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A LOCALIZATION ALGORITHM FOR A GPS-FREE SYSTEM WITH STATIC PARAMETER

TUNING*

K. PADIA, G. A. VIKAS, H. S. IYER, V. R. DARSHAN, N. P. GANESH PRASAD, A. SRINIVAS

Department of Computer Science, PES Institute of Technology, 100 feet Ring Road, BSK 3rd Stage

Bangalore, Karnataka 560085, India

H. KHAN, A. GUPTA, S.OLARIU

Department of Computer Science, Old Dominion University,

Norfolk, Virginia 23508, USA

Localization in wireless network refers to determining the location of a mobile user which may either be stationary or in motion. This

paper presents the design and evaluation of an algorithm for localization of mobile nodes in GSM networks. The proposed algorithm

does not use GPS and has the advantages of being cost effective and reliable. The received signal strength from the base stations in the

proximity of the mobile form the basis for the proposed algorithm. The algorithm concentrates on improving the accuracy of estimated

location of the mobile by using a prediction-interpolation technique. The key aspects of the proposed localization technique are that it

assumes linear dependency between the accuracy of the estimated mobile location and the received signal strengths from the

neighboring base stations, and tunes the location estimate based on this mapping.

Keywords: Received signal strength, Deviation detection, Prediction, Triangulation, Interpolation.

* This results of this paper are a part of the PESIT – ODU collaborative research initiative.

1. Introduction

One of the major challenges in GSM networks is

determining the relative position of the mobile nodes

with respect to surrounding base stations. This involves

tasks which strive to annul the effects of motion of the

mobile node. Recent surveys have revealed that 25

percent of cell phone users are not able to provide their

location information. The use of GPS in emergency

location management is problematic, the reason being

the requirement of the GPS system to have three or more

satellites visible to the GPS receiver. Moreover GPS

does not work indoors and is seen to be inaccurate in

poor atmospheric conditions. Also, GPS based devices

are expensive and less compact. Hence there is a need to

develop efficient GPS-free localization algorithms

which provide for high levels of accuracy and

subsequently yield reliable results.

The existing localization techniques can be

classified into two categories: range based and range

free. Range based techniques exploit the range of base

station and the distance of mobile node from it.

Examples of this category include RSS, TOA, TDOA,

AOA based techniques. These techniques call for extra

hardware requirements. Range free methods are less

accurate and used for applications which can tolerate

small permissible errors in location estimation.

In [1], the described technique uses the RSS based

measurements as the starting point. At this instant, a

prediction method based on the mobile velocity and

direction is employed. The author then suggests an

interpolation technique using the above two coordinate

values to obtain a better estimate of the mobile location

coordinates. It is also stated in [1] that either RSS

estimate or the predicted position may be responsible for

deviation. The algorithm proposed by us in this paper

initially concentrates on determining the factor

responsible for deviation and then uses this information

to fine tune a parameter defined to counter the effect of

deviation. We have also presented a method to predict

the position of the node at any time instant. All

computation is done at the mobile device.

In the next section we briefly present some of the

available range based techniques and related localization

techniques. In section 3, we explain our algorithm using

progressive prediction and interpolation. Section 4

presents case studies and the associated NS-2 simulation

results. Conclusion and scope for future work is

addressed in section 5.

2. Related Work

A wide variety of approaches to mobile localization

have been developed previously. These include

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popularly used methods like AOA, TDOA, TOA, TA,

U-TOA and their variants. More information can be

found in [3], [4], [6], [10] and [11]. The accuracy of

these range based techniques depends on the accuracy of

the range measurements. Considerable amount of

inaccuracy is introduced in these measurements due to

two factors, viz. Non-Line of Sight (NLOS) error and

measurement error. The measurements in cellular

systems, taken by Nokia [12], show that NLOS error

dominates the standard measurement noise, and tends to

be the main cause of the error in range estimation. They

also show that the location estimation error linearly

increases with the distance error. Following these

measurements, Wylie and Holtzman propose a method

for the detection and correction of NLOS errors [14].

They show that it is possible to detect a NLOS

environment by using the standard deviation of the

measurement noise and the history of the range

measurements. They propose a method for LOS

reconstruction and they show that the correction is only

possible if the standard measurement noise dominates

the NLOS error. In [13], Chen presents a Residual

Weighting Algorithm for localizing mobile nodes which

relies on the basis that correction of the localization

estimation errors is possible when the number of range

measurements exceed the required minimum.

[15] presents a significantly different approach to

mobile localization. The algorithm in [15] describes a

connectivity metric method which utilizes the RF

communication capabilities of the mobile devices and at

the same time addresses the problem of bad

environmental conditions. In [16], Srdan proposes an

algorithm for mobile localization in Ad hoc networks.

The GPS-free algorithm devised in [16] uses the

distances computed between mobile nodes to build a

relative two dimensional coordinate system. [17] puts

forth a two phase TOA based distributed mobile

localization algorithm to minimize the number of

messages exchanged and the coordinate setup time. The

algorithm as proposed in [17], assumes that establishing

a network with small subset of mobile nodes can

successfully establish the coordination system for the

overall network.

The Global System for Mobile Communications

(GSM) is the most prevalent phone and data service in

use today. GSM provides only RSS measurements and

hence GSM based mobiles cannot make direct use of

location techniques based on TOA, AOA and TDOA

[5]. Hence new techniques have to be devised to localize

GSM mobiles and at the same time strive to achieve

high accuracy. Consequently, significant research has

been made in providing solutions to the localization of

GSM mobiles. Some of the developed techniques in this

regard and their variants can be found in [2], [5], [7], [8]

and [9].

The next section describes the proposed GPS-free

static parameter-tuning algorithm for localization in

mobile ad-hoc networks which is the main contribution

of this paper.

3. Prediction–Interpolation with Static

Parameter Tuning

As described in [1], the real path of the mobile user is

indicated by a sequence of points Ri. The sequence of

prediction based coordinates Pi represent the predicted

path. Similarly, the RSS path is represented by the

sequence Si of RSS based estimation coordinates. As

proposed in [1], we have:

Ln = λ* Sn + (1-λ)* Pn (1)

Here Sn is the RSS based estimation at time instant

Tn. Pn is the prediction based point and finally Ln is the

final estimate achieved after interpolation. λ is the

parameter defined to counter the deviations in prediction

and RSS based coordinate estimations.

The prediction process starts with the premise that

the velocity (speed and direction) of the mobile in

continuous transition is available. These parameters are

measured by a speedometer and an odometer on the

mobile. Figure 1 depicts a scenario at time instant Tn.

With reference to Figure 1, d is the distance travelled by

the moving node and this value is computed using the

velocity information. The predicted coordinate Pi is then

obtained from Li-1 by traversing a distance equal to d in

the direction indicated by the odometer. The distance

between Pi-1 and Pi is designated as dp. The angle made

by the line segment Pi-1Pi with the direction of motion of

the mobile (represented here by a dashed line) is

represented by θp. Similarly, the angle made by the line

segment Si-1Si with direction of motion of the mobile

(represented by another dashed line) is designated as θs.

The distance between Si-1 and Si is represented as ds .

It is important to note that we consider only the

acute or right angles between the direction of real

motion and the direction of predicted (or RSS) path. If

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the angle between the two of them, θ, is obtuse, we

consider the angle to be π – θ.

Figure 1. The prediction process

The next step is the determination of the parameter

that is responsible for deviation from the real path and

forms the basis of this paper. This procedure is primarily

based on determining the projections of the real path on

both predicted path and RSS coordinate based path.

As shown in figure 2, we first compare |(dp-d)| with

|(ds-d)|. This comparison is made to figure out which

among the two is closer to 0 and hence determine the

distance (either dp or ds) that is closer to d. Next θp is

compared with θs. If θp is found to have a lower value

than θs and dp closer to d than ds, it is inferred that the

majority of the deviation is caused by the RSS estimate

and hence the predicted value better approximates the

real value than the RSS value. Thus the value of λ is

reduced as per [1] in order to give more priority to the

predicted value.

The proof for the above deduction is explained

using figure 2.

Proof. In figure 2,

CD = d. cos(θp) (2)

GH = d. cos(θs) (3)

If,

θp < θs,

then,

cos(θp) > cos(θs) (4)

Thus,

d. cos(θp) > d. cos(θs) (5)

i.e.

CD > GH (6)

This implies that the component of real path is more

in triangle BCD than in triangle FGH or equivalently the

projection of real path is more in the predicted path than

in RSS path, hence the greater preference for the

predicted coordinate and subsequent reduction in the

value of the parameter λ. □

Figure 2. Detecting the parameter that experiences more

deviation

Similarly, if θp is greater than θs and |(dp-d)| has a

lower value compared to |(ds-d)|, the reason for

deviation from the real path is ascribed to the errors in

prediction and hence preference is given to the RSS

based estimate over the predicted value. In this case, the

value of λ is increased to annul the effect of incorrect

prediction. For all other situations apart from the two

previously discussed, decision is made based on

previous history, i.e., the value of λ which was

calculated and employed in the previous iteration is

reused in the current iteration.

Once the parameter to be preferred in the current

iteration is determined by the method discussed above,

the value of λ for the present step is determined. This

represents the amount of preference given to the chosen

parameter.

The method employed is based on two static look

up tables. Table 1 is referred to when the prediction

based coordinate is preferred over RSS estimate and

Table 2 is referred to if it is the other way round.

The value of λ in Table 1 ranges from 0.0 to 0.5 to

ensure that the interpolated point is closer to the

predicted point than the RSS point. It can be observed

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from Table 1, that the algorithm assumes linear

dependency of λ on the value of |dp-d|/dp. The lowest

value of λ as shown in Table 1 indicates maximum

amount of preference given to the prediction based

coordinate which infers that the prediction based

coordinate is very close to the real coordinate compared

to the RSS coordinate. A value of λ = 0.5 infers that

RSS based coordinates and the prediction based

coordinates are given equal importance.

Table 1.Value of the ratio Table 2. Value of the ratio

(dp - d)/dp and corresponding (ds - d)/ds and corresponding

value of λ vaue of λ

Range for

(dp - d)/dp

λ

0 – 0.1 0.05

0.1 – 0.2 0.10

0.2 – 0.3 0.15

0.3 – 0.4 0.20

0.4 – 0.5 0.25

0.5 – 0.6 0.30

0.6 – 0.7 0.35

0.7 – 0.8 0.40

0.8 – 0.9 0.45

Similarly, if the algorithm determines that the RSS

based estimate is to be preferred over predicted

coordinate values, the value of λ is obtained by hashing

the value of the expression |ds-d|/ds into the look up

table shown in Table 2. Here the value of λ ranges from

0.5 to 1.0. This is to ensure that the interpolated point is

closer to the RSS point as per [1]. A value of λ = 0.95

indicates that the RSS based coordinate is extremely

close to the real mobile location coordinate compared to

the prediction based coordinate.

The number of intervals for either of the look up

tables can be varied by varying the step length and

hence there is always a flexibility to obtain the desired

level of accuracy. For the purpose of simulation, we

have used a step length of 0.1. In the next section we

discuss the simulation results for different case scenarios

and demonstrate the effectiveness of the proposed

algorithm in these scenarios.

4. Implementation and Results

The experiments have been conducted on the network

simulator NS2. The graphs for each simulation scenario

presented below depict the real path of the mobile user,

the path obtained by connecting predicted points, the

path obtained by connecting RSS based coordinates and

finally the path obtained by the connecting the

interpolated coordinates which is the final result. All

distances measured are in meters and it can be seen that

the resolution of accuracy is very high.

Figure 3. Test Scenario 1

Figure 4. Test Scenario 2

Figure 3 depicts a scenario in which a random path

with sharp and prominent deviations has been chosen as

the real path of mobile user for simulation. Inaccuracies

in prediction and RSS based estimation are clearly

depicted in Figure 3. The objective is to bring the

interpolated point close to the real point at any time

instant Tn. The measurements are taken at regular

intervals of 0.8 seconds under the assumption that either

the direction of movement of the mobile node or its

velocity cannot vary by a large amount in this very short

Range for

(ds - d)/ds

λ

0 – 0.1 0.95

0.1 – 0.2 0.90

0.2 – 0.3 0.85

0.3 – 0.5 0.80

0.4 – 0.5 0.75

0.5 – 0.6 0.70

0.6 – 0.7 0.65

0.7 – 0.8 0.60

0.8 – 0.9 0.5

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interval of time. From figure 3, it can be observed that

the inevitable inaccuracies associated with the prediction

and RSS based estimation are addressed suitably by the

proposed algorithm and the interpolated path converges

towards the real path with a maximum deviation of 10-

15 meters towards the end of simulation.

In Figure 4, the path chosen as the real path

comprises of sudden deviations, curves, vertical and

horizontal movements of the mobile node. Since the

proposed static look up table approach controls and

assigns the amount of preference to either prediction

based coordinates or RSS based coordinates depending

on the deviations caused by either of them, the algorithm

handles the scenario depicted in figure 8 effectively and

convergence is achieved with a maximum deviation of

5-10 meters as is evident from the results in Figure 4.

5. Future Work

The future work lies in predicting the position of mobile

node without the use of additional hardware like

odometer and compass which may not be provided by

a mobile device. The challenge here lies in prediction of

mobile location based on only the received signal

strength information. The static method makes use of

predetermined look up tables and thus reduces the

flexibility with which the algorithm can operate. Thus a

method for dynamically computing the value of the

parameter λ has to be devised. The dynamic choice of

λ to adapt to the ambient conditions is likely to result in

more accurate interpolated mobile location coordinates.

Work is underway in this direction.

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