Sensors & Transducers 014 by IFSA Publshng, S L http://wwwsensorsportalcom Wreless Sensor Network Localzaton Research Lang Xn School of Informaton Scence and Engneerng, Hunan Internatonal Economcs Unversty, Changsha, 41005, Chna Tel: 86-0731-8817113 E-mal: matlab_wf@16com Receved: 1 June 014 /Accepted: 9 August 014 /Publshed: 30 September 014 Abstract: DV-Hop algorthm s one of the mportant range-free localzaton algorthms It performs better n sotropc densty senor networks, however, t brngs larger locaton errors n random dstrbuted networks Accordng to the localzaton prncple of the DV-Hop algorthm, ths paper mproves the estmaton of average sngle hop dstance by usng the Least Equal Square Error, and revses the estmated dstance between the unknown node and the anchor node wth compensaton coeffcent consderng the wreless sensors deployed n the non-planar applcaton scenaros Ths localzaton algorthm s based on compensaton coeffcent Smulaton results show that the mproved algorthm has better locatng performance n locatng precson by ncreasng approprate computaton overhead, and s a feasble locatng scheme n WSN n both random dstrbutng and dynamc topology networks Copyrght 014 IFSA Publshng, S L Keywords: Wreless Sensor Networks (WSN), DV-Hop, Compensaton coeffcent, Localzaton, Algorthm 1 Introducton Wreless sensor networks (Wreless Sensor Networks, WSN) s composed of a large number of sensor nodes wth randomly dstrbuted structure, nformaton collecton, processng, self-organzng network forwardng can be done n ts cover area In WSN applcatons, the locaton nformaton of the sensor s crtcal to montor network actvty In montorng and trackng the target, routng based on the poston nformaton, load balancng of the network, the network topology, and other applcatons [1], these are requred to know the network node own poston n advance, the poston nformaton s appled n the communcaton and collaboraton process, and these applcatons are completed Thus, the wreless sensor network postonng technology s the foundaton of the entre network, whch acheves a varety of functons Exstng node localzaton algorthm can be dvded nto two categores n the dfferent locatng ways [], there are algorthm based on the dstance (range-based) and algorthm wthout dstance (rangefree) In postonng algorthm wthout rangng, DV-Hop (dstance vector-hop) algorthm s one of the typcal postonng algorthm, t s one of the dstrbuted localzaton methods, whch are proposed n advantage of dstance vector routng and postonng beacon nodes, the method s smple, and there s good scalablty [3-4], but t s the use of umpng dstance nstead of straght lne dstance, deal postonng effect s acheved only n the sotropc dense network In ths paper, because there are the lmtatons of DV-Hop algorthm n the randomly dstrbuted network envronment, the network average value per hop dstance s obtaned by usng mnmum mean square error method, and the mpact on the postonng results are taken nto account when montorng regon s non-planar, through the use of compensaton coeffcent, the fluctuaton of the montored area s reduced, the effects of the 106 http://wwwsensorsportalcom/htl/digest/p_361htm
calculatng dstance s down between the unknown node and beacon node calculaton, the postonng accuracy of the algorthm s mproved DV-Hop Localzaton Algorthm The basc dea of DV-Hop localzaton algorthm s that the dstance between unknown nodes and beacon nodes s equal to the product of the network average dstance of the per hop and the hop number between them When the dstance wth three or more beacon nodes s obtaned on the unknown node, ther own postonng can be realzed Its postonng s generally dvded nto three stages [-3]: Frst the dstance vector broadcast protocol s used between nodes and nformaton s forwarded, n all network nodes, the mnmum number of hops between each beacon nodes s obtaned; Secondly, after the poston of the other beacon nodes and a mnmum hop count are obtaned n the beacon node, the average network hop dstance s calculated, and then t s as a correcton s broadcasted to the network The frst correcton s only receved and record, and t s forwarded to the neghbor nodes, and then based on the smallest hop records, the hop dstance s calculated near each beacon node Fnally, when the dstances are obtaned from an unknown node to three or more beacon nodes, and the trlateraton method or maxmum lkelhood estmaton method are performed to calculate ther coordnates Beacon nodes,, k are shown n Fg 1, the lnear dstances d, d k can be calculated between them accordng to the dstance formula If the mnmum number of hops from to, and k s hops, and hops, k the average network hop dstance of the beacon node s obtaned by the followng formula to calculate HopSze ( x x ) + ( y y ) hops (1) The average dstance per hop s d + dk C hops + hopsk Assumng that p s to be postoned node, the number of hops s mnmum between beacon nodes and p, that dstance s mnmum from beacon nodes to p Thus, p obtans the average dstance value at each hop from, Cp C, the estmated dstance of each beacon node are Cphopsp, Cphopsp, C phops from p Then the pk poston of the node p s calculated by usng trlateraton d p d k Fg 1 Schematc dagram of a DV-Hop localzaton algorthm example 3 Improved DV-Hop Localzaton Algorthm DV-Hop localzaton algorthm s the exchange of nformaton based on network connectvty and dstance vector, the straght-lne dstance s nstead of hop dstance, and average hop dstance s only obtaned n the sotropc dense network, thus t s closer to the actual dstance value, otherwse there s an error larger [7] In the practcal applcaton, WSN nodes are generally randomly dstrbuted between the nodes and the beacon nodes, they are often not known lnear path, and the nodes are deployed n the montor area, these nodes are not completely n the same plane, and then the calculated resultng dstance s the estmated value from unknown nodes along the ground curve to the beacon nodes Ths s generally greater than the proecton of the dstance between unknown node and the beacon nodes n the horzontal plane [8] If you use ths estmate to calculate the coordnates of the unknown node, t wll exacerbate the error of the estmate coordnate values Ths secton s for DV-Hop algorthm lmtatons n the randomly dstrbuted network envronment Frst, the orgnal algorthm to calculate the average dstance per hop s mproved by usng mnmum mean square error method, and then the estmated dstance between the unknown node and the beacon nodes s corrected by usng the compensaton factor, the postonng accuracy of the algorthm s mproved 31 nmum ean Square Error ethod to Calculate the Average Hop Dstance The conventonal methods are to calculate the average each hop dstance value C by unbased estmaton, and because the Formula () value s equal to zero, the estmated value of the average hop dstance s obtaned [5] 1 f1 ( d C hops ), () m 1 k 107
m s the number of beacon nodes n network The average hop dstance value C s estmated by ths method, the mean of ther estmaton error s zero, but n general, the error meets the normal dstrbuton, accordng to the parameter estmaton theory, t s as the cost functon of estmaton error, usng the mean square error s more ratonal than ust to use varance or devaton [6] Therefore, we use the mnmum mean square error method to calculate the average hop dstance, f the Formula (3) s mnmzed the estmated value of the average hop dstance can be obtaned 1 f ( d C hops ) (3) m 1 If f 0, the average dstance per-hop can be C obtaned based on mnmum mean square error method, and the estmated value s as follow: C ( hops d ) hops (4) For example n Fg 1, the average hop dstance s obtaned by calculatng beacon nodes accordng to hops d + hopsk dk Formula (4), t s C hops + hops 3 Calculaton of Compensaton Coeffcent After the nter-node nformaton s mutually forwarded n the frst stage, each beacon node can get the coordnate nformaton of other beacon nodes and mnmum hops away At ths tme, the actual dstance of each beacon node the calculated to the other beacon nodes based on the dstance formula between two ponts, respectvely, and the average hop dstance s calculated accordng to Formula (4) For example, the coordnates of the beacon node and beacon node are respectvely ( x, y),( x, y ) Accordng to the dstance formula, the obtaned actual dstance between them s d, then the estmated dstance s d EST, whch s calculated based on the average hop dstance and mnmum hops between them, the dfference value between the estmated dstance and actual dstance s Δ d dest d, thus ths growth rato of two Δd beacon nodes s m Fnally, the d nformaton wth the average dstance per hop and growth rato wll be broadcasted n each beacon node, so that each unknown node receves the average dstance per hop and the growth rato of every par k beacon nodes, and ther values are stored Thus each unknown node wll obtan the followng data: (1) coordnate values of each beacon node; () to estmate the dstance between the node own and each beacon nodes; between (3) rato of ncreasng dstance between each par of beacon nodes Let the estmated dstance be d EST between the par of beacon nodes,, the ncreasng rato s m, the estmated dstance between unknown node p and beacon nodes, s respectvely d, d, then pest pest Dp dpest + dpest dest (5) D represents the devaton degree factor of p connectons n whch the unknown node p devate beacon nodes,, the greater D p, the greater the connecton whch the unknown node p devates from the beacon nodes, Snce a sngle m growth rato does not fully reflect the communcated state between the node p and the beacon nodes,, n order to maxmze the dstance between unknown nodes and beacon nodes closer to the actual dstance, the weghted average method s used [9], the compensaton coeffcent values of unknown node hops are calculated, and there are least ones of three beacon nodes Specfc methods are as follows: Assumng the known hops from the unknown node p to all beacon nodes, three beacon nodes are dentfed at least hops That s three beacon nodes nearest from an unknown node, they are beacon nodes,, k Frst, the degree of devaton factor s calculated from the unknown node p to the connectons between beacon node and all the other beacon nodes, e Dpt d pest + d pest dest t 1,,, n, and t, (6) where n s the number of nodes n the beacon To take the smallest three ones of the degree of devaton factors from unknown node p to the connecton lnes between beacon nodes and all other beacon nodes, they are Dp, D, 1 p D, and p 3 accordng to the weghted average method, the correspondng compensaton coeffcent p are calculated from the unknown node p to beacon node p m 1 m m3 + + D + D D + D D + D 1 1 1 + + D + D D + D D + D p1 p p p3 p3 p1 p1 p p p3 p3 p1, (7) where m 1, m, m are respectvely the smallest 3 three ones of the degrees of devaton factors from unknown node p to the connecton lnes between 108
beacon nodes and all other beacon nodes Smlarly avalable from unknown node p to beacon node, k, ther correspondng compensaton coeffcent are p, pk 33 The Dstance between Unknown Nodes to Beacon Node s Corrected by Usng the Compensaton Factor By the above method, we obtan the approprate compensaton factor of nearest three beacon nodes from the unknown node, the estmaton dstance between them can be corrected For example, the estmated dstance between the unknown node p and the beacon node s d, the approprate pest compensaton coeffcent s p, the corrected d pest dstance s d prev, Smlarly avalable, the 1 + p corrected dstances are dpest dpkest dprev, dpkrev from p to 1+ p 1+ pk beacon node, k Such corrected dstance nformaton of unknown node p s gotten after t got away from ts recent three beacon nodes the general postonng error s defned as the rato of error value between the estmated node poston and the actual node poston and communcaton radus that s as follow ˆ + ˆ (8) error ( x x) ( y y) / R wheren ( x, yˆ ) and ( x, y ) are the estmated poston and the actual poston of the unknown node, the average locaton error s defned as error error()/ un, error() s the postonng error of the unknown node, un s the number of unknown nodes In ths paper, DV-Hop algorthm has been mproved n two aspects: Frst, the network average, estmated value of each hop dstance s calculated by usng the mnmum mean square error method, the second, compensaton coeffcent s ntroduced to correct the estmated dstance between the unknown nodes and beacon nodes The smulaton s done n the mprovement method of the frst aspect, on ths bass, further mprovements are made n the smulaton method of the second aspect, the postonng accuracy s compared between the mproved algorthm and the orgnal algorthm, the smulaton results are shown n Fg and Fg 3 34 The Coordnates of the Unknown Node are Calculated After the dstance nformaton between unknown node and ts nearest three beacon node s obtaned by the above method, the coordnates of the unknown node are calculated by usng trlateraton However, the aforementoned calculated dstance from unknown nodes to the nearest three beacon nodes have some errors wth the actual stuaton, whch may cause that the trlateraton equatons has no soluton To avod ths stuaton, we use the least squares method [10] to calculate the fnal coordnates of unknown nodes [11-14] 4 Expermental Evaluaton By usng atlab, smulaton comparatve analyss s done on the DV-Hop localzaton algorthm and ts mproved algorthms based compensaton coeffcent Let node dstrbuton be 100m 100m square regon, the sensor nodes are randomly dstrbuted n the smulaton area, the number of nodes s mantaned at 150, each node has the same communcaton dstance R 35m, whch the coordnate poston of the beacon node s known, the unknown node coordnate poston s obtaned by algorthm The dfferent number of beacon nodes are set n smulaton, the average locaton error s compared n the dfferent algorthms In wreless sensor network postonng, Fg By dfferent methods, calculatng average postonng error of two algorthms n the average hop dstance As can be seen from Fg, when the number of partcpatng poston beacon nodes s ncreasng, the postonng error of the two algorthms s reduced In the begnnng, the postonng accuracy of the mproved algorthm s lttle dfference wth the orgnal algorthm, but wth the ncrease n the beacon nodes, by usng mnmum mean square error method, the calculated average network hop dstance s closer to the actual average dstance per-hop n random network, thereby the postonng error of nodes s effectvely reduced, wheren the lower maxmum value s reached to 8 % 109
the algorthm wll ncrease the cost How to mantan good locaton accuracy, whle reducng the overhead of communcaton and the amount of computaton s the future content of further study References Fg 3 SNR comparson of three algorthms In Fg 3, the estmated dstance between the unknown nodes and the beacon nodes s corrected further by compensaton coeffcents, and t s closer to the actual dstance, thus the postonng error of unknown nodes s further reduced, t can be seen from the fgure that the postonng error s reduced by an average of 15 % to 18 % n the mproved algorthm than tradtonal DV-Hop localzaton algorthm, postonng accuracy s sgnfcantly mproved When the number of beacon nodes s 60, n two algorthms, the mproved ampltude of the postonng accuracy becomes smaller, the average locaton error changes are stablzed In summary, the average error s always less n ths paper mproved postonng algorthm than the orgnal DV-Hop algorthm, and there s good stablty However, durng the executon of the algorthm, the growth rato n the many beacon nodes s broadcasted, and the compensaton coeffcents are calculated, the mproved algorthm of ths paper wll ncrease n terms of communcaton overhead and computaton than the orgnal algorthm 5 Conclusons and Outlook In ths paper, because there are the lmtatons of DV-Hop algorthm n the random dstrbuted network envronment, frst by usng mnmum mean square error method, the mprovements are made to the orgnal algorthm to calculate the average dstance per hop, and then the compensaton factor s ntroduced to correct the dstance between the unknown nodes and beacon nodes, DV-Hop algorthm s proposed based on a compensaton coeffcent Through smulaton, the mproved algorthm average locaton error s less than one of the orgnal algorthms, and there s good stablty However, the postonng accuracy s mproved n the mproved algorthm, whch s addng the amount of communcaton and the amount of computaton, and [1] Peng Yu, Wang Dan, A revew: wreless sensor networks localzaton, Journal of Electronc easurement and Instrument, 5, 5, 011 [] Sun Lmn, L Janzhong, Chen Yu, Wreless sensor networks, Tsnghua Unversty Press, Beng, 005, pp 149-151 [3] Nculescu D, Nath B, Ad-hoc Postonng System (APS), n Proc of the IEEE GLOBECO, San Antono, 001, pp 96-931 [4] Nculescu D, Nath B, DV Based Postonng n Ad hoc Networks, Journal of Telecommuncaton Systems,, 1-4, 003, pp 67-80 [5] J Wewe, Lu Zhong, Study on the Applcaton of DV-Hop Localzaton Algorthms to Random Sensor Networks, Journal of Electroncs & Informaton Technology, 30, 4, 008, pp 970-974 [6] Zhang Xanda, odern sgnal processng, Tsnghua Unversty Press, Beng, 00, pp 40-4 [7] Lu Shaofe, Zhao Qnghua, Wang Huaku, DV-Hop Localzaton Algorthm Based on Estmate of Average Hop Dstance and Correcton n Poston, Chnese Journal of Sensors and Actuators,, 8, 009, pp 1154-1158 [8] Xu Janbo, Lu Huya, Sensor localzaton algorthm n wreless sensor network based on dfferent plane, Computer Engneerng and Applcatons, 44, 4, 008, pp 115-117 [9] Huang Deka, You Tantong, Improved DV-Hop Algorthm Based on Hop Estmaton, Computer and odernzaton, 1, 01 [10] Ln Jnchao, Chen Bng, Lu Habo, Iteratve algorthm for locatng nodes n WSN based on modfyng average hoppng dstances, Journal on Communcatons, 30, 10, 009, pp 107-113 [11] Jan L, Janmn Zhang, Xande Lu, A Weghted DV-Hop Localzaton Scheme for Wreless Sensor Networks, n Proceedngs of the Internatonal Conference on Scalable Computng and Communcatons; the Eghth Internatonal Conference on Embedded Computng, 009, pp 69-7 [1] Bulusu N, Hedemann J, Estrn D, GPS-less low cost outdoor localzaton for very small devces, IEEE Personal Communcatons, 05, 000, pp 8-34 [13] Hongyang Chen, Kaoru Sezak, Png Deng, Hng Cheung So, An Improved DV-Hop Localzaton Algorthm wth Reduced Node locaton Error for Wreless Sensor Networks, Communcatons and Computer Scences, 08, 008, pp 3-36 [14] Koen Langendoen, Nels Reers, Dstrbuted Localzaton n Wreless Sensor Networks: A Quanttatve Comparson, Computer Networks, 003, pp 499-518 014 Copyrght, Internatonal Frequency Sensor Assocaton (IFSA) Publshng, S L All rghts reserved (http://wwwsensorsportalcom) 110