Weighted Centroid Localization Algorithm Based on Least Square for Wireless Sensor Networks

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1 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp Sesors & Trasducers 4 by IFSA Publishig, S. L. Weighted Cetroid Localizatio Algorithm Based o Least Square for Wireless Sesor Networs Shaoguo Xie, Yaju Hu, 3 Yi Wag, 4 Yiggua Wag,, 3 Key Laboratory of Itelliget Computig & Sigal Processig, Miistry of Educatio, Ahui Uiversity, Hefei Ahui 339, Chia 4 Key Laboratory of Wireless Sesor Networ & Commuicatio, Shaghai Istitute of Microsystem ad Iformatio Techology, Chiese Academy of Scieces, 865 Chagig Road, Shaghai 5 Chia Tel.: 65754, fax: xieshaoguo@6.com Received: March 4 /Accepted: 3 July 4 /Published: 3 August 4 Abstract: Localizatio algorithm is a importat ad challegig topic i today s wireless sesor etwors (WSNs). I order to improve the localizatio accuracy, a weighted cetroid localizatio algorithm based o least square to predict the locatio of ay sesor i WSNs is proposed i this paper. The proposed algorithm proposes a Least-Square-based weight model which ca reasoably weigh the proportio of each achor ode i the uow ode. I the weight model, we utilize least square method to compute the weight. The, we icrease the weight of achor odes closer to the uow ode, itroduce the parameter ito the proposed lielihood model, ad we determie the optimal value of the parameter through our real experimets. Simulatio ad experimetal results show that the proposed weighted cetroid algorithm is better tha Weighted Cetroid Localizatio (WCL) ad Achor-optimized Modified Weighted Cetroid Localizatio based o RSSI (AMWCL-RSSI) i terms of the localizatio accuracy. Copyright 4 IFSA Publishig, S. L. Keywords: Localizatio, RSS, Wireless sesor etwors, Least square, Weight.. Itroductio Recet advacemets i the wireless commuicatios ad hardware techology field have facilitated the developmet of wireless sesor etwors (WSNs) for a wide variety of real-world applicatios, icludig evirometal moitorig, disaster relief, site security, medical diagostics, battlefield surveillace, home automatio, assisted livig, ad so o [-6]. A recet outdoor applicatio for WSNs is the localizatio of movig targets. This applicatio is motivated primarily by the low cost of this solutio ad the lac of effective positioig ad tracig systems worig iside buildigs. Ideed, the global positioig system solves may localizatio problems outdoor, where the devices ca receive the sigals comig from satellites. Moreover, wireless odes show some advatages i terms of system miiaturizatio, scalability, quic ad easy etwor developmet, cost, ad lower eergy cosumptio. Most of the proposed localizatio algorithms rely o received-sigal-stregth (RSS) measuremets. I fact, RSS ca be used to estimate the distace betwee a uow ode (called a target ode) ad a umber of achor odes with ow coordiates. 4

2 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp The locatio of the target ode is the determied by multilateratio [7-9]. Ufortuately, due to the degradig effects of reflectios, shadowig, ad fadig of radio waves, some studies have show the large variability of RSS [-]. As a result, localizatio methods usig RSS are affected by large errors ad lac of accuracy. However, RSS-based techiques remai a appealig approach [3]. This is maily due to the fact that RSS measuremets ca be obtaied with miimal effort ad do ot require extra circuitry, with remarable savigs i cost ad eergy cosumptio of a sesor ode. I fact, most of WSN trasceiver chips have a built-i RSS idicator (RSSI), which provides RSS measuremet without ay extra cost. There exist several algorithms that ca be used to determie the positio of a target through RSS measuremets. Some of them are geometric methods, such as lateratio or a miimum maximum method, whereas some others are based o statistical approaches, such as maximum lielihood. Alippi et al. have tested a RSS-based outdoor localizatio methodology exploitig a miimum least square (LS) algorithm, after modelig a propagatio chael [4]. The deploymet of achors has a desity of oe ode over 5 m o a area of 5 m. The average distace error obtaied is about 3 m. I [5], a extesive idoor RSS measuremet campaig is carried out i order to tue the parameters of the assumed chael model. The, the collected RSS data have bee used offlie as iputs for two localizatio methods, i.e., the mi max ad Bayesia filterig algorithms. A distace error of the order of 5 ad m is achieved for the two algorithms, respectively. Cetroid localizatio (CL) ad weighted cetroid localizatio [6-], have attracted a lot of iterest because of their simplicity ad robustess to chages i wireless propagatio properties such as path loss. This characteristic maes them suitable cadidates for systems requirig coarse graied, but reliable ad cost-effective techiques. Strictly speaig, weighted cetroid localizatio is ot a etirely rage-free techique because it requires additioal iformatio aside from simple coectivity. Recetly may proposed approaches o weighted cetroid localizatio focused more o error cotrol ad maagemet. Weighted cetroid localizatio (WCL) is firstly proposed i [3]. I order to avoid the creatio of RSS maps, complicate probability models, or high-computatioal-effort algorithms, Reichebach ad Timmerma proposes approximated idoor localizatio based o a weighted cetroid approach combied with RSS measuremets i a IEEE sesor etwor [4]. The weights are defied as iversely proportioal to the RSS values measured betwee the target ad each achor ode. The solutio is tested i a square room with a side legth of 3 m, usig four achor odes displaced at the corers ad oe target ode located i 3 differet positios. The obtaied relative localizatio error varies betwee 7.8 % ad 6 %. I [5], Hogyu et al. proposes a achor_optimized modified weighted cetroid localizatio algorithm based o RSSI (AMWCL- RSSI). Other schemes are to discuss iexact positio problems [6], or aalyze the performace of weighted cetroid localizatio algorithm [7], or ehace its performace for specific scearios [8-9]. The aim of this paper is to improve the localizatio accuracy of weighted cetroid localizatio, ad we propose a weighted cetroid localizatio algorithm based o least square for WSNs. We compare our proposed scheme with some existig solutios via simulatios ad experimets. The rest of this paper is orgaized as follows. Sectio presets proposed localizatio algorithm, followed by Performace evaluatio i Sectio 3. We coclude the paper i Sectio 4.. Proposed Localizatio Algorithm.. Overview of Localizatio System The aim of the RSS-based localizatio is to see a mappig betwee the measuremets to a physical locatio. Oe of the most importat mappig fuctios is the probabilistic model fidig the weight pi () [3, 3]. The, the locatio ca be regarded as a regressio problem [3] as ( x, y) = I p( i) ( i ), where is the umber of achor odes, I i represets the coordiate of the ith achor ode ad ( x, y ) represets the estimated result. This paper adopts a ovel approach to compute the weight... RSS Model RSS model ca be expressed as RSS PL β log ( d / d) N α = +, () where d is the real distace, PL is the received sigal stregth at referece distace d ( d = m), β is the path loss expoet, ad N α is a zero-mea Gaussia oise with stadard deviatio α..3. Weighted Cetroid Localizatio Algorithm Based o Least Square (WCLLS) I this sectio, we will itroduce the proposed weighted cetroid Localizatio Algorithm for locatio estimatio. Let d i deote the Euclidea distace betwee the coordiator of achor i ad the 4

3 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp ^ ^ coordiate ( x, y ) for a specific uow ode. We assume that each uow ode ca hear at least ~ ~ ~ ~ achor odes. The variables D = ( d, d, d3,, d ) represet the set of measured distaces to achor odes,, 3,, from the uow ode. The coordiate ( x, y ) is a estimated positio of a uow ode. The coordiate ( x ^, ^ y ) is the positio of each achor ode. Accordig to [3] ad [3], the estimated positio ( x, y ) ca be expressed by ( i ), () ( x, y) = I p( i) where I i represets the i th achor ode locatio, ad I = ( x, y ). i i i pi () =, i =,,, (3) With the geometric relatioships, the measured distaces d ~ i ca be expressed by ~ di = ( x xi) + ( y yi) (4) ~ ~ ( x x) x+ ( y y) y= [( x + y) ( x+ y) ( d d ~ ~ ( x x3) x+ ( y y3) y= [( x + y) ( x3+ y3) ( d d3 ~ ~ ( x xi) x+ ( y yi) y= [( x + y) ( xi + yi ) ( d di ~ ~ ( x x) x+ ( y y) y= [( x + y) ( x+ y) ( d d ( i =,, ) (5) With () ad (5), we ca get ~ ~ [( x x) xj+ ( y y) yj] p( j) = [( x + y) ( x+ y) ( d d j= ~ ~ [( x x3) xj+ ( y y3) yj] p( j) = [( x + y) ( x3+ y3) ( d d3 j= ~ ~ [( x xi) xj+ ( y yi) yj] p( j) = [( x + y) ( xi + yi ) ( d di j= ~ ~ [( x x) xj+ ( y y) yj] p( j) = [( x + y) ( x+ y) ( d d j= (,, ; j =,, ) (6) Accordig to (3) ad (6), we ca get ( x x) x+ ( y y) y ( x x) x+ ( y y) y ( x x) xj + ( y y) yj ( x x) x+ ( y y) y ( x x3) x+ ( y y3) y ( x x3) x+ ( y y3) y ( x x3) xj + ( y y3) yj ( x x3) x+ ( y y3) y Q = ( x xi) x+ ( y yi) y ( x xi) x+ ( y yi) y ( x xi) xj + ( y yi) yj ( x xi) x+ ( y yi) y ( x x) x+ ( y y) y ( x x) x+ ( y y) y ( x x) xj + ( y y) yj ( x x) x+ ( y y) y (7) 4

4 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp. 4-48, p() p() p = p( j) p ( ), ~ ~ [( x + y ) ( x + y ) ( d d ~ ~ [( x + y ) ( x3 + y3 ) ( d d3 S = ~ ~, ( i =,, ; j =,, ) [( x + y ) ( xi + yi ) ( d di ~ ~ [( x + y ) ( x + y ) ( d d Qp = S By usig least square method, pi () ca be expressed as: T ( ) T = (8) p Q Q Q S p() i is as the weight of achor ode i (,,, ), but p() i ca t fully reflect the bidig o the estimated positio of the uow ode due to the iterferece of exteral eviromet. To this problem, we propose a ovel weight model. I the ovel weight model, we icrease the weight of achor ode closer to the uow ode. Because the closer achor ode gets to the uow ode, the greater weight achor ode has [3]. Meatime, we itroduce the parameter ito the weight model. The reasoable parameter ca further weigh the proportio of each achor ode i the uow ode. () pi () ( ) p i is the improved weight model, ad pi () pi () ( ) > pi () ( is the umber of achor odes, is a parameter, ad < < ). Here, we cosider the impact of the umber of achor odes to () localizatio accuracy i pi () ( ) pi. () After pi () ( ) p i ormalizatio, the weight ca be expressed as: pi () p( j) j= wi ( ) = pi ( ) ( ) / ( p( j) ( ) ), < < (9) i ( x, y) = I w( i) ().4. The Optimal Value of the Parameter I this sectio, we obtai the optimal value of the parameter through the real experimet. A wireless ode is based o a MSP43 microprocessor ad equipped with a IEEE compliat Chipco CC5 radio module. The atea is a.4 GHz plaar iverted-f atea. I our experimets, achor odes are radomly distributed i a 5 m x 5 m regio. The positio of a uow ode is radomly deployed i this regio. Here, we choose the umber of achor odes = 4,5,6 respectively for our experimet, ad all odes are able to commuicate with each other. Fig., Fig. ad Fig. 3 show the average localizatio error whe chooses a differet value. From Fig., whe the umber of achor odes = 4 ad the parameter = 4, WCLLS has a sigificat chage i the localizatio accuracy. Clearly, it ca be see that whe the umber of achor odes = 4, should be closer to 4, but ot equal to 4. From Fig., whe the umber of achor odes = 5 ad the parameter = 5, WCLLS has a sigificat chage i the localizatio accuracy. Clearly, it ca be see that whe the umber of achor odes = 5, should be closer to 5, but ot equal to 5. Localizatio error ( m ) Number of achor odes Fig.. Localizatio error versus the umber of achor odes. = =3 =3.5 =4 43

5 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp Localizatio error ( m ) =4. =4.5 =4.8 = Number of achor odes Fig.. Localizatio error versus the umber of achor odes. From Fig. 3, whe the umber of achor odes = 6 ad the parameter = 6, WCLLS has a sigificat chage i the localizatio accuracy. Clearly, it ca be see that whe the umber of achor odes = 6, should be closer to 6, but ot equal to 6. From the aalysis above, it ca be see that should be closer to, but ot equal to, ad <. Hece, we assume = b as the value of the parameter, where <, < b<. Next, we determie the value of the parameter b through MATLAB simulatio. Localizatio error ( m ) =5. =5.5 =5.8 =6 Table, we ca choose. as the optimal value of the parameter. Table. The parameter b. Path loss expoet b Therefore, the weight model wi () i Eq. (9) ca be expressed as follows: pi () p( j) wi () = pi () / ( p( j) ).. () j=.5. Process of Localizatio Algorithm The algorithm process of the proposed localizatio algorithm is as follows: Step : Beaco odes periodically trasmit iformatio of themselves which iclude ode ID ad positio iformatio of themselves; Step : After uow ode receives sigals, it records RSS values which come from beaco odes; Step 3: Compute the measured distace d ; Step 4: Compute the weight pi () ad the () improved weight pi () ( ) pi ; Step 5: Compute the weight p() i p( j) wi () = pi () / ( p( j) ).. j = ~ i through Eq. (); Step 6: Compute the estimated positio ( x, y) = Iiw( i) Number of achor odes Fig. 3. Localizatio error versus the umber of achor odes. We assume that a uow ode ad 8 achor odes are radomly deployed i a 5m 5m regio, ad the uow ode is radomly placed i differet positios. We set PL= 6dB ad choose β =,.5,3,3.5, 4, 4.5, the zero-mea Gaussia oise N α has a stadard deviatio of 3dB. The simulatio results are as show i Table. From 3. Performace Evaluatio I this sectio, we aalyze the performace of the studied localizatio schemes through simulatios ad experimets. We compare the proposed weighted cetroid localizatio algorithm with WCL [3] ad AMWCL-RSSI [5]. We set the degree g = i all experimets. 3.. Localizatio Error Versus the Number of Achor Nodes I this experimet we evaluate the effect that the umber of achors has o the locatio accuracy. 44

6 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp Fig. 3 depicts the effect o localizatio error whe varyig the umber of achors. All odes are deployed i a m x m area. Achor odes are radomly deployed at the edge of the selected area, sesor odes are radomly placed i the regio. We assume that PL= 6dB ad the zero-mea Gaussia oise N α has a stadard deviatio of 3dB. We set β =. From Fig. 4, it ca be observed that WCLLS outperforms AMWCL-RSSI ad WCL i localizatio accuracy. The explaatio is that WCLLS icreases the weights of achors closer to the uow ode. It is also show that the icrease of the umber of achor odes ca reduce the localizatio error of WCLLS. Whe the umber of achor odes is 8, the average localizatio error of WCLLS is approximately.6 m which is sigificatly lower tha the average localizatio error of AMWCL-RSSI ad WCL. it is show that whe β is about, WCLLS ca obtai relative compariso small localizatio error. Whe the pass loss expoet β =, the average localizatio error of WCLLS is about.54 m. Localizatio error ( m ) AMWCL-RSSI WCL WCLLS.5..5 path loss expoet Localizatio error ( m ) AMWCL-RSSI WCL WCLLS Number of achor odes Fig. 4. Localizatio Error versus the Number of Achor Nodes. 3.. Localizatio Error Versus the Path Loss Expoet I this experimet we evaluate the effect that the pass loss expoet has o the locatio accuracy. Fig. 5 depicts the effect o localizatio error whe varyig the pass loss expoet. All odes are deployed i a m x m area. Four achors are respectively placed i four corers, sesor odes are radomly placed i the regio. We assume that PL= 6dB ad the zero-mea Gaussia oise N α has a stadard deviatio of 3dB. From Fig. 5, it ca be observed that as the pass loss expoet icreases, the error i locatio estimatio icreases for WCLLS. Whe β >., the average localizatio error of WCLLS is greater tha the average localizatio error of WCL. So, we ca see that the pass loss expoet has a importat impart o the localizatio error of WCLLS. Clearly, Fig. 5. Localizatio Error versus the Path Loss Expoet Localizatio Error Versus the Stadard Deviatio I this experimet we evaluate the effect that the stadard deviatio has o the locatio accuracy. Fig. 5 depicts the effect o localizatio error whe varyig the stadard deviatio. All odes are deployed i a m x m area. Four achors are respectively placed i four corers, sesor odes are radomly placed i the regio. We assume that PL= 6dB ad β =. From Fig. 6, it ca be observed that as the stadard deviatio icreases, the error i locatio estimatio icreases for WCLLS. Obviously, the stadard deviatio has a impact o the localizatio error of WCLLS. Additioally, WCLLS obviously outperforms WCL ad AMWCL-RSSI i localizatio error. Localizatio error ( m ) AMWCL-RSSI WCL WCLLS stadard deviatio Fig. 6. Localizatio Error versus the Stadard Deviatio. 45

7 Sesors & Trasducers, Vol. 76, Issue 8, August 4, pp Localizatio Error Versus Networ Size I this simulatio, we evaluate the effect the size of the etwor has o the locatio error. We simulated three etwor sizes: 5m x 5m, m x m ad m x m. Four achors are respectively placed i four corers, sesor odes are radomly placed i the regio. We assume that PL= 6dB ad β =, ad the zero-mea Gaussia oise N α has a stadard deviatio of 3dB. From Table, it ca be observed that as the etwor size icreases, the localizatio error icreases for all three localizatio algorithms. The explaatio is that the error of the RSS measuremet icreases as the etwor size icreases. It also ca be observed that WCLLS outperforms AMWCL-RSSI ad WCL i localizatio accuracy. From Table, we ca clearly ow that the average localizatio errors of WCLLS i three etwor sizes are respectively about. m,.53 m ad m. Table. Localizatio error. Localizatio algorithm 5 m 5 m m m m m (m) AMWCL- RSSI WCL WCLLS Experimets I this sectio, we aalyze the performace of the studied localizatio schemes through experimets. We compare the proposed algorithm with WCL ad AMWCL-RSSI. I this experimet, the proposed algorithm is tested i a m m regio of our Uiversity s campus law, achors are radomly placed i the regio ad a uow ode is placed i 5 differet positios. Fig. 7, a wireless ode is based o a MSP43 microprocessor ad equipped with a compliat Chipco CC5 wireless module. We obtai the measured distace by (). Table 3 shows the localizatio error of three localizatio algorithms i real experimet. I Table 3, the localizatio error of WCLLS is. m which is lower tha that of AMWCL-RSSI ad WCL. Clearly, WCLLS outperforms WCL ad AMWCL-RSSI i the localizatio accuracy. Table 3. Localizatio error. Localizatio algorithms Localizatio error (meters) AMWCL-RSSI 8.3 WCL 4. WCLLS. 4. Coclusios May weighted cetroid localizatio schemes have bee widely used for WSNs. However, these schemes do ot help, sice the localizatio errors are high i practical deploymets. To solve these problems, i this paper we have researched ad aalyzed may weighted cetroid localizatio algorithms ad RSS-based localizatio algorithms, ad we have proposed a localizatio scheme, called Weighted Cetroid Localizatio Algorithm Based o Least Square. WCLLS presets a Least-Square-based weight model which ca reasoably weigh the proportio of each achor ode i the uow ode. I the proposed weight model, firstly, we utilize least square method to compute the weight. Secodly, the proposed weight model icreases the weight of achor ode closer to the uow ode to estimate the locatio. Thirdly, the parameter is itroduced ito the proposed weight model, ad we get the optimal value of through our real experimets. We have aalyzed the performace of WCLLS through the etwor size, the umber of achor odes, the stadard deviatio ad the path loss expoet. All the experimetal results demostrate that WCLLS is superior to WCL ad AMWCL-RSSI i the localizatio accuracy. From the experimetal results, we ca see that WCLLS is also suitable for a outdoor eviromet. More importatly, WCLLS has a lower localizatio error. Acowledgemets The wor is supported by Natioal 863 Project (3AA4) ad the Project of Ahui Uiversity. Refereces Fig. 7. Sesor ode. []. D. Debashis, A Itegrated Method for Locatio Registratio of Mobile Termials Based o Time, Distace ad Zoe, Joural of Computatioal Itelligece ad Electroic Systems, Vol., No., 3, pp

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