Elimination of Gaussian Noise Using Entropy Function for a RSSI Based Localization

Ashutosh Patri Dept. of Mining Engineering

National Institute of Technology, Rourkela, India

ashutosh.patri@gmail.com

Sai Prasanna Rath Dept. of Mining Engineering

National Institute of Technology Rourkela, India

sanjay.arati@gmail.com

Abstract—In this paper a novel algorithm is proposed for nearly precise localization of a mobile sensor node from less number of low cost anchor nodes, using the received signal strength Index (RSSI) of a very high frequency wireless signal. Often the loss of signal, called as the shadow fading generates spurious data in RSSI, due to Gaussian noise, which is removed using entropy function. The viability of the proposed system is practically experimented. The error analysis is done using analysis of variance (ANOVA) method for the proper validation of results obtained.

Keywords—RSSI; Gaussian Noise; Entropy; ANOVA

I. INTRODUCTION In wireless sensor network (WSN), sensor node localization

is a problem of paramount importance. Low cost and accuracy in localization are the two governing factors; where range free localization is the minimum cost system and the range based localization is more accurate one. Due to rapid development in the Micro-electromechanical System (MEMS) technology low cost wireless sensor nodes are easily available ; but more sophisticated hardware is needed to calculate the accurate location of mobile node, that are more and more complex, utilizing the angle of arrival (AOA), time of arrival (TOA), time difference of arrival (TDOA) [1,2]. Without using any extra hardware only the RSSI can be measured in an economical way with less accuracy.

In range free localization system the location services does two things i.e. anchor node localization and mobile or sensor node localization. Anchor nodes are mostly fixed at some strategic point and there locations are already fed to the location service database. The target node can be localized actively or passively, where in passive localization the anchor node sense the targets and in active localization the target node communicates with the anchor node and its location is sent to the sensor network. To decrease the cost of system, active localization should be performed, as the number of anchor nodes is very high as compared to the target nodes and the traffic hindrance will be less in WSN by using the active system.

A. Localization Assumptions Practically the mobile node localization is very difficult.

However the complexity of the problem can be scaled down, by taking some simple assumptions. Most of the localization schemes are based on assumptions that are not always valid,

or are impractical e.g. circular radio-range & symmetric radio- connectivity [3, 4].

B. Shadow Fading of Wireless signal For wireless sensor network operated at 2.4GHz frequency

the path losses are different in different directions. A typical shadow fading environment is shown in figure 1. Therefore representation of this variation in a deterministic model is not feasible, and hence a statistical model is used to define the relation more properly.

Fig. 1. Shadow Fading Environment

This power loss is due to the blocking offered by objects around the receiver and is usually known as Shadow fading or large-scale fading [5]. The mathematical expression for the shadow fading of wireless signal is given by eqn.1. 10η log (1)

Where,

Signal Strength at a distance d in dBm.

Signal Strength at a reference distance d0 in dBm η Path loss index of shadow fading

Gaussian noise with zero mean

The above equation can be represented as the ratio of received power at distance d and d0 respectively.

Proceedings of the 2013 IEEE Second International Conference on Image Information Processing (ICIIP-2013)

978-1-4673-6101-9/13/$31.00 ©2013 IEEE 690

dB

Where, √ exp B B

Generally, the near earth reference distanc1 meter for simplicity and then the A0 bestrength at a distance of 1m.

Due to the addition of Gaussian noise to incorrect distance is calculated by the anchoshows a typical scatter plot of the variatdistance due to the addition of Gaussian noRSSI. In this figure the distance is in logarithstraight line has the slope η i.e. the pshadow fading. ‘e1’ and ‘e2’ are the errors inoise, thus the D0 is the flawed distance for and D2.

Fig. 2. Error in localization due to shad

II. GAUSSIAN NOISE AND ITS ENTROPY F

The theory of maximum entropy deals wdistribution function, that indicates the expernot agree with the prediction made by the cwhich in turn is based from the current know[6]. The phenomenon being studied behavesway that finds a previously unseen constraientropy over the distributions and this fulfillsup till now aware of. The maximum entropfunction p(x) in continuous domain can be cin the eqn.4. ln

In this paper the area of interest is the Pdistribution function. So the eqn.4 can be wrrepresents the entropy function for the foresai

(2)

BB (3)

ce d0 is taken to be ecomes the signal

the RSSI value an or nodes. Figure 2 tion in calculated oise at a particular hmic scale and the

path loss index of n RSSI due to the both distances D1

dow fading

FUNCTION

with the probability rimental data, does chosen distribution wledge on the data s in an unexpected int and maximizes s all the constraints py of a probability calculated as given

(4)

P(x) i.e. a Gaussian ritten as eqn.5 that id distribution.

√The final result from the a

eqn.6 that clearly shows thadependent on the mean of the d1

For variance value near to has a negative entropy valuevariance value a significant pofunction (PDF) has values grep log p < 0. Thus the negcontinuous domain indicates adistribution, compared to the u[0, 1].

III. SYSTEM DESIGN USIN

The maximum entropy valucalculated as described in the semaximum possible error contenis a theoretical value. Experimeincrease in the standard deviasensing coverage decreases sevthe standard deviation, the sens10% [7, 8, 9].

The variance of the additivvarious environments and wmaximum variance of the placeof the entropy function. So byentropy function properly, Gaefficiently. The relation depesensitivity of the device. With tscale the entropy for every RShigher accuracy.

The shadow fading occurs environment and the objectsexperience the RSSI values ferroneous data with increaenvironment. So the data colleanchor node has less randomnfarther one i.e. entropy is smavalue.

A linear relationship beproposed, with RSSI on X-axstraight line has a negative slopof ‘c’ on Y-axis. These values alower and upper boundary of tanchor node.

At first the collected RSScorresponding entropy values avalue the variance is determinethree inequalities are obtained f

R1 <

H1 >

√2 (5)

above equation is given by the at the entropy function is not distribution. 2 (6)

zero, the Gaussian distribution e. Graphically, for very small ortion of the probability density eater than 1 and in that portion ative value of the entropy in

a more concentrated probability uniform distribution in the range

NG ENTROPY FUNCTION ue for a specific variance can be ection 2. This value indicates the nt in the collected data, but this entally it was found that with the ation of shadowing effects, the verely. For an increase of 2 dB in ing coverage decreases by about

ve Gaussian noise changes with with increase in distance. The e gives the upper threshold limit y correlating the RSSI with the aussian noise can be eliminated ends mainly upon the receiver the higher resolution in the RSSI

SSI value can be calculated with

mainly due to the surrounding s. According to the practical fluctuates more or gives more ase in distance in the same ected at a nearer distance to the ness in its value compared to a aller for a lower negative RSSI

etween RSSI and entropy is xis and entropy on Y-axis. The pe of ’m’ and makes an intercept are completely dependent on the the RSSI readings given by the

SI readings are sorted and the are calculated. For every entropy ed from the eqn.6. The following from the above conditions.

< R2 < R3

> H2 > H3

Proceedings of the 2013 IEEE Second International Conference on Image Information Processing (ICIIP-2013)

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R1, R2, R3 are the RSSI values found from different anchor nodes at a distance of d1, d2 & d3 respectively. Three Gaussian noises are generated with corresponding variances with their mean at R1, R2 and R3 respectively.

With a known variance, the distribution of the population can be calculated for a particular portion. In this normally distributed population, with the mean i.e. the RSSI value and variance , and then the interval 1.96 include 95% of the population where the z-score is 1.96 for 95% population coverage in a Gaussian distribution.

Fig.3. Gaussian function with tolerance interval.

The figure 3 represents a Gaussian distribution function with mean 80 i.e. the RSSI value with a tolerance limit of 95%. The variance is calculated from the relation as given in eqn.6.

From these three RSSI ranges corresponding distances are calculated. These distances can be treated as radius vectors with a centre at the corresponding anchor nodes with a varying angle range [0,2π]. A common point for the three vectors gives the 2-D co-ordinate of the mobile sensor. The algorithm of the proposed system is described by the flowchart given in figure 4.

In the above flowchart i, j, k, var1, var2, var3 are the counter variables. H & V are the arrays used for storing the entropy and the variance respectively, for each RSSI. Similarly ‘a’ and ‘b’ are the arrays used for storing the upper and lower limits of RSSI range respectively. ‘d’ is a 2-d array for storing the range of distances generated for each RSSI range. E, F, G represent the values which the corresponding circles give on putting the co-ordinates of the grid in their respective equations. X, Y indicates the grid dimensions (in metre) setup for the test. Xsim, Ysim are the simulated x and y co-ordinates of the experimental position of the mobile sensor.

Fig.4. Flowchart of the proposed system

START

Input the raw RSSI data collected

i=1

i <= 3

H[i] = m*RSSI[i] + cv[i] = [e^(2H[i] -1)](2*3.14)

j=1

j <= 3

k =1

a[ j ] = RSSI[ j ]+1.96*v[ j ]^0.5b[ j ] = RSSI[ j ] -1.96*v[ j ]^0.5

i = 1+1

j = j+1

k <= 3

s =1R = b[ k ]

var1 = 1

var1 <= n[1]

var2 =1

var2 <= n[2]

R <= a[k]

k = k+1

n[k] = s

var1 =var1 +1

R =R+0.0001

d[k][m]= 10^[(Ao - R)/10*n]s =s+1

var3 =1var3 <= n[3]p =1

p <= X

q =1

q <= Y

p = p+ 0.0001

var3 =var3 +1

E=p^2 + q^2 - d[1][var1]^2 - 2YF=p^2 + q^2 - d[2][var2]^2

G=p^2 + q^2 - d[3][var3]^2 - 2X

q = q +0.0001

E=0F=0G=0

Print XsimPrint Ysim

STOP

NO

NO

NO

NO

NO

NO

NO

NO

NONO

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

Xsim=pYsim=q

Proceedings of the 2013 IEEE Second International Conference on Image Information Processing (ICIIP-2013)

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IV. EXPERIMENTAL SETUP For experimental simplicity the three

placed at the three corners of a square of 10height of 0.6 m and all the experiments areenvironment. Tests have been performed in and in each area the sensor node is placepositions within a 100 square meter grid. Allanalysis and simulations are done using M8.1.0.604 R2013a.

The MICAz (MPR 2400) is used as mobile node. MICAz operates using a Tinyall the low level communication layers sucapplications of TinyOS are written in nesdialect of the C language which has bememory limits of sensor networks. The supwhich it uses are mainly in the form of Javfront-ends. Associated libraries and tools, compiler and Atmel AVR binutils toolchwritten in C. The processor board used is Mbased on ATMEL ATmega 128L.

It’s a Zigbee compliant radio and it offerskbps with the AES-128 hardware secusequence spread spectrum (DSSS) moduprovides resistance to RF interference and 51-pin expansion connector supports DigUART & SPI interfaces and Analog transceiver features IEEE 802.15.4 hardwsecurity operations that includes standalonein which [10], one 128 bit plaintext is encrycipher-text.

The A0 value for this instrument is 41.14 2.83 for outdoor scenario. For the shadow fain the experimental conditions the varianceadditive noise is taken 0.6.

Fig. 5. Common point of radius vectors with diff

Figure 5 represents the simulated positinode by implementing the above algorithm aof the mobile node during the field experim

anchor nodes are 0 meter length at a e done in outdoor 30 different areas

ed at 30 different l the mathematical MATLAB version

both anchor and yOS which covers ch as routing. The sC [9]. nesC is a een optimized for upplementary tools va and shell script such as the NesC hains, are mostly

MPR2400 which is

s a speed upto 250 urity. The Direct ulation technique data security. The gital I/O & I2C,

Inputs. CC2420 ware with MAC

e AES encryption, ypted to a 128 bit

dBm with η value ding of the signals e of the Gaussian

ferent variances

ion of the mobile and actual position

ment at a particular

‘area A’. The two dotted crepresent the range of varyingfrom the corresponding anchoobtained in determining the smobile node in that particular ‘

V. RESULT & ERAfter calculating the Xsim an

simulation, the errors in both tby eqn. 7 and 8, where Xmea, Ysensor node. The error in distan | |

Figure 6 represents the rsensor nodes taken at 30 differemeter area i.e. ‘area A’. The ma0.84 & 0.02 respectively for thi

Fig. 6. Error in simul

Fig. 7. Box plot on readi

Similar experiments are caThe overall experimental resul1.3480 m with a minimum of

circles for each radius vector g distance of the mobile node or nodes. ‘e’ denotes the error simulated position of the same area A’.

ROR ANALYSIS nd Ysim coordinate from the said the axes are calculated as given

Ymea is the real co-ordinate of the nce is calculated from the eqn. 9. | (7) | (8)

(9) real and simulated position of ent locations inside a 100 square aximum and minimum errors are is particular area.

lated results for area A

ings obtained from Anova

arried out at 30 different areas. t gives out a maximum error of

f 0 m as shown in the box plot

Proceedings of the 2013 IEEE Second International Conference on Image Information Processing (ICIIP-2013)

693

figure 7. The mean error for the overall observation turns to be 0.3589 m. The one-way ANOVA test for set of data without assuming equal variance is done using R statistical software version 3.0.1. The P-value and the F-value for this statistical analysis are found to be 0.9753 and 0.5425 respectively. Hence, the data appear to be consistent with the aforementioned assumptions.

VI. CONCLUSION For simultaneous comparison of 30 groups of data,

ANOVA is used as it gives a single p-value for the whole system. Usually when the p-value is less than 0.05 the null hypothesis is rejected, whereas in this paper the p-value of 0.9753 indicates the strong evidence for the hypothesis proposed [11]. The analysis and system is evaluated using only three number of anchor nodes. So, the increase in the number of anchor nodes will increase the accuracy significantly. The error analysis shows that the distribution is uniform and the proposed system is very stable and the errors generated fluctuate within a small range. The algorithm is proposed for locating a 2-D coordinate assuming the radio signal as a circle, but it can be certainly merged with any other advanced system which can be integrated with it for locating a mobile sensor node for its 3-D coordinates with high accuracy.

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[3] Wong. W.H. et al., “Large-scale location estimation over GSM networks: the gear approach”, Proc. 24th Int. Conf. Distributed Computing Syst. Workshops (ICDCSW), IEEE, 2004.

[4] Radu Stoleru et al., “Range-Free Localization”, Springer US, Advances in Inform. Security, vol. 30, 2007, pp. 3-31.

[5] K. Pahlavan et al., “ Modeling and Simulation of Narrowband Signal Characteristics” in Wireless Information Networks, Wiley,2005, pp. 94-122.

[6] Keith Conrad, “Probability Distributions And Maximum Entropy”,Available:http://www.math.uconn.edu/~kconrad/blurbs/analysis/entropypost.pdf

[7] Tian He et al. , “Range-Free Localization Schemes for Large Scale Sensor Network”, MobiCom. ’03, 2003.

[8] Yuh-Ren Tsai,” Sensing Coverage for Randomly Distributed Wireless Sensor Networks in Shadowed Environments”, IEEE trans. on veh. technology, vol. 57, no. 1, 2008.

[9] Wikipedia,TinyOs, Available: http://en.wikipedia.org/wiki/TinyOS [10] Y W Zhu et al., “The Design of Wireless Sensor Network System Based

on ZigBee Technology for Greenhouse.”, J. Physics, Conf. Series, vol. 48,2006.

[11] ANOVA,Available:http://www.statisticallysignificantconsulting.com/Anova.html

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