each vector of

RSS values, i.e. each FRM[i,j] can be modeled by a

probability distribution function and therefore, sum-

marize its features by the parameters of the distribu-

tion. In our case we use a Weibull distribution func-

tion for the modeling since this distribution models

this type of radio wave propagation better than the

normal distribution function (Pei et al., 2010). The

Weibull distribution has two parameters, scale (λ) and

shape (k), and is given by the following expression:

g(x;k, λ) =

(

)

k−1

−(

)

(2)

After this step we have a new array, the Weibull Ra-

dio Map (WRM), in which WRM[i,j] contains the k

and λ parameters of the Weibull probability distribu-

tion function that best models the set of values from

??FRM[i,j], i.e: W RM[i, j] = (k

i j

, λ

i j

). This matrix

has the features that model our radio map and that

will be used in the localization process.

Localization Stage

For the localization of the mobile device after the

training stage, we use data from an inquiry launched

from the mobile device. To begin with, the data col-

lection is preprocessed just as in training stage, i.e.:

• All RSS values are stored ??in a vector, denoted

te, where te[ j] is the set of values ??measured

from the BS j.

• Elimination of the lowest RSS values in order to

have the ﬁltered test set (tef ).

Following is the classiﬁcation step, which is based on

Bayesian inference:

• First, an RSS value is selected at random from

each vector tef [j], i.e. tef [ j][l

• RSSs are assumed to have a Weibull distribution;

AN INDOOR LOCALIZATION ALGORITHM BASED IN WEIBULL DISTRIBUTION AND BAYESIAN

CLASSIFIER

339

therefore, in order to get the probability value of

the tef [ j][l

], given a zone (z

), we perform:

P(te f [ j][l

] | z

) = g(te f [ j][l

]; k

, λ

) (3)

• The joint probability for tef is calculated as:

P(te f | z

) =

∏

j=1

P(te f [ j][l

] | z

) (4)

where N

is the number of base stations.

• The highest probability value obtained determines

the z

target zone.

The last step is the voting process, which is the repe-

tition of the above steps t times. As a result, a number

t of target zones are obtained, and the one with the

highest number votes is selected as the deﬁnite target

zone.

3.2 Experimental Setup

The experimental testbed is located in a private house.

Its dimensions are 13 × 12 meters, and it includes

rooms and corridors. Each room is divided in zones

of approximately 6 square meters. There are 20 zones,

denoted by z

, and labelled as shown in Figure 1.

l1 l2

bs4

bs1

bs3

bs2

Bluetooth base station

1 m

Figure 1: Map of the experimental area.

We placed 4 ﬁxed Bluetooth transceivers attached

to personal computers, they are the Base Stations

(BS), denoted by bs

. All BSs are running Windows

XP except for bs

which runs on Unbuntu 10.04.

For data acquisition, an Acer Aspire 1 laptop with

a plugged Bluetooth 2.0 EDR receiver was used. The

laptop was in Bluetooth ”inquiry mode”, transmitting

a discovery packet every 11 seconds, while BSs are

set to ”discoverable” responding to these packets with

their identiﬁcation (MAC Address) and RSS informa-

tion. To obtain the RSS information from the Linux

Bluetooth protocol stack (BlueZ 4.60), a python pro-

gram was executed in the laptop. In order to build

the radio map, 60 inquiries per zone were launched.

The total time for surveying each zone was around 10

minutes. The number of inquiries required to survey

the area of interest was 1200.

The R

statistical software package was used for

the calculations. All RSS values obtained (65010)

were stored in a 20 × 4 matrix, the ORM, kept in

the R environment. The tr data set was the base for

the ORM, we will explain later how these tr and te

sets were obtained from the 1200 inquiries. From

the ORM map the FRM was obtained. The FRM

was modeled by the Weibull distribution, by using the

Surv and survreg functions of the R survival package,

that provides methods for survival analysis. Based on

those functions we calculated the parameters λ, k that

deﬁne a Weibull distribution for each vector FRM[i,j].

Validation

We decided to develop a 4-cross validation model. In

order to do this task, the data set was divided into:

3/4ths of the data for the tr set and the remaining 1/4th

for the te set. This was done 4 times changing the

1/4th te part.

Since our goal is to identify the zone based in a

single inquiry (which takes about 11 s), the whole te

set was not used, only data corresponding to a ran-

domly selected inquiry.

From the ﬁltered te set, the tef is got. Then the

classiﬁcation is done and the whole process was re-

peated 20 times. A ﬁnal voting was done in to order

obtain the predicted zone. Again, the whole process

was repeated 4 times (classiﬁcation and voting).

4 RESULTS AND DISCUSSION

A summary of results is shown in Table 1. The second

column has the correct classiﬁcation per cross valida-

tion, the 3rd column gives the correct classiﬁcation in

terms of room (all zones belonging to the same room),

the last column is the mean error in terms of distance.

The last row has the columns’ mean values.

We can see that errors are in very speciﬁc areas.

Most of them are in c1 and n2, which are both close to

a BS. Our hypothesis is that in the areas nearby a BS,

the signal is so strong that many waves are reﬂected.

These waves were received by the mobile device and

they were not removed by the threshold.

The average percentage of correct classiﬁcation

The R Ofﬁcial page, http://cran.r-project.org/

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

340

Table 1: Summary of the 4-cross validation.

Cross Hits Room level Mean error

validation (%) (%) (m)

1st 88.75 92.50 0.77

2nd 86.25 100.00 0.79

3rd 97.50 100.00 0.71

4th 95.00 95.00 0.73

Mean 91.875 96.875 0.75

Table 2: Number of misclassiﬁcations by zone.

Cross- Cross- Cross- Cross-

Zone valid. 1 valid. 2 valid. 3 valid. 4 Total

c1 3 4 2 - 9

c3 - 1 - - 1

l1 2 - - - 2

n2 4 4 - 4 12

s1 - 2 - - 2

is 91.875% for the 4-cross validations, as shown in

Table 1.

Following the method for the mean error calcula-

tion developed by us in previous work (Orozco-Ochoa

et al., 2011) and based on the results from Table 2, an

average error of 0.75 meter was obtained. The mean

error is below other researchers’ mean error, which is

also around 2 meters, as has been shown in section 2.

5 CONCLUSIONS AND FUTURE

WORK

This paper describes an algorithm suitable for indoor

location based on a Bayesian classiﬁer and Weibull

distribution. The results are very promising, better

than those of the literature.

This method would allow the monitoring of el-

derly people at home, not only the room where the

person is at each moment, but also the area within the

room where the person is. In this way, we can try

to identify the actions he is performing (sitting on the

couch, standing by the window, etc). We plan to study

the problem detected in areas close to a BS. A possi-

ble ﬁx may be changing the type of ﬁlter used for re-

moving the reﬂected waves. Eventually, we will work

on the integration of our algorithm with multisenso-

rial and intelligent monitoring system: a system that

includes the use of video cameras and other sensors.

ACKNOWLEDGEMENTS

This work was supported by the Xunta de Galicia un-

der grant 08SIN002206PR.

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