MDS and Trilateration Based Localization in Wireless Sensor Network

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1 Wreless Sensor Network, 011, 3, do:10.436/wsn Publshed Onlne June 011 (htt:// MDS and Trlateraton Based Localzaton n Wreless Sensor Network Abstract Shalaja Patl, Mukesh Zaver Deartment of Comuter Engneerng, Sardar Vallabhbha Natonal Insttute of Technology, Surat, Inda E-mal: {.shalaja, mazaver}@coed.svnt.ac.n Receved March 31, 011; revsed Arl 7, 011; acceted May 10, 011 Localzaton of sensor nodes s crucal n Wreless Sensor Network because of alcatons lke survellance, trackng, navgaton etc. Varous otmzaton technques for localzaton have been roosed n lterature by dfferent researchers. In ths aer, we roose a two hase hybrd aroach for localzaton usng Multdmensonal Scalng and trlateraton, namely, MDS wth refnement usng trlateraton. Trlateraton refnes the estmated locatons obtaned by the MDS algorthm and hence acts as a ost otmzer whch mroves the accuracy of the estmated ostons of sensor nodes. Through extensve smulatons, we have shown that the roosed algorthm s more robust to nose than revous aroaches and rovdes hgher accuracy for estmatng the ostons of sensor nodes. Keywords: Wreless Sensor Network, Localzaton, Multdmensonal Scalng, Trlateraton 1. Introducton The feld of Wreless Sensor Network () s a multdsclnary area of research offerng a wde varety of alcatons rangng from home to ndustry, medcal to mltary. Sensors ntegrated to structures [1], sread across a battlefeld [], and embedded n forest [3]; delver the sensed nformaton effcently, to take further acton for a artcular alcaton. Generally, these alcatons requre large scale networks wth hundreds of very small, battery owered and wrelessly connected nodes. Intrnscally nodes have lmtatons of battery ower, constraned communcaton comutatons and storage caablty. When a large number of nodes are to be used n the alcatons, these sensor nodes are requred to be cheaer, smaller n sze, and robust to sustan envronmental changes. Consderng all these lmtatons,.e., scalablty, storage, ower; develong accurate and effcent localzaton algorthm s a challengng task. Localzaton algorthm should ossess characterstcs of energy effcency, dstrbuted comutaton, scalablty, and hgh recson. Rado sgnal roagaton and message exchange consume consderable amount of energy of nodes, so algorthms need to run wth least communcaton between nodes due to energy scarcty. The lfetme of network ncreases f there s balanced energy consumton of every node, and ths requres an algorthm should referably be dstrbuted n nature. Also, t should be robust enough to nosy nut, mmune to node falure. Another mortant factor s that, t should be scalable, and even f the number of nodes s ncreased, algorthm s effcency should not be hamered. Smlarly, the localzaton algorthm needs to have hgh recson. The recson s measured by a rato of oston error and communcaton radus. Also, the algorthm should work wth mnmum densty of reference nodes. The reference nodes are known as anchor nodes. Usually, anchor nodes use GPS or are dsosed manually. Manual dsoston of large number of anchors s mossble for large scale s. Also, as GPS nodes are exensve, there s lmtaton on use of more number of anchors, and so the algorthm should rovde accurate estmaton wth low densty of anchor nodes. Consderng all these factors, determnng recse oston of each node s a dauntng task for a network wth large number of nodes. It s unlkely that localzaton of each node can be done accurately. Hence a lot of research s beng carred out for fndng out accurate or near to accurate ostons wthout usng GPS suort. Few technques were develoed to localze the nodes wth GPS free ostonng [4]. These algorthms yeld a relatve ma of the nodes sread across the hyscal area. Such technque s useful n alcatons lke drecton

2 S. PATIL ET AL. 199 based routng [5,6]. Few alcatons lke geograhcal routng [7], target trackng [8], and localzaton [9], need exact ostons of nodes. Multdmensonal Scalng (MDS) s one of the technques whch yeld two tyes of outut mas called relatve and absolute ma [10]. The ntal outut of MDS s relatve ma and s converted to absolute ma wth suffcent known locaton of nodes. MDS has ts orgn n sychometrcs and sychohyscs [11,1]. In lterature, a number of localzaton technques have been reorted whch use Multdmensonal scalng. It s a set of data analyss technques whch dslay dstance lke data as geometrc structure. Ths method s used for vsualzng dssmlarty data. It s often used as a art of data exloratory technque or nformaton vsualzaton technque. MDS based algorthms are energy effcent as communcaton among dfferent nodes s requred only ntally for obtanng the nter-node dstances of the network. Once all dstances are obtaned, further comutaton for fndng ostons does not need communcaton among nodes. In ths aer, we resent an energy effcent hybrd algorthm for localzaton of nodes usng MDS and trlateraton. MDS s not only energy effcent but also rovde good ntal or startng onts for any otmzaton technque [13]. In our roosed algorthm, ntal locatons are obtaned usng MDS and later these locatons are refned usng otmzaton method of trlateraton by adjustment. Trlateraton s bascally a surveyng technque whch nvolves the determnaton of absolute or relatve ostons of onts by measurement of dstances, usng the geometry of sheres or trangles [14]. Advantage of usng trlateraton by adjustment s that, t estmates locatons accurately gven good ntal onts. We have shown that, our roosed aroach rovdes hgher accuracy n estmatng the sensor node ostons as comared to revous aroaches reorted n the lterature. The next secton resents a bref overvew of related work n ths area. In Secton 3, the roosed algorthm s resented. Secton 4 deals wth the smulatons results for sotroc toology. Concluson s descrbed n Secton 5.. Related Works Locaton awareness s of great mortance for several wreless sensor network alcatons. Precse and quck self localzaton caablty s hghly desrable n wreless sensor network. Localzaton algorthms have been develoed wth varous aroaches. A detaled survey of localzaton technques s rovded n [15,16]. Localzaton technques can be classfed as range free or range based, deendng on whether the range measurement methods are used or connectvty nformaton s used. Range based methods requre range measurement nformaton, such as Receved Sgnal Strength Indcator (RSSI) [17], Angle of Arrval (AOA) [18], Tme of Arrval (TOA) [18] and Tme Dfference of Arrval (TDOA) [18] etc. However, the measurement accuracy of these methods can be affected by the envronmental nterference [15]. Though, range free methods [19] cannot rovde accurate locaton estmaton, they are cost effectve and robust to nose snce range measurements are not nvolved n t. The range-based methods have connectvty or roxmty nformaton between neghbor nodes who can communcate wth each other drectly. A trangulaton based method s resented n Adhoc Postonng System (APS) by Nculescue and Nath [0]. Three methods are roosed by authors namely, DV- Ho, DV-Dstance and Eucldean dstance. In DV-Ho method only connectvty nformaton s used, whereas n DV-Dstance, the dstance measurements between neghborng nodes are used, and Eucldean uses the local geometry of the nodes. Intally anchors flood ther locaton to all the nodes n the network and every unknown recever node erforms trangulaton to three other anchor nodes to estmate the oston. These methods do not erform well wth ansotroc or rregular network toology. Savarese [1] mroved Nculescu s algorthm by ntroducng refnement hase. In ths hase, dstance measurements between neghborng nodes are used to mrove localzaton accuracy. Though accuracy s mroved sgnfcantly, t only works for well connected nodes. In another trangulaton based aroach [], a technque of teratve multlcaton s used. It rovdes good results f the number of anchor nodes s hgh. Nodes connected to 3 or more anchors comute ther oston by trangulaton and ugrade ther locaton. Ths oston nformaton s used by the other unknown nodes for ther oston estmaton n the next teraton. Nculescue and Nath s algorthm of APS [0] s refned usng trlateraton by adjustment by Feng Tan and We Gao, called as LATN [3]. In ths method wth DV-Ho or DV-Dstance the ostons are estmated and trlateraton s erformed on unknown nodes for reducng the localzaton error. Savvdes [4] used least squares estmaton wth Kalman flter to locate the ostons of sensor nodes to reduce error accumulaton n the same algorthm. Ths method needs more anchors to work well than other methods. Doherty [5] used aroach of convex otmzaton usng semdefnte rogrammng (SDP). The connectvty of the network has been reresented as a set of convex localzaton constrants for the roblem of otmzaton. Ths method works well, f anchor nodes are laced on the outer boundary, referably at the corners. When all anchors are laced n the nteror of the network, a large estmaton error s obtaned due to the shft

3 00 S. PATIL ET AL. of oston estmate of outer nodes towards the center. Bswas [6] has extended the technque of Doherty s algorthm [5] by takng the non- convex nequalty constrants. Bascally, ths technque converts the non- convex quadratc dstance constrants nto lnear constrants wth ntroducton of relaxaton to remove the quadratc term of the equaton. The dstance measurements among nodes are modeled as convex constrants, and semdefnte rogrammng (SDP) methods were adoted to estmate the locaton of nodes. Bswas's method was further mroved by Tzu-Chen Lang [7], usng a gradent search technque. The man dsadvantage of semdefnte rogrammng s amount of comutaton, whch s O(n 3 + c 3 ), where n s the number of rows (or columns) of the matrx and c s the number of constrants [8]. Shang et al. [13] resented a centralzed algorthm based on MDS, namely, MDS-MAP(C). Intally, usng the connectvty or dstance nformaton, a rough estmate of relatve node dstances s obtaned. Then, MDS s used to obtan a relatve ma of the node ostons and fnally an absolute ma s obtaned wth the hel of anchor nodes. The ntal locaton estmaton s refned usng least square technque n MDS-MAP(C,R) [13]. Both technques work well wth few anchors and reasonably hgh connectvty. 3. Proosed MDS-RT Algorthm The refnement ste n MDS-MAP(C,R) s slower than MDS tself. To further mrove the accuracy and comlexty of localzaton, we are roosng a hybrd algorthm here, namely, MDS wth refnement usng trlateraton by adjustment (MDS-RT). As dscussed earler n ths aer, MDS s energy effcent localzaton method, so t has been used n the roosed algorthm. The accuracy of estmates obtaned usng MDS deends uon the accuracy of sensor observatons. The oor accuracy of sensor observatons results nto oor estmates of locatons. To overcome ths roblem, the method of trlateraton by adjustment s used as an otmzaton tool. The estmates obtaned usng MDS are refned usng trlateraton method whch ncreases the recson of estmates. The MDS-RT algorthm s descrbed n the followng secton. Frst, MDS technque s revewed and ntroduced n bref. There are many tyes of MDS technques and usually classfed accordng to the way smlarty/ dssmlarty data or matrx s formed. One way of classfcaton s whether the smlartes data are qualtatve or quanttatve. Qualtatve and quanttatve MDS are also known as Nonmetrc, and Metrc MDS resectvely [10]. The Non-metrc MDS (NMDS), also called as ordnal MDS, s develoed by Sheard [1]. In NMDS, a monotonc relatonsh between nter-ont dstance and desred dstance s establshed and assumed that data s measured at ordnal level. Accordng to the number of smlarty matrces and the nature of the MDS model, MDS s classfed as classcal MDS (CMDS), relcated MDS (RMDS), and weghted MDS (WMDS). In CMDS sngle matrx s used whereas, RMDS and WMDS requre several matrces. The RMDS uses unweghted matrces, whereas WMDS uses weghted matrces [10]. The dstance model of weghted MDS uses dfferent weght to each dmenson. Another way of classfcaton of MDS s determnstc or robablstc [11]. In determnstc MDS each object s reresented as sngle ont whereas robablstc MDS uses robablty dstrbuton n the MDS sace. In our roosed algorthm, we have used CMDS, where data s quanttatve and object roxmtes are dstances n Eucldean sace. Ths algorthm conssts of two hases; frst hase s localzaton usng MDS and second refnement usng trlateraton by adjustment Localzaton Usng MDS Nodes are randomly scattered n the regon of consderaton. Let j refer to the roxmty measure between objects and j. The smlest form of roxmty can be reresented usng Eucldean dstance between two objects. Ths dstance n m dmensonal sace s gven by (1) m j ak bk (1) k 1 d X X Where, X x, x,, x and X x, x,, x a a1 a am b b1 b bm are dstance vectors. The stes of localzaton usng MDS are llustrated as follows: STEP 1: Obtan the dstance between all ar of nodes usng any rangng technque to construct dstance matrx for MDS. Run the shortest ath algorthm such as Floyd s or Djktra s algorthm to get all dstances and comlete the dstance matrx. STEP : Comute the matrx of squared dstances of roxmtes namely D. 0 d n d1 0 d3.. dn D () dn 1 dn dn3.. 0 STEP 3: Aly double centerng to matrx of D. In CMDS, roxmty matrx P.e. D s shfted to the center. Centerng s lacng the centrod of the confgu- d

4 S. PATIL ET AL. 01 raton of onts at orgn. It s requred to overcome the ndetermnacy of the soluton due to arbtrary translaton. Double centerng s done by multlyng both sdes of () by centerng matrx, 1 T J = I 11 (3) n Here, I s Identty matrx of n n sze, where n s number of nodes and 1 s a vector of ones. Double centerng of squared dstance matrx leads to equaton (4) B dc JD J (4) STEP 4: Comute sngular value decomoston (SVD) of double centered matrx B dc.. Perform SVD on B- T B QAQ (5) Where A dag( 1,,, n ) ; s the dagonal matrx of egen values and Q s the matrx of corresondng egenvectors. STEP 5: Modfy SVD outut of matrx B accordng to dmensons. To get soluton n lower dmenson we have to retan the frst m largest egenvalues and egenvectors. Ths s the best low rank aroxmaton n the least-squares sense. For examle, for a D network, consder the frst largest egenvalues and egenvectors to construct the best D aroxmaton. The modfed B now becomes B dc B Q AQ (6) T STEP 6: Obtan coordnates from matrx B. The coordnate matrx can be estmated from B usng Q 1 and A 1 as shown n followng equaton 1 X QA 1 1 (7) Ths coordnate matrx gves relatve ma. STEP 7: Transform relatve ma to absolute ma usng anchor nodes. The recovered matrx X s rotated, translated, shfted as t has dfferent orentaton than orgnal. 3.. Refnement Usng Trlateraton by Adjustment Once the estmaton of dstance matrx usng RSSI and consequently the locaton estmaton by MDS are erformed, the next ste s to refne the locatons. For ths task the technque of trlateraton by adjustment s used as ost otmzaton tool. The trlateraton refnes the estmates usng successve adjustments. Here, every lnk s assgned a weght accordng to the sgnal qualty. Frst, trlateraton by adjustment s revewed n bref and then stes of refnement are llustrated. Consder Fgure 1, consstng of two onts P and Q. Fgure 1. Lnk PQ. Let the estmated coordnates of P and Q be P( X, Y ), Q ( X q, Y q) and true coordnates be P ( X, Y ), Q ( X q, Yq) resectvely. The dstance between them s lnk value of PQ exressed as L. The true dstance.e. Eucldean dstance can be exressed as n (8)- L X X Y Y q q The relaton between X and X and remanng coordnates s gven by followng set of equatons. X X x, Y Y y X X x, Y Y y q q q q q q In (9), varables x, y, xq, y q are the correctons n estmated coordnates, whch gve us adjusted values n lnk L. L L v (10) Where v s correcton n L. Accordng to Taylor s exanson, above equaton can be wrtten as: X X Y Y L Z x x y y q q q q q Z q Z q Where q q q (8) (9) (11) Z X X Y Y (1) Let the correcton n lnk PQ be l, and relaton between l and v can be obtaned usng (10) and (11): X q X Y q Y v l x x y y (13) q q Z q Z q Where l L Z q Consder Fgure, consstng of known nodes A(X 1, Y 1 ), B(X, Y ), and C(X 3, Y 3 ) and unknown node D(X 4, Y 4 ). The lnks between nodes are ad, bd, cd, ab, ac, and bc. As seen before, the lnk value obtaned by rangng devce may not be equal to Eucldean dstance due to resence of nose. Let varances of the lnk ad, bd, cd be σ ad, σ bd σ cd, and σ 0 be the varance of unt weght whch s selected arbtrarly. From these values lnk weght can be comuted as - σ W ( = ad, bd, cd) (14) σ 0 STEP 1: Form a cluster of four nodes as shown n Fgure, Obtan the weght matrx W.

5 0 S. PATIL ET AL. T 1 B WB T B Wf (0) The fnal estmated coordnates are- X, Y X, Y 4 4 new 4 4 old (1) STEP 5: Obtan correcton vector v to the lnk The corresondng correcton n dstance v can be obtaned from above equaton as- Fgure. Trlateraton. The Eucldean dstance between known and unknown nodes of Fgure can be exressed as- d X4 X Y4 Y (15) Where vary from 1 to 3. The objectve functon can be formed from (15) f d X X Y Y (16) STEP : The frst estmate of ostons s obtaned wth frst hase. These values are used as ntal values of non-anchor node (X 4, Y 4 ). STEP 3: Usng lnk value between all the four nodes and objectve functon as gven n (16), obtan Jacoban matrx J and f vector of objectve functons. F1 X F1 Y B F X F Y (17) F 3 X F3 Y Functons F1, F, F3 are evaluated at X 4 and Y 4. The vector matrx f can be obtaned by: F1X4, Y4 f FX4, Y4 (18) F3X4, Y4 Now, we wll comute correctons n coordnates (Δ) and n lnk value (v). STEP 4: Obtan correcton vector Δ, of the coordnates (X 4, Y 4 ). Solvng (16) for fndng correctons Δ n (X 4, Y 4 ), we get 4c 4c X, Y (19) Where Δ s comuted by followng equaton v f B*Δ () So the estmated values of dstance for correcton n (X 4, Y 4 ) s d d v (3) ˆ Here v can also be obtaned by followng equaton 4new 4old 4new 4old v X X Y Y (4) STEP 6: Estmate new lnk value for (X 4, Y 4 ) X, Y X, Y X, Y (5) 4new 4new 4 4 4c 4c STEP 7: Kee teratng for new values of (X 4, Y 4 ) tll Δ vector values.e. correcton n coordnates does not reach the redetermned recson value or gven number of teratons are not comleted. The refned estmate of oston of a non-anchor node obtaned usng the stes descrbed above allow us to use ths node as an anchor node for refnng the ostons of other non-anchor nodes. STEP 8: Reeat stes 1 to 7 for remanng non-anchor nodes. Thus, correcton n oston s determned by lnk measurement error and number of teratons s determned by ntal oston error of nodes. If ths error s less, number of teratons requred s less. Also, f lnk measurement recson s hgh, the fnal oston error wll be low. The trlateraton method tself suffers from oor accuracy due to errors n rangng measurements. Our roosed algorthm overcomes ths roblem as ntal locatons are estmated by MDS algorthm and ths serve as good ntal estmates for trlateraton method. The advantages of our roosed algorthm are: 1) The oston accuracy s hgh. ) The algorthm reles on no exlct communcaton other than that between mmedate neghbors, whch avods excessve communcaton. 3) It s robust even when the measured dstance between the neghborng nodes s degraded wth nose Comlexty Analyss Frst Phase (MDS-MAP(C)): In ths algorthm, to comlete the dstance matrx, shortest ath (Floyd s) algo-

6 S. PATIL ET AL. 03 rthm s aled. Its tme comlexty s O(N 3 ), where N s the number of nodes. MDS uses sngular value decomoston (SVD) of matrx B. The comlexty of SVD s O(N 3 ). The result of MDS s a relatve ma that gves locaton of nodes, relatve to each other. The relatve ma s transformed to absolute ma through a lnear transformaton, whch may nclude scalng, rotaton and reflecton. Comutng the transformaton arameters takes O(k 3 ) tme, where k s the number of anchors. Alyng the transformaton to the whole relatve ma to obtan absolute ma takes O(N) tme. Refnement Phase (MDS-MAP(C,R)): Refnement hase use Levenberg-Marquardt algorthm. Its comlexty s O (N 3 ), where N s number of nodes. Refnement Phase (MDS-RT): The basc trlateraton algorthm does j teratons (here 10) n worst case. For N number of nodes j(n-3) tmes the algorthm wll run. If the rado range of anchor s less and all nodes are not n range of three anchors, then nearest (at a dstance of sngle ho) localzed node wll start actng as seudo anchor node. Thus n worst case the comlexty wll be O(jN ) as the algorthm wll run for j(n-3)(n-3) tmes and n best case comlexty wll be O(jN). the effect of varous factors lke dfferent node densty, range error, connectvty and anchor nodes on RMSE. We erformed Monte-Carlo smulatons and the number of smulatons for each exerment s set to 50. Errors are normalzed wth rado range. We have smulated and comared erformance of our roosed algorthm MDS- RT wth standard algorthms MDS-MAP(C) and MDS- MAP(C,R) resectvely. Fgure 3 shows 50 and 100 nodes randomly laced n 10l 10l square area. Lnes between onts show connectvty of nodes at connectvty level of 9 and 6.1. Above fgure shows connectvty of 50 and 100 nodes wth 0% error n rado range. Here, the connectvty or connectvty level reresents the average number of nodes connected wth each other n the network,.e., the average number of nodes wthn the rado range of a artcular node. Fgure 4 shows the connectvty nformaton for 00 nodes wth connectvty level of 1.5 and 10% range error. Fgure 3 & 4 reresent the scenaros wth low node densty to hgh node densty. In these fgures, lne jonng nodes are connectvty lnks. Fgure 5(a) & (b) show scatter-lots of 00 nodes 4. Exermental Results We have erformed exhaustve smulatons wth varyng number of nodes. Tycally, the number of nodes s vared from 50 to 00. These nodes are laced randomly wth a unform dstrbuton n a square area of 10l 10l of l unt length. The erformance of MDS-RT has been examned for varous rado ranges wth dfferent range errors, anchors and node denstes. Rado range s blurred wth nose to ntroduce error n rado lnk. Presently the dstance-only case of MDS-MAP s consdered, where each node knows dstance to each neghbor node. An unform rado roagaton s consdered. The erformance measure used for evaluaton s root mean square error (RMSE), as shown n (6). (a) X X Y Y N (6) RMSE j j Where (X, Y ) are estmated locatons, (X j, Y j ) are corresondng true locatons, and N s number of nodes. As rado range ncreases, connectvty ncreases, leadng to connectng more number of nodes of the network. For observng effect of ncrease n range error and connectvty on RMS error, the range error s ncreased from 5% to 50% of communcaton range and connectvty s ncreased from 1.5 to 45 for 00 nodes. Ths allows evaluatng our roosed method wth worst scenaros. The smulatons are erformed wth varyng number of anchor nodes from 4 to 10. Followng secton descrbes Fgure 3. Network connectvty wth (a) 50 and (b) 100 nodes. (b)

7 04 S. PATIL ET AL. Fgure nodes laced randomly at connectvty of 1.5 and 10% error. (a) wth connectvty of 1.6 and range error of 0% for MDS-MAP(C) and MDS-RT resectvely. Orgnal ostons are shown by symbol O, estmated ostons by * (astersk) and anchor ostons by sold damonds. Black lnes show error. Longer the lne, larger s the error. Same nomenclature s alcable to all the remanng scatter-lots. The RMSE obtaned n Fgure 5(a) s 18.5% wth MDS-MAP(C) and n Fgure 5(b), t s 0.04% wth MDS-RT. Wth ncrease n rado range, connectvty between nodes s ncreased and more number of nodes artcates n network formaton. Fgure 6 shows connectvty Vs RMSE wth 4 anchor nodes and 5% error n rado range for all the three algorthms. RMS Error decreases from 11.4% to.7% for MDS-MAP(C) when connectvty level s ncreased from 1.63 to Smlarly, reducton n RMSE can be observed for MDS-MAP(C,R) and MDS-RT as well. The RMSE obtaned for MDS- MAP(C,R) and MDS-RT at connectvty of 6. are 1.5% and 0.7% resectvely. Wth connectvty level of these values are 0.83% and 0.033% resectvely. As the number of anchor nodes s ncreased the total RMSE decreases. Fgure 7 shows a comaratve lot of RMSE vs. connectvty wth 5% nose and 6 anchors. The average RMSE obtaned at connectvty of for MDS-MAP(C,R) s 1.11% and for MDS-RT t s 0.05% resectvely whch s a very large reducton n RMSE usng our roosed algorthm. Ths result shows that our roosed MDS-RT outerforms MDS-MAP(C,R) algorthm. A sgnfcant amount of reducton s observed n RMSE of MDS-RT as the anchor nodes are ncreased from 6 to 10 whch s dected n Fgure 8. At connectvty of 6. and the amount of RMS Error s [1.67%, 0.68%] for MDS-MAP(C,R) and [0.19%, (b) Fgure 5. Scatter lot of 00 localzed nodes wth (a) MDS- MAP(C) and (b) MDS-RT. Fgure 6. RMSE vs. connectvty wth 5% range error and 4 anchors.

8 S. PATIL ET AL. 05 Fgure 7. RMSE vs. connectvty wth 5% error and 6 anchors. Fgure 8. RMSE vs. connectvty level wth 5% range error and 10 anchors %] for MDS-RT resectvely. Thus the accuracy ncreases by about 45% for connectvty of The effcency and excellent erformance of the roosed algorthm s very much evdent from these grahs. Secfcally when number of anchor nodes s 10, RMS error obtaned s neglgble and t s shown as zero here. When smulatons were erformed for 10% range error, RMSE obtaned at connectvty of 1.6 s 4.e-04, and as the rado range goes on ncreasng, the error goes on decreasng. At connectvty level of 45, error s reduced to.1e-05. Next, we wll analyze erformance of algorthm n resence of varous levels of nose. It s obvous that wth ncrease n nose level, RMSE wll also ncrease. The comaratve lot of effect of ncrease n range error on RMSE usng all three methods s shown n Fgure 9. It s obtaned at connectvty level of 9.1 wth 6 anchors. Fgure 9. Effect of ncrease n rage error on RMSE. When the range error s ncreased from 5% to 50% (worst scenaro), the RMSE ncreases from 3.9% to 8.1% for MDS-MAP(C), 0.87% to 4.45% for MDS-MAP(C,R) and 0.067% to.35% for MDS-RT resectvely. Wth ncrease n the number of anchors, the locaton estmate s more accurate and reducton n RMSE s observed. When range error s ncreased to 10% the effect on RMSE s seen as shown n Fgure 11. Comarng Fgures 10 and 11, t can be observed that, the RMSE of MDS-MAP(C) ncreases to 9.6% from 9.%, when error ncreases from 5% to 10% wth 4 anchors. Wth MDS-MAP(C,R), RMSE ncreases from 1.3% to 1.5%, and wth MDS-RT t ncreases from 0.4% to 0.7% resectvely. Wth 10 anchors, RMSE of MDS-RT ncreases from 0.08% to 0.038% whereas MDS-MAP(C,R) ncreases from 0.5% to 0.9% resectvely. Table 1 shows the erformance of all three algorthms wth 4, 6, and 10 anchors. The data shows the effect on RMSE wth 5% and 10% range error at connectvty of Fgure 10. Effect of ncrease n number of anchors on RMSE wth 5% range error.

9 06 S. PATIL ET AL. Fgure 11. Effect of ncrease n number of anchors on RMSE wth 10% range error. Table 1. Performance comarson at connectvty of 6.. Range Error (%) MDS-MAP(C) 4 Anchors Anchors Anchors RMSE(%) ths roblem. As MDS rovdes good ntal estmate of locatons, even though the anchor nodes are collnearly located, trlateraton refnes the estmated locatons only. If anchors are not n rado range of each other or non-anchor nodes are not n the range of anchor nodes then algorthm may gve erroneous results. However, ths roblem can be overcome wth dense network toology. Fgure 1 shows the localzaton usng MDS-MAP(C) and MDS-RT for 50 nodes when nodes are laced colnearly. At connectvty of 1.6, wth 0% range error and 4 number of anchor nodes, the RMS Error s 50% for MDS-MAP(C) and 15% for MDS-RT. As the densty of nodes ncreases, wth less rado range also nodes start communcatng as they get enough connectvty. Fgure 13 and 14 show smulaton for 100 and 00 nodes wth 0% range error. At connectvty of 6.1 wth range error of 0%, RMSE obtaned s 37% and 0.% for MDS-MAP(C) and MDS-RT resectvely for 00 nodes. From all the grahs and scatter-lots, t s clear that our roosed algorthm MDS-RT outerforms MDS- MAP(C,R) algorthm. If accuracy s not to be comro- MDS-MAP(C,R) 4 Anchors Anchors Anchors MDS_RT 4 Anchors Anchors Anchors The RMSE s normalzed to rado range and ercentage error s comuted. As t s clear from above fgures and Table 1, our roosed method erforms better than MDS-MAP(C,R). As can be seen from Fgure 11, the error aroaches nearly to zero even n the case of 10% range error. The remarkable dfference s seen when number of anchor nodes are hgh.e. > 5 and connectvty > 6.1. We have also erformed the smulaton of lacng anchor nodes colnearly for 50, 100 and 00 nodes. Placement of anchors lays a very mortant role n any localzaton algorthm. Ths s very mortant to note that the trlateraton method fals, f anchor nodes are collnearly located. The roosed algorthm MDS-RT overcomes (a) (b) Fgure 1. (a)(b): Scatter lot of 50 nodes for MDS-MAP(C), and MDS-RT.

10 S. PATIL ET AL. 07 (a) (b) Fgure 14. (a)(b): Scatter lot of 00 nodes localzed wth MDS-MAP(C) and MDS-RT. msed, then at the cost of ncreased rado range or more anchors, the algorthm erforms best. 5. Conclusons (b) Fgure 13. (a)(b): Scatter lot of 50 nodes wth MDS- MAP(C), MDS-RT. Localzaton usng Multdmensonal Scalng s one of the robust algorthms n the lterature of localzaton n sensor network. MDS-MAP(C) has roved ts effcency as comared to other algorthms lke SDP, APS etc. Error n basc MDS-MAP(C) has been mroved n MDS-MAP(C,R) algorthm. However, MDS-MAP(C,R) s comutatonally ntensve. We have shown that, f refnement ste s erformed usng trlateraton by adjustment (MDS-RT), the algorthm not only becomes comutatonally lght weght but also sgnfcant error reducton s observed and more accurate results are obtaned. The current work assumes that the network s sotroc. The roosed method may be extended to a network wth rregular toology as a future work. 6. References (a) [1] M. L and L. Yunghao, Underground Structure Montorng wth Wreless Sensor Networks, Proceedngs of Internatonal Symosum on Informaton Processng n Sensor Networks, Cambrdge, 5-7 Arl 007, do: /ipsn [] N. Alsharab, L. R. Fa, F. Zng and M. Ghurab, Wreless Sensor Networks of Battlefelds Hotsot Challenges and Solutons, Proceedngs of the 6th Internatonal Symosum on Modelng and Otmzaton n Moble, Ad Hoc and Wreless Networks and Workshos, Berln, 1-3 Arl 008, do: /wiopt [3] M. Hefeeda and M. Bagher, Wreless Sensor Networks for Early Detecton of Forest Fres, Proceedngs of Internatonal Conference on Moble Ad Hoc and Sensor

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