INDOOR LOCATION USING WIRELESS NETWORKS

BASED ON BAYESIAN REASONING

Jes

us F. Rodr

ıguez-Arag

on, Vidal Moreno Rodilla, Bel

en Curto Diego

Fco. Javier Serrano Rodr

ıguez, Ra

ul Alves Santos and M. Jos

e Polo Mart

ın

Computer Science and Automatic Department, University of Salamanca, Pza. Los Ca

ıdos S/N, Salamanca, Spain

Keywords:

Indoor location sensing, Bayesian networks, Positioning algorithm, Wiﬁ location.

Abstract:

This paper describes a solution for the indoor location in the context of wireless local networks. Firstly, the

processes of sampling and training are done by off-line scene analysis. Secondly, the mobile entity can be

localized in a self-positioning fashion according to the Bayesian Network based method.

1 INTRODUCTION

At present, indoor location systems have created ex-

pectations in certain environments. To mention some

examples, we make reference to locating people in

hospitals or nursing homes (both medical staff and pa-

tients), locating products in a warehouse or guidance

systems in museums (Segvic et al., 2009). The over-

whelming growth of the use of wireless technology in

recent years has been due mainly to the appearance of

low cost products on the market that let us create an

indoor wireless network easily. Almost every public

building has a wireless network that can be used as

the basis of a tracking system.

Wireless location techniques can be classiﬁed ac-

cording to the method used for signal measurements:

Time of Arrival (TOA), Angle of Arrival (AOA) and

Received Signal Strength (RSS) (Liu et al., 2007;

Kanaan and Pahlavan, 2005).

The ﬁrst of the three techniques has been the most

investigated up to date. However, problems are still

unsolved due to the difﬁculties of predicting the signal

propagation indoors. This same happens with AOA,

since AOA is based on TDOA (Time Difference of

Arrival) which also depends on the signal propaga-

tion. Radio propagation suffers from multipath effect

(Alavi and Pahlavan, 2003). The method described

in the present paper is found among the ones that

use RSS to calculate current position based on a prior

scene analysis, since RSS method doesn’t depends on

multipath effect.

This work focuses on developing a self-

positioning indoor location algorithm based on

the ratio of RSS loss/position from different visible

access points (AP) in a speciﬁc area. In the present

case, the environment is a public building with a

wireless network structure, so that issuers (Wiﬁ

access points) already exist, i.e. it’s not necessary to

build a new infrastructure, and the detector (simple

or multiple devices with a wireless network card) is

the one that moves on the environment.

Each position has a range of possible signal

strength losses of near visible APs. Using statistical

techniques (Ladd et al., 2004; Wang et al., 2003), we

can infer a number of possible positions from a mea-

surement of signal strength loss of visible APs. The

more APs providing information, the greater reliabil-

ity of the prediction will be achieved.

In this sense, we make a proposal for uncertainty

treatment similar to (Ladd et al., 2004). In order to

improve the accuracy of the algorithm, we perform

several data processing prior to infer a possible result.

Each of the processes composing the indoor loca-

tion system based on wireless networks is described

in this paper. Firstly, the sampling method is detailed

and then the training and location processes are de-

ﬁned. Finally, a detailed description of the particular

implementation of the algorithm is shown, as well as

the results obtained.

2 WLAN IEEE 802.11

STRUCTURE

An 802.11 WLAN is based on a cellular architecture

(the system is subdivided into cells). Each cell, called

107

F. RodrÃ guez-AragÃ¸sn J., Moreno Rodilla V., Curto Diego B., Javier Serrano RodrÃ guez F., Alves Santos R. and JosÃl’ Polo MartÃ n M.

INDOOR LOCATION USING WIRELESS NETWORKS BASED ON BAYESIAN REASONING.

DOI: 10.5220/0002808001070112

In Proceedings of the 6th International Conference on Web Information Systems and Technology (WEBIST 2010), page

ISBN: 978-989-674-025-2

BSS (Basic Service Set), is controlled by a base sta-

tion, called AP (Access Point). An 802.11 WLAN can

be composed of a single AP, and therefore, for a sin-

gle cell.

The whole interconnected WLAN, including the

different cells with their respective APs, is considered

as a 802 single network by the upper levels of the OSI

model, and it is called ESS (Extended Service Set).

Beacon frames are one of the management frames

in the 802.11 standard. An access point periodically

sends a Beacon frame to broadcast its presence and

network information to the client stations in its envi-

ronment. Stations can get a list of available access

points looking for Beacon frames continuously in all

802.11 channels. Beacon frames contain the neces-

sary information to identify network characteristics

and to be able to connect to the desired access point.

Some of the ﬁelds contained are: AP MAC address,

SSID (Service Set IDentiﬁer), RSSI (Received Signal

Strenght Indicator), supported rates, timestamp (used

in synchronization), etc.

3 BAYESIAN NETWORKS

Classical inference models avoid considering any a

priori information. However, in certain occasions the

use of a priori knowledge can be a very useful contri-

bution to the process of inference. Models including

a priori information are based on the Bayes Theorem

(Equation 1).

P(H

E, c) =

P(H

c ) ·P(E

H, c)

P(E

(1)

where P(H

E, c ) is the probability that an hy-

pothesis H is fulﬁlled after considering the effect of

evidence E in the context c (a posteriori probabil-

ity); P(H

c ) is the probability that an hypothesis H

is fulﬁlled in an isolated context c (a priori probabil-

ity); P(E

H, c ) is the probability of occurrence of evi-

dence E assuming the hypothesis H as true in the con-

text c (conditional probability); P(E

c ) indicates the

probability of occurrence of evidence E in the context

In our case, the hypothesis H is being in a partic-

ular cell; the evidence E is the current measurement;

and the context c is the path previously done until the

current measurement is taken and it provides informa-

tion on the following possible positions.

All these are conditional probabilities, i.e., they

specify the reliability of an hypothesis based on the

assumption that some other initial hypothesis be true.

Therefore, theory makes no sense if there are no a

priori values of previous probabilities.

Signal strength values received from different vis-

ible APs are the main data source in this work. A sig-

nal strength value is linked to the position where the

measurement has been obtained. Therefore, a poste-

riori probability is the probability of receiving a par-

ticular signal strength value for an AP conditioned on

being at a particular cell.

4 SCENE ANALYSIS

In this work, we consider three main processes

throughout the workﬂow for the location method:

sampling, training and location as shown in Figure 1.

During the sampling and the training process, an of-

ﬂine scene analysis is performed, and during location

process, the mobile receptor is online localized from

a particular measurement.

Figure 1: Location Workﬂow.

4.1 Signal Strength Map Creation

Initially, the sample area is represented by a grid map

which is discretized into cells. Each position is iden-

tiﬁed by three values: (x, y, θ), where (x, y) are planar

spatial coordinates of the cell and θ is the orientation

with which the sample has been taken. Figure 2 shows

graphically these three values. Signal strength of ev-

ery visible AP is measured in each cell.

Figure 2: Sampling area.

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108

Information about the different visible APs in the

sampling area is collected and a study in order to re-

move those APs that provide unusefull information is

performed.

Unlike (Ladd et al., 2004), sub-sampling is per-

formed at lower resolution for each cell, i.e., the cell

is divided into 9 possible positions in order to have a

more complete probabilities distribution. Thus, mea-

surements are taken at the center of the cell and they

are also taken away from the center (in two conﬁgu-

rations, × or +, as shown in Figure 3).

Figure 3: Possible sub-sampling conﬁgurations.

Therefore, the sampling process consists of sets

of 10 measurements with × conﬁguration and others

with + conﬁguration. These sets of measurements are

performed with the greatest possible randomness, tak-

ing place at different times in a day in order to com-

pensate variations in the environment that may occur,

as the difference of network users, greater number of

obstacles in the measurements (due to more people

walking through corridors, etc). Each of the sets are

stored in a data structure for each position, in which

the visible APs and measures (central and unfocused)

are speciﬁed.

4.2 Generating an Heuristic Matrix

The analysis of the scene also includes the calculation

of an heuristic in order to take into account the prob-

ability evolution depending on distance between two

positions A and B. If position B is far away from po-

sition A, the probability of moving from one position

to another will be less than if position B is adjacent to

position A.

To deﬁne the evolution of probability depending

on the distance between two positions, an exponen-

tial function is used, since the probability of moving

from one position to another decreases exponentially

depending on the distance traveled (Equation 2)

P = e

−λd

(2)

where d is the distance between positions. For

determining the distance between two positions, we

consider the number of cells of separation plus the

number of changes in direction. λ is a constant that re-

ﬂects the importance of distance between positions in

the heuristic. When d > 6, we consider the probabil-

ity is zero. The heuristic is implemented by a square

matrix of dimensions D × D, where D is the number

of locations in the sampling area.

4.3 Training Process

Once all the measurements have been completed,

there is a set of values of signal strength for each of

the visible access points at each cell. The probability

of being in a cell is conditioned to the signal strength

measurement of an AP. For each AP in each cell con-

ditional probabilities are calculated using

p =

(3)

where L

is the number of samples of a same sig-

nal strength value, and N is the number of total sam-

ples.

Figure 4: Grouping of probabilities.

To prevent the frequencies of certain signal

strength values are zero around the maximum fre-

quency zone, ranges for the evidences are deﬁned.

Each group contains n probabilities of signal strength

values (Figure 4).

5 LOCATION

The schema of the location algorithm used is shown

in Figure 5.

The location algorithm calculates an estimated po-

sition of the receiver agent from a vector R of signal

strength measures that contains a measure for each of

the visible APs taken in an unknown position.

R =

, R

, . . . , R

(4)

INDOOR LOCATION USING WIRELESS NETWORKS BASED ON BAYESIAN REASONING

109

Figure 5: Schema of the Location Algorithm.

5.1 Calculating the Conditional

Probabilities Vector

From the measures vector, we now proceed to calcu-

late the conditional probabilities vector, CPV, which

represents the location probability for each cell. This

vector has as many components as cells considered.

Each component of CPV is calculated by the follow-

ing expression shown in Equation 5.

CPV

∏

i=1

(AP

, R

) (5)

where AP

refers to the ith AP; R

is the current re-

ceived signal strength from AP

; and P

(AP

, R

) is the

probability of receiving the signal strength R

from

while being at the jth cell. This probability is

found in the Bayesian network obtained during train-

ing process.

Once CPV is calculated, we can infer the current

position based on the cell with the greatest probability

within the vector. However, it is possible to process

the data in order to obtain a more reliable result, incor-

porating the neighborhood function. What is sought is

to select the candidate cell using a criterion different

from only maximum probability. The new criterion

takes into account that candidate cells will be found

in those areas having a higher accumulated probabil-

ity.

There were cases where the cell with the highest

probability was most likely without context, i.e., there

are more or less contiguous cells whose probability is

high, but on the other hand, there is an isolated and

remote in distance cell whose probability is the high-

Figure 6: Neighborhood error.

est. Noting Figure 6, it suggests that the isolated cell

is surely not the candidate cell.

5.2 Calculating the Neighboring

Probabilities Vector

To avoid such errors, we recalculate the entire vec-

tor of conditional probabilities, inﬂuencing the prob-

ability of a cell with the probability of adjacent cells.

Thus, the new vector, called neighboring probabilities

vector, NPV, is calculated by Equation 6.

NPV

= αCPV

i−1

+ βCPV

+ αCPV

i+1

(6)

where NPV

is the ith component of the neigh-

boring probabilities vector, i.e., the probability

of the ith cell of being the current position;

CPV

i−1

,CPV

i+1

are the conditional probabili-

ties of the immediately preceding, current and imme-

diately following cells, respectively; and α and β are

weighting constants. Figure 7 shows the neighboring

probabilities vector for the example shown in Figure

Figure 7: Neighboring Probabilities Vector.

Current position may again be inferred from this

new vector. However, we apply an heuristic to obtain

a more reliable result.

5.3 Calculating the a Priori

Probabilities Vector

An a priori Probabilities Vector, PrPV, is generated

with as many components as possible cells. Each

component represents the probability of that cell be-

ing the candidate cell. In short, PrPV provides a pre-

diction of the ﬁnal result. This vector is updated each

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110

run. On the ﬁrst run, all components have the same

value,

, where S is the number of cells of the sam-

ple area. This means that the initial prediction is the

same for all cells in the sample space. This is logical

because there is no prior information.

5.4 Calculating the a Posteriori

Probabilities Vector

The vector from which the ﬁnal results are calculated

is the a posteriori Probabilities Vector, PoPV, that

is calculated from Neighboring Probabilities Vector,

NPV, and a priori Probabilities Vector, PrPV, using

the Equation 7.

PoPV

NPV

· PrPV

∑

i=1

NPV

· PrPV

(7)

where PoPV

is the jth component of the a pos-

teriori probabilities vector; NPV

is the jth compo-

nent of the neighboring probabilities vector; PrPV

the jth component of the a priori probabilities vec-

tor; S is the number of cells of the sample area; and

∑

i=1

NPV

·PrPV

is used in order to normalize the re-

sult.

Figure 8: A posteriori Probabilities Vector.

Current position is now inferred based on the cell

whose probability is the greatest (Figure 8).

5.5 Update the a Priori Probabilities

Vector

Having obtained the estimated cell, the algorithm has

to be prepared for the next execution. At this point,

current position is known and it provides heuristic in-

formation about the next possible cell, assuming the

continuity of the path. For that purpose, the heuristic

matrix generated during the training process is used.

This matrix provides information on the probability

of moving from one cell to another.

Dismissing discontinuities in the path, cells that

are found within a certain distance from current cell

may be removed from the set of possible candidate

cells. The update of the a priori probabilities vector

is performed using Equation 8.

PrPV

(t + 1) = H · PrPV

(t) (8)

where H is the heuristic matrix; PrPV

(t) is the ith

component of the current a priori probabilities vector;

and PrPV

(t + 1) is the ith component of the a priori

probabilities vector which is being calculated.

6 RESULTS

Using the wiﬁ network infrastructure available in the

Science Faculty of the University of Salamanca, the

sample area was situated on the second ﬂoor and is

compound by two perpendicular corridors and dis-

cretized in cells of 2.40m×2.40m. Cells are identiﬁed

with three values: (x, y, θ), as was shown in Figure 2.

Sample space is compound by 43 cells with 2 possible

orientations, and a central cell (located at the intersec-

tion of the two corridors) with 4 possible orientations.

Our experiments were conducted by a human op-

erator carrying a HP iPAQ H3850 with a PCMCIA

Compaq WL110 wireless Ethernet card. This particu-

lar card uses an Orinoco chipset. An Acer C500 PDA

with Windows Mobile 5.0 was also used in our exper-

iments. The access to the device was implemented in

C/C++ after performing a study of the Orinoco Linux

driver.

In our case, the number of visible APs used dur-

ing the training and location process was 24. A prior

study was done in order to remove APs that don’t pro-

vide relevant information.

Having established the visible APs, we started

with the sets of measurements. In this work, data used

to train the Bayesian network consist of 10 sets of 10

measurements each. These measurements were per-

formed at different times and on different days, so that

the presence of extraneous factors were reﬂected in

the data: in a college building, there are more people

in the morning than in the afternoon, there are some

rush hours between lectures, etc.

During the sampling process, measurements per-

formed away from the center of the cell have been in-

corporated in order to achieve a more accurate distri-

bution of the data. Proposed sub-sampling at a lower

resolution was reached by dividing each cell in differ-

ent positions as shown in Figure 3. Thus, 6 central

measurements and 4 unfocused measurements were

performed for each set. 5 sets, with 10 measurements

each, were taken with × conﬁguration and another 5,

with 10 measurements each, with + conﬁguration.

The heuristic matrix used in the location algorithm

is a matrix whose dimension is 90 × 90, since there

are 90 possible positions in our sample space. Rows

and columns are the different possible cells located

in the same order. The function used to generate the

heuristic matrix is deﬁned by Equation 2. In our case,

INDOOR LOCATION USING WIRELESS NETWORKS BASED ON BAYESIAN REASONING

111

using λ = 0.3, the results are satisfactory.

During the bayesian network training process, sig-

nal strengths values are grouped, so that conditional

probabilities are calculated in groups composed of 3

signal strengths values. Before calculating the loca-

tion from a particular measurement is necessary to

ﬁnd the group of that measurement.

In the location process, a data post-treatment has

been performed, as the usage of the neighborhood

function and the actual usage of the heuristic matrix

to update the a priori probabilities vector.

The neighborhood function used in our case is de-

ﬁned by Equation 6 taking as weighting factors α =

and β =

, so that neighboring probabilities vector is

deﬁned by Equation 9.

NPV

CPV

i−1

CPV

i+1

(9)

In order to check the accuracy of the proposed al-

gorithm, we take a testbed of 100 different paths. The

results improve considerably once traversed the ﬁrst

positions (5 - 6) of each path, when heuristic is being

taken into account. Testbed results provide an algo-

rithm accuracy close to 60%.

Figure 9 shows the implemented application dur-

ing the location process of a person carrying a PDA

and walking through the corridors.

Figure 9: Application during the location process.

7 CONCLUSIONS

Due to the included optimizations and, after analyzing

the results of the algorithm, that can be considered

efﬁcient for location with cells of 2.40m × 2.40m.

The sampling process is performed trying to in-

clude a more accurate data distribution, including

different cases to add more information into the

sampling. The location algorithm uses statistical

techniques and, therefore, during sampling process,

fullest possible information must be collected. Com-

pared with the method proposed in (Ladd et al.,

2004), data processing has been performed in order

to achieve a better effectiveness for the position in-

ference. Heuristic information is used, assuming that

movements are continuous and great distance move-

ments between two measurements are not real. Cur-

rent position provides information about the next fu-

ture position.

Working lines of research are open in the opti-

mization of the sampling process collecting more in-

formation about the nature of the measures: indepen-

dence of the environment, periodical behavior, etc.

so that the result is based not only in terms of sig-

nal strength loss/position, but adding new informa-

tion, date, time, temperature, etc. Improvements can

also be achieved in the location algorithm itself, with

heuristic optimizations, etc.

ACKNOWLEDGEMENTS

The work has been carried out within projects ﬁ-

nanced by the Junta de Castilla y Le

on SA030A − 07

and the Spanish Ministry of Science and Innovation

DPI2007 − 62267. The main author has also worked

under the support of a Junta de Castilla y Le

on fel-

lowship.

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