FUZZY TOPOGRAPHIC MODELING IN WIRELESS SIGNAL

TRACKING ANALYSIS

Eddie C. L. Chan, George Baciu and S. C. Mak

The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Keywords: Wireless signal tracking, Topographic Mapping, Received Signal Strength, Fuzzy Logic.

Abstract: Fuzzy logic modelling can be applied to evaluate the behaviour of Wireless Local Area Networks (WLAN)

received signal strength (RSS). The behavior study of WLAN signal strength is a pivotal part of WLAN

tracking analysis. Previous analytical model has not been addressed effectively for analyzing how the

WLAN infrastructure affected the accuracy of tracking. In this paper, we propose a novel fuzzy spatio-

temporal topographic model. We implemented the proposed model with a large (9.34 hectare), built-up

university, over 2,000 access points to survey and collect WLAN received signal strength (RSS). We

applied the Nelder-Mead (NM) method to simplify our previous work on fuzzy color map into a

topographic (line-based) map. The new model can provide a detail and quantitative strong representation of

WLAN RSS. Finally, it serves as a quicker reference and efficient analysis tool for improving the design of

WLAN infrastructure.

1 INTRODUCTION

Wireless Local Area Networks (WLAN) tracking

analysis is a crucial part for deploying the efficient

indoor positioning system. The analytical models

can be used to visualize the distribution of signal and

help to improve the design of positioning systems,

for example by eliminating installation of WLAN

access points (APs) and shortening the sampling

time of WLAN received signal strength (RSS) in

location estimation. The most typical techniques for

locating WLAN enabled device are location-

fingerprinting-based (LF-based). LF based method

(Taheri et al., 2004)(J. Kwon et al., 2004)(K.

Kaemarungsi and P. Krishnamurthy, 2004)(B. Li et

al., 2005) locate a device by accessing a training

database containing the location fingerprint to

estimate the location. Location fingerprint (LF) is a

set of the RSSs and coordinates in a region.

Recent research on WLAN RSS analytical

model (K. Kaemarungsi and P. Krishnamurthy, 2004)

and (N. Swangmuang and P. Krishnamurthy, 2008)

are based on the accuracy of positioning systems and

proximity graphs, such as Voronoi diagram,

clustering graph. They assume the distribution of the

RSS is in Gaussian and pair wise. Some research

works (N. Swangmuang and P. Krishnamurthy,

2008), (M. B. Kjaergaard and C. V. Munk, 2008),

and (S. Fang et al., 2008) ignores the radio signal

properties. Such assumptions may ignore or distort

the real behavior of RSS and provides inadequate

and inaccurate RSS analysis. The fuzzy visualization

map concepts widely applied in other fields, such as

temperature, rainfall and atmosphere. Topographic

mapping has been also highly recognized as a

comprehensive method to visualize geographical

information, such as the reflectance of slope and

terrain. NM method also is used in many other fields

such as data mining (S. Satapathy et al., 2007) and

antenna optimization (B. Kolundzija and D. Olcan,

2003). Fuzzy, topographic and NM modelling could

well be applied to modelling in WLAN RSS

analytical model.

In this paper, we propose a novel analytical

model that provides a visualization of the RSS

distribution. We make use of the Nelder-Mead (NM)

method to simplify our pervious works on the multi-

layer fuzzy color model (C. L. Chan et al., 2008) to

topographic (line-based) model. We develop a

topographic model as analytical tools for evaluating

and visualizing where the RSS is denser and

clustering different RSS in different topographic

level. The proposed model offers two benefits. First,

it serves as a quicker reference and efficient analysis

tool. Second, it can provide a detail and quantitative

strong representation of WLAN RSS.

Chan E., Baciu G. and Mak S. (2009).

FUZZY TOPOGRAPHIC MODELING IN WIRELESS SIGNAL TRACKING ANALYSIS.

In Proceedings of the International Joint Conference on Computational Intelligence, pages 17-24

DOI: 10.5220/0002312700170024

 SciTePress

The rest of this paper is organized as follows:

Section 2 presents the topographic model design.

Section 3 presents the experimental setup of large

scale site RSS surveying in 9.34 hectare campus area

over 2,000 access points. Section 4 discusses the

analysis result of obstacles, human bodies and

WLAN APs location. Finally, Sections 5 offers our

conclusion and future work.

2 TOPOGRAPHIC MODEL

DESIGN

The basic idea of topographic model is to plot a

curve connecting minimum points where the

function has a same particular RSS value. The sets

of APs are known as topographic line nodes.

Topographic line nodes are the APs residing on the

topographic lines around contour region. In this

section, we introduce the major operations of

topographic model including propagation-based

algorithm, fuzzy membership function in our

previous work (C. L. Chan et al., 2008), topographic

line node measurement, Nelder-Mead method and

topographic model generation.

2.1 Propagation-based Algorithm

The propagation-based algorithm (K. Kaemarungsi

and P. Krishnamurthy, 2004) which is used to

calculate the RSS as follows:

wallLossddrdr

kikii

−−= )(log10)()(

,1000,

(1)

where

{

}

dddD ℜ∈= |...

is a set of

locations, R =

{

}

rrr ℜ∈|...

is a set of sampling

LF vector respect to known d

, α is the path loss

exponent (clutter density factor) and wallLoss is the

sum of the losses introduced by each wall on the line

segment drawn at Euclidean distance d

i,k

2.2 Fuzzy Membership Function

In this subsection, our fuzzy membership function

has been published in (C. L. Chan et al., 2008) and

we will make use of it. Nonetheless, for

completeness in the following we briefly describe.

Using fuzzy logic, the proposed model offers an

enhanced LF hyperbolic solution that maps the RSS

from a 0 to 1 fuzzy membership function. Instead of

using a numeric value, the fuzzy logic determines

the RSS as “strong”, “normal” and “weak”.

Figure 1: The RSS fuzzy membership graph.

The normalization distribution is used to represent

the fuzzy membership functions.

)(

μα

πσ

−

= exP

where p(x) is the probability function, x is the

normalized RSS, σ is the standard deviation of

normalized signal normalized strength in a region, μ

is the mean of signal strength in a region. The

WLAN network is fully covered for the whole

campus.

The membership function of term set,

μ(RSSDensity) = {Red, Green,Blue}. Red means the

signal strength density is high, green means the

signal strength is medium and blue means the signal

strength density is low. The fuzzy set interval of

blue is [0, 0.5], [0, 1] is green and [0.5, 1] is red.

For the blue region, σ = 0.5, μ = 0.

()

00.5

Blue

−

<< =

(2)

For the green region, we substitute, σ = 0.5, μ = 0.5.

()

Green

−−

<< =

(3)

For the red region, σ = 0.5, μ = 1.

()

0.5 1

−−

<< =

(4)

Figure 1shows the fuzzy membership function. X-

axis represents the normalized signal strength from 0

to 1 (from -93dBm to -15dBm). The width of

membership function depends on the standard

deviation of the RSS. The overlap area will be

indicated by mixed colors. We can use different

colored regions to represent the WLAN RSS

distribution. Conceptually we define a spatio-

temporal region as follows:

Assume that B is a finite set of RSS vector

belonging to a particular color region,

IJCCI 2009 - International Joint Conference on Computational Intelligence

where

{}

... |

Bbbb=∈ℜ, i.e.,

bS∈ , SR

∀

∈ ,

and

[

]

,Slu∀∈ , where l is the lower bound of fuzzy

interval and u is a upper bound of fuzzy interval. To

analyze the distribution surfaces S, there always

exists a spatio-temporal mapping,

SBq →:

∫

dSSbxhxq )()()(

(5)

where h(x) is the characteristic function of S, i.e.,

⎩

⎨

⎧

)(xh

∈

∉

(6a)

(6b)

and b(S) is a weight function that specifies a prior on

the distribution of surfaces S. We can explicitly

define b(S) by (1). By (2), (3), (4), (5) and (6), the

RSS distribution can be illustrated.

2.3 Topographic Node

Each topographic node consists of three components

and can be expressed as < l, d, g >, in which l

represents topographic level, d represents the

locations of WLAN received signal, g represents the

gradient direction of the RSS distribution. The

spatial data value distribution mapped into the (x, y, l)

space, where the co-ordinate (x, y) represents the

location and l = f(x, y) describes a function mapping

from (x, y) co-ordinates to level l. The gradient

vector g denotes the direction of RSS where to

degrade in the space. The gradient vector can be

calculated by:

()

yxfg

⎟

⎠

⎞

⎜

⎝

⎛

=−= ,,

(7)

2.4 Nelder-Mead Method

The Nelder-Mead (NM) method is a commonly used

nonlinear optimization algorithm for finding a local

minimum of a function of several variables has been

devised by Nelder and Mead (J. Mathews and K.

Fink, 1998). It is a numerical method for minimizing

an objective function in a many-dimensional space.

Instead of using (1) and (2), we estimate the location

by NM method.

First, we collect the location fingerprint, r with an

unknown location (x,y). We define f(n)=|n-r|, where n

is any location fingerprint. Second, we select three

location fingerprints (LFs) to be three vertices of a

triangle.

We initialize a triangle BGW and function f is to

be minimized. Vertices B, G, and W, where f(B) is

the smallest value (best vertex), f(G) is the medium

value (good vertex), and f(W) is a largest value

(worst vertex). There are 4 cases when using NM

method. They are reflection, expansion, contraction

and shrink. We recursively use NM method until

finding the point which is the local minimum (nearest)

in B, G, W that they are the same value.

The midpoint of the good side is

(8)

2.4.1 Reflection using the Point R

The function decreases as we move along the side of

the triangle from W to B, and it decreases as we move

along the side from W to G. Hence it is feasible that

function f takes on smaller values at points that lie

away from W on the opposite side of the line

between B and G. We choose a test point R that is

obtained by “reflecting” the triangle through the side

BG. To determine R, we first find the midpoint M of

the side BG. Then draw the line segment from W to

M and call its length d. This last segment is extended

a distance d through M to locate the point R (See

Figure 2). The vector formula for R is

()2

MMW MW

+−= −

(9)

2.4.2 Expansion using the Point E

If the function value at R is smaller than the function

value at W, then we have moved in the correct

direction toward the minimum. Perhaps the minimum

is just a bit farther than the point R. So we extend the

line segment through M and R to the point E. This

forms an expanded triangle BGE. The point E is

found by moving an additional distance d along the

line joining M and R (See Figure 3). If the function

value at E is less than the function value at R, then

we have found a better vertex than R. The vector

formula for E is

()2

RRM RM

+− = −

(10)

2.4.3 Contraction using the Point C

If the function values at R and W are the same,

another point must be tested. Perhaps the function is

smaller at M, but we cannot replace W with M

FUZZY TOPOGRAPHIC MODELING IN WIRELESS SIGNAL TRACKING ANALYSIS

because we must have a triangle. Consider the two

midpoints C

and C

of the line segments WM and

MR, respectively (see Figure 4). The point with the

smaller function value is called C, and the new

triangle is BGC. Note. The choice between C

and C

might seem inappropriate for the two-dimensional

case, but it is important in higher dimensions.

= (M - W)/2 (11)

= R - (M - W)/2

(12)

2.4.4 Shrink toward B

If the function value at C is not less than the value at

W, the points G and W must be shrunk toward B (see

Figure 5). The point G is replaced with M, and W is

replaced with S, which is the midpoint of the line

segment joining B with W.

S = (B - W)/2 (13)

Figure 2: Reflection using

the Point R.

Figure 3: Expansion using the

Point E.

Figure 4: Constraction

using the Point C.

Figure 5: Shrink toward B.

2.5 Topographic Model Generation

We generate topographic model based on our

previous work (C. L. Chan et al., 2008) and NM

algorithm. We apply NM method to a many-

dimensional RSS distribution space problem to

simplify the fuzzy color map down to a contour

(line-based) map.

First, we select three LFs to be three vertices of a

triangle:

→

, and

→

, where

→

is a location with

high RSS (best vertex),

→

is a location with medium

RSS (good vertex), and

→

is a location with the low

RSS (worst vertex). The location vector of RSS at

use in function, N(x, y). We use (1) to define

N(x, y). There are 4 cases when using NM method.

They are reflection, expansion, contraction and

shrink. We recursively use NM method until finding

the point which is the local minimum in

→

, and

→

that they are the same value. Table 1 summarizes

the procedure.

Table 1: Nelder-Mead Method Procedure.

IF f(R)<f(G), THEN Perform Case (i) {either reflect or

extend}

ELSE Perform Case (ii) {either contract or shrink}

BEGIN {Case(i).}

IF f(B)<f(R) THEN

replace W with R

ELSE

compute E and f(E)

IF f(E)<f(B) THEN

replace W with E

ELSE

replace W with R

ENDIF

END {Case (i)}

BEGIN {Case(ii).}

IF f(R)<f(W) THEN

replace W with R

ENDIF

compute C = (W + M)/2

or C = (M + R)/2 and f (C)

IF f(C)<f(W) THEN

replace W with C

ELSE

compute S and f(S)

replace W with S

replace G with M

ENDIF

END {Case (ii)}

A contour function is then used to plot a curve

connecting minimum points where the function has a

same particular value. We normalize the minimum

value between 0 and 1, and the contour line is 0.1 in

each level.

3 EXPERIMENTAL SETUP

In this section, we describe experiment setup in 9.34

hectare campus area. We use the same setting as

used in (J. Kwon et al., 2004), (R. Jan and Y. Lee,

2003), (Taheri et al., 2004), (K. Kaemarungsi and P.

Krishnamurthy, 2004), (K. Kaemarungsi and P.

Krishnamurthy, 2004), (W. Wong et al., 2005) and

(P. Bahl et al., 2000). RSS site survey measurement

will be in The Hong Kong Polytechnic University

(PolyU) campus. The approximate total area of the

campus is 9.34 hectare. A standard laptop computer

equipped with an Intel WLAN card and client

manager software was used to measure samples of

RSS from access points (APs) of PolyU campus.

IJCCI 2009 - International Joint Conference on Computational Intelligence

The WLAN card is chipset inside the laptop.

There are basically 26 buildings from Core A to

Core Z and 7 extra buildings with WLAN access.

Each core building is covered by at least 13 APs.

The radio frequency (RF) channels of IEEE 802.11b

are in the 2.4 GHz band which is shared by other

equipment in the industrial, scientific, and medical

(ISM) band such as Bluetooth. The number of non-

overlapping channels for 802.11b is three. We

observe that the RSS value reported by the WLAN

card is an average value over a sampling period and

in integral steps of 1 dBm. The received signal

sensitivity of the WLAN card also limits the range

of the RSS to be between -93 dBm and -15 dBm.

Nevertheless, the highest typical value of the RSS is

approximately -30 dBm at one meter from any AP.

The sampling schedule is to collect the RSS data

every 5 seconds. The vector of RSS data at each

location forms the location fingerprint with around

20 RSS elements in the vector. Total 27 locations of

measurement are chosen in the campus.

Figure 6 and 7 show the 27 locations site plan.

The radio channels used for each AP are channel 1,

6, and 11 respectively. The sampling will be taken

with two periods of time, (7:30am-9:30am (leisure)

and 4:30pm - 6:30pm (busy)). From (K.

Kaemarungsi and P. Krishnamurthy, 2004), the

presence or absence of people in the building

significantly affects the RSS values. The data were

collected four times with four different directions,

North, South, East and West. The duration of

sampling was 2 weeks with total 12 days (from Mon

to Sat). In mean while, temperature, weather,

sampling time and humidity were recorded. The

total number of RSS samples would be 12 days X 4

directions X 27 buildings X 20 APs X 2 times =

51840.

Figure 6: The satellite photo of PolyU campus from

Google Earth.

For 27 locations on the floor, we collected

environmental readings at these locations over two-

week period of time. At each testing location, we

picked a frequency 2.4GHz and calculated their

average amplitude respectively. Note that the RSS is

the received signal from a beacon packet, while the

spectrum energy is the ambient RF energy

corresponding to a specific frequency range. Table 2

summaries the campus area measurement setup

Figure 7: The site plan for PolyU Campus with 27

buildings.

Table 2: Summary of Experiment Setup in PolyU Campus.

Item Description

Total campus area 9.34 hectare

26 core + 7 extra buildings

Sampling period 2 weeks

7.30am - 9.30am

4.30pm - 6.30pm

RSS variation Between -93 dBm and -15

dBm

No. of sample points 51,840 sample points

WLAN channel 1, 6, and 11

Facing direction North, South, East, and West

4 DISCUSSION AND ANALYSIS

In this section, we discuss the effect of the presence

of human and LOS factor in our topographic model.

There are three RSS features to

be analyzed, LOS, the presence of human and RSS

variation.

4.1 Effect of LOS on RSS

Figure 8 and 9 show the effect of LOS in two major

clusters of RSS. The two major centers of high

intensity locate at F core and S core.

The distance between F core to S core buildings

is around 600m apart. The RSS should be covered

evenly. Moreover, between M core (Lee Ka Shing

FUZZY TOPOGRAPHIC MODELING IN WIRELESS SIGNAL TRACKING ANALYSIS

Figure 8: Fuzzy RSS Distribution with the campus floor plan.

Figure 9: Topographic RSS Distribution with the campus floor plan.

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Tower) to R core buildings (Shirley Chan Tower),

the RSS distribution is relatively low. The heights of

two buildings in M core and R core are around 80m

and 70m respectively. The distance between M to R

core is around 200m apart.

As we can see the topographic map in Figure 11a

and 11b, the slope of contour line from M core to R

core is steep in the edge area, it means that the RSS

is weaken quickly in the middle from M core to R

core due to NLOS effects. For LOS conditions, RSS

should fit into log-normal distribution. A multi-story

building in a campus area will experience lower

signal strengths within tall buildings due to the

absence of LOS propagation.

4.2 Behavior Study on the Human’s

Presence

As the previous section mention, we collected the

RSS data in 2 periods, one is in the morning leisure

period (7.30am-9.30am) and the other is in the busy

evening period (4:30pm - 6.30pm). We would like to

observe the difference between two periods. Figure

10 and 11 show the difference RSS pattern which

the RSS collect in the two different time slot. We

can see that there is significant change of the RSS

value. Figure 11a shows the topographic region in

0.9 level is larger than Figure 11b. We can observe

the slope on Figure 11b degrades larger than Figure

11a. As a result, it verifies the effect of the user’s

presence can affect the mean of the RSS value.

4.3 Effect of the RSS Variation on

Accuracy

The accuracy of the tracking system is highly

dependent on RSS variation. If the standard

deviation of the RSS increases, the accuracy of the

tracking system falls. To maintain high accuracy, the

suggested standard deviation of RSS should be

under 4dBm in this paper. (Elsewhere, a standard

deviation of 2.13dBm has been assumed. (Taheri et

al., 2004)) However, as the standard deviation

depends on the real environment, including the

density of human traffic, in some situations the

standard deviation will be large.

(a) In the leisure morning period (b) In the busy evening period

Figure 10: RSS Distribution in Fuzzy Analytical Model.

(a) In the leisure morning period (b) In the busy evening period

Figure 11: RSS Distribution in Topographic Model.

FUZZY TOPOGRAPHIC MODELING IN WIRELESS SIGNAL TRACKING ANALYSIS

5 CONCLUSIONS

In this paper, we propose NM optimized topographic

model for RSS distribution. The new model provides

quicker references and efficient analysis tool for

improving the design of WLAN infrastructure to

achieve localization accuracy. In our university site

experiment, we provide a spatial analytical model

for WLAN tracking in a campus. The fuzzy

topographic RSS analytical map provides easier

understanding of WLAN RSS pattern in a region.

The usage of model can improve the efficiency

usage of WLAN infrastructure substantially. Future

work will consist in building a 3D pervasive

tracking and a dynamic spatio-temporal filtering

technique.

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