Study of the Improved Location Algorithm Based on Chan and Taylor

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1 Send Orders for eprnts to 58 The Open Cybernetcs & Systemcs Journal, 05, 9, 58-6 Open Access Study of the Improved Locaton Algorthm Based on Chan and Taylor Lu En-Hua *, Xu Ke-Mng and Jang Yu Jangsu College of Informaton Technology, Wux, Chna Abstract: Combnng the advantages of Chan algorthm and Taylor seres expanson method, the artcle has proposed an mproved localzaton algorthm n the LTE postonng system. The algorthm elmnates much devaton of the postonng results n Chan algorthm, offers the optmzed result as the ntal value of Taylor seres expanson method, then get the weghted sum of the postonng of the results of the two nds of algorthm, fnally put the fnal result as the locaton of the moble staton coordnates. Expermental results show that the proposed algorthm can effectvely mprove the postonng precson n the nose envronment. Keywords: Chan algorthm, Taylor seres method, Improved locaton algorthm, Postonng accuracy, Poston Coordnates.. ITODUCTIO Chan algorthm [] s one nd of locaton algorthm whch has analytcal solutons, and solves the locaton coordnates of moble statons on the bass of least square method (LS or weghted least square method (WLS. Ths algorthm uses non-recursve method to conduct resoluton on hyperbolc equatons. The basc concept of Chan algorthm s: frstly, one ntermedate vable s used to convert nonlnear equaton nto lnear equaton, and the locaton coordnates of moble statons are rough estmated by usng weghted least square method, then the locaton coordnates and other constrant condtons are rough estmated, the locaton coordnates of moble statons are precsely estmated by usng weghted least square method agan and the ultmate coordnate could be obtaned. Taylor seres expanson method [] s one nd of recursve algorthm. Its basc concept s: frstly, one ntal estmates locaton value of moble staton s needed, then Taylor seres expanson s conducted on ths locaton, the nonlnear equaton could be converted nto lnear equaton by gnorng second order and above second order terms, then least square method s used to estmate, each obtaned results by recurson s used n locaton correcton of moble statons to mprove the precson of estmate, fnally the estmated locaton could approach the real locaton of moble statons s dfferent Compared wth Chan algorthm, Taylor seres expanson method has no analytcal soluton and ts operaton s relatvely complcated. Besdes, the ntal estmated locaton value of moble staton could not devate from the real locaton excessvely, otherwse Taylor seres expanson wll not convergence.. MODIFIED LOCATIO ALGOITHM BASED O CHA AD TAYLO The classc Chan algorthm could attan all TDOA by measurng, and obtan a specfc analytcal soluton, however, the performance would be affected n LOS envronment. Taylor seres expanson method could conduct recursve operaton on the ntal estmated locaton value of moble staton and contnuously correct the estmated locaton value of moble staton to mae t approach the real locaton value, however, ths algorthm would sgnfcantly affected by the ntal locaton, and the operaton process s rather complcated. Therefore, we can explore some locaton algorthm to obtan one relatvely precse ntal locaton at frst, then the obtaned ntal locaton can be used to conduct resoluton wth Taylor seres expanson method and fnally the locaton result whch s more precse wll be receved. The lterature [3, 4] presented a locaton algorthm whch was based on Fang algorthm and Taylor seres expanson, t elmnated the locaton estmaton whch had elmnated the estmated locaton value whch devated excessvely to mprove the precson of locaton. The lterature proposed another synergy locaton algorthm, t conducted weghted calculaton of the results attaned by dfferent locaton algorthm, and the estmated value whch had been treated was used as the locaton coordnates of moble staton. Accordng to the thoughts n lterature, we present a modfed locaton algorthm whch s based on Chan algorthm and Taylor seres expanson. Assumed that the base staton of communty where the moble staton s located s noted as o., and meanwhle t act as the servng base staton for the locaton system. If the measured TOA of base statons has been attaned, these TOA values are subtracted from the measured TOA values of servng base staton and ( - TDOA values would be got. If data of the nvolved m(mn- base statons s always used durng each locaton, m TDOA values can be randomly 874-0X/5 05 Bentham Open

2 Study of the Improved Locaton Algorthm Based on Chan and Taylor The Open Cybernetcs & Systemcs Journal, 05, Volume 9 59 chosen from these ( - ones to become one group and t has C m nds of possbltes. Chan algorthm s used to obtan the ntal estmated locaton value of moble staton under C m nds of condtons respectvely. It s noted as ( xˆ, besdes,,,, C m. Wth the ncreasng dstance between moble staton and base staton error of the estmated ( xˆ also ncreasewhch would sgnfcantly affect the ultmate estmated locaton result of moble staton, therefore, the ntal estmated values whch devates excessvely should be elmnated accordng to some dscplnes. ( xˆ should be elmnated when the followng condton was satsfed x xˆ + ( y threshold ( Where, threshold s one threshold, whch could be alternatve to control the error of ( xˆ as requred. Assumed that estmated values of ntal coordnates remaned after elmnatng the values whch devates excessvely, the values of the coordnates are averaged and got: ( xˆ ( x 0 ( y0 ( x 0 0, y s the ntal estmated locaton value of moble statons whch s attaned wth Chan algorthm. ( x, y s 0 0 substtuted nto Taylor seres expanson method to conduct recursve resoluton and one locaton result could be attaned. The locaton results attan wth Chan algorthm and Taylor seres expanson method should be weghted (Fg.. The resdual between the measured value and locaton result s defned n the lterature [4]: ( ˆ (3 es Where, ˆ ( xˆ x + ( y, ( x, ˆ s the obtaned locaton coordnates of moble staton wth locaton algorthm, (x,y s the coordnates of o. base staton nvolved n locaton, s the obtaned dstance between the moble staton and o. base staton accordng to TOA value, s the amount of base statons nvolved n locaton. When some locaton algorthm s adopted, f es s relatvely small, t demonstrates that the obtaned coordnate locaton of the moble staton usng ths algorthm s more precse; f es s relatvely large, t ndcates that errors of the obtaned results usng ths algorthm s relatvely large. The algorthm whch s more precse should mae up larger proporton n ultmate weghtng. The calculaton formula of weghng coeffcent s gven n lterature [5]. If nds of locaton algorthms are used to conduct operaton on the same group of TDOA, respectvely, weghtng coeffcent of o. locaton algorthm could be expressed as: es ( ˆ ( ( xˆ x + y besdes, ( xˆ s obtaned locaton result by usng o. locaton algorthm, so the ultmate locaton coordnate of xˆ s: moble staton ( K ( xˆ K xˆ (5 ( K K Chan algorthm Elmnate the excessve error of locaton result Calculatng the average esult of Chan algorthm Taylor seres expanson esult of Taylor seres Fg. (. Flow chart of modfed algorthm based on chan and taylor. 3. SIMULATIO AD AALYSIS Smulaton s carred out ndependently for 000 tmes on Chan algorthm, Taylor seres expanson method and the modfed locaton algorthm whch s based on Chan and Taylor, respectvely. The model of multple base staton s used n smulaton. Assumed that the locaton system contans seven base statons, and the communty radus s 000 meters, schematc dagram of dstrbuton of base statons are shown n (Fg.. The measured TDOA [6] values whch s obtaned by usng fve base statons and usng sx base statons are smulated, respectvely, locaton of moble staton s A or B. Calculatng the weghted coeffcent Calculatng the fnal locaton result (4

3 60 The Open Cybernetcs & Systemcs Journal, 05, Volume 9 En-Hua et al. The model of sgnal transmsson dstance could be expressed: Fg. (. Schematc dagram of dstrbuton of base statons. r + C randn( + C rand( (6 Gauss LOS where, s the real dstance between moble staton and base staton, randn( s one random number between 0 and,c Gauss s the nose coeffcent whch satsfes the normal dstrbuton, rand(s one random number between 0 and whch satsfes unform dstrbuton, C LOS s LOS coeffcent. Fg. (3 shows the MSE graph wth changng the nose coeffcent [7, 8] when moble staton s at locaton A. We can fnd that the errors of three algorthms all ncreased wth the ncrease of nose coeffcent. The real coordnates of moble staton s adopted as the ntal value durng smulatng the Taylor seres expanson method n nose envronment, therefore, the precson of Taylor seres expanson method s sgnfcantly hgher than Chan algorthm. The modfed algorthm presented n ths paper can mae the ntal value whch s used to substtute nto Taylor seres expanson method approach to the real coordnate values of moble staton for t elmnates the estmated values whch are excessvely devated after usng Chan algorthm, therefore, the error of the modfed algorthm s smaller than Chan algorthm [9, 0]. Due to some devatons exstng between the ntal values adopted n modfed algorthm and real values, ts errors are larger than that of Taylor seres expanson. When the moble staton s located n locaton A, the ncreasng amount of base staton mae the results of Chan algorthm more precse, however, t has lttle effects on the error of Taylor seres expanson. To the modfed algorthm whch s based on Chan and Taylor, for the ncreasng amount of base staton decreases the error of Chan algorthm, and ncreases the precson of ntal values to some extent, thus mang the results of Taylor seres expanson method more precse, the errors of weghted results became smaller. Fg. (4 shows the MSE graph wth changng the nose coeffcent when the moble staton s at locaton B. From the graph t could be seen that locaton varaton has some effects on locaton precson. When the moble staton s at locaton B, the ncreasng amount of base statons also mprove the locaton precson of Taylor seres expanson method. From (Fgs. 3 and 4, we can fnd that n nose envronment, the proposed algorthm attans better performance than Chan algorthm at dfferent locatons. Fg. (3. MSE graph wth changng the nose coeffcent when moble staton s at locaton A.

4 Study of the Improved Locaton Algorthm Based on Chan and Taylor The Open Cybernetcs & Systemcs Journal, 05, Volume 9 6 Fg. (4. MSE graph wth changng the nose coeffcent when moble staton s at locaton B. Fg. (5. MSE graph wth changng nlos coeffcent when moble staton s at locaton A. Fgs. (5 and 6 show the MSE graphs wth changng LOS coeffcent when moble statons are at locaton A and B, respectvely. From these graphs we fnd that wth the ncrease of LOS coeffcent, performance of the three algorthms all decrease. In LOS envronment, the locaton precson of Taylor seres expanson method s obvously better than Chan algorthm, and the locaton varaton of moble staton also effects on locaton results. Because of ntegratng the advantages of Chan algorthm and Taylor seres expanson method, the performance of our proposed algorthm s also better than Chan algorthm n LOS envronment. COCLUSIO In ths artcle, we present a modfed locaton algorthm whch s based on Chan and Taylor. Frstly, ths algorthm uses Chan algorthm to estmate the locaton of moble

5 6 The Open Cybernetcs & Systemcs Journal, 05, Volume 9 En-Hua et al. Fg. (6. MSE graph wth changng nlos coeffcent when moble staton s at locaton B. staton, then the obtaned results are optmzed by elmnatng the contaned locaton results whch devated excessvely, the obtaned optmzed results are acted as the ntal value used n Taylor seres expanson method to conduct another locaton operaton, fnally, the obtaned locaton results usng these two algorthms are weghted summed, and the ultmate result s the locaton coordnate of moble staton. The experment ndcates that n the nose envronment, the performance of the proposed algorthm n the artcle s better than Chan algorthm, whch could effectvely mprove the locaton precson. COFLICT OF ITEEST The authors confrm that ths artcle content has no conflct of nterest. ACKOWLEDGEMETS Declared none. EFEECES [] T. Yang, L. Jn, and J. Cheng, An mprovement CHA algorthm based on TOA poston, Acta Electronca Snca, vol. 4, p. 06, 009. [] W. H. Foy, Poston-locaton solutons by Taylor-seres estmaton, IEEE Transactons on Aerospace and Electronc Systems, pp , 976. [3] M. C-Kun, C. S-Xn, W. Hao, and Z. Y-Hang, ecurson leastsquares passve locaton algorthm based on angle nformaton, Computer Measurement & Control, vol., no.9, pp , 004. [4] W. Cu, C. Wu, Y. Zhang, Z.-x. Ja, and L. Cheng, "GMM-based localzaton algorthm under LOS condtons," Journal on Communcatons, vol. 35, pp , 04. [5] G. F-Xang, W. Qng, and Z. Xao-Guo, TDOA/AOA hybrd wreless locaton algorthm n cellular networs wth LOS condton, Journal of Southeast Unversty, vol.9, pp , 00. [6] G. Fuxang, W. Qng, and Z. Xaoguo, "Hybrd GPS/TDOA steepest decent locaton algorthm n non-lne-of-sght envronment," Chnese Journal of Scentfc Instrument, vol. 7, p. 009, 0. [7] T. J. Khanzada, A.. Al, and A. S. Omar, "Tme dfference of arrval estmaton usng super resoluton algorthms to mnmze dstance measurement error for ndoor postonng systems," In: IEEE Internatonal Multtopc Conference, IMIC, 008, pp [8] P.-C. Chen, A non-lne-of-sght error mtgaton algorthm n locaton estmaton, In: Wreless Communcatons and etworng Conference, IEEE, 999, pp [9] P. J. Voltz and D. Hernandez, Maxmum lelhood tme of arrval estmaton for real-tme physcal locaton tracng of 80. a/g moble statons n ndoor envronments, In: Poston Locaton and avgaton Symposum, 004, pp [0] Y. Chan and K. Ho, A smple and effcent estmator for hyperbolc locaton, IEEE Transactons on Sgnal Processng, vol. 4, pp , 994. eceved: June 0, 05 evsed: July 9, 05 Accepted: August 5, 05 En-Hua et al.; Lcensee Bentham Open. Ths s an open access artcle lcensed under the terms of the ( whch permts unrestrcted, noncommercal use, dstrbuton and reproducton n any medum, provded the wor s properly cted.