Geometric Algorithm for Received Signal Strength Based Mobile Positioning

Transcription

1 RADIOENGINEERING, VOL. 4, NO., APRIL 005 Geometrc Algorthm for Receved Sgnal Strength Baed Moble Potonng Peter Brída, Peter Čepel, Ján Dúha 3,, 3 Dept. of Telecommuncaton, Unverty of Žlna, Unverztná 85/, 00 6 Žlna, Slovak Republc brda@fel.utc.k, cepel@fel.utc.k, duha@fel.utc.k Abtract. Moble potonng one of the fatet growng area for the development of new technologe, ervce and applcaton. Th paper decrbe a mple and effcent geometrc algorthm ung receved gnal trength meaurement extracted from at leat three bae taton. Th method compared wth tandard Leat Square method. The mulaton reult how, that geometrc algorthm gve more accurately locaton etmaton than LS algorthm n multpath propagaton. Keyword Receved Sgnal Strength (), Leat quare (LS), NonLneofSght (NLoS), LneofSght (LoS), Rado channel.. Introducton Recently, Moble Staton (MS) locaton nformaton ha receved gnfcant nteret. Dfferent locatonbaed applcaton nclude locaton entve bllng, fleet trackng, package and peronnel trackng, moble yellow page, locaton baed meagng, route gudance and provdng traffc nformaton. The frequency and accuracy of locaton requet vary wth the requred applcaton. Locaton baed ervce one of the mot mportant ervce for the next generaton moble ytem. Wrele locaton ytem uually requre two or more bae taton (BS) to ntercept a moble taton (MS) gnal. Common locaton approache are baed on Cell Identfcaton (Cell ID), tmeofarrval (TOA), receved gnal trength (), tmedfferenceofarrval (TDOA), or angleofarrval (AOA) meaurement determned from the MS gnal receved at the BS [7, ]. In th correpondence, we focu on moble potonng ung the nformaton. Advantage of the technque n farly low cot nce power meaurement are already made by handet (part of the handoff algorthm). If the propagaton model known, power meaurement can be mapped to a dtance meaurement. If the dtance from the moble termnal to three or more bae taton known, the moble termnal poton can be calculated. Unfortunately, etmaton error hgher than the other localzaton method. Alo, the moble termnal uually move and fat fadng caued by multpath propagaton caue gnfcant error. Th howed n the next part of artcle. The reult acqured by geometrc approach are compared wth tandard LS reult.. Channel propagaton model The moble rado channel defne fundamental lmtaton on the performance of wrele communcaton ytem and wll play an mportant role n thee potonng ytem. Radolocaton ung gnal trength a well known locaton method that ue a mathematcal model decrbng gnal path lo wth dtance []. Therefore utable to defne bac parameter neceary for locaton method. Rado channel generally hotle n nature. It very dffcult to predct t behavour. Therefore, rado channel modelled n a tattcal way ung real propagaton meaurement data. In general, the gnal fadng n a rado envronment between a tranmtter and recever can be decompoed nto a largecale path lo component together wth a medumcale lowvaryng component (havng a lognormal dtrbuton) and a mallcale fat varyng component (wth Rcan or Raylegh dtrbuton).. Largecale propagaton model A path lo predct gnal power attenuaton wth the dtance from a BS. Well known model for path lo are Hata, Lee, COST3 model etc. Hata [35, 0] developed a ueful model for path lo n macrocell on the expermental reult of Okumura []. The model expree the path lo a a functon of BS heght, MS heght, carrer frequency and the type of envronment (urban, uburban or rural). In Hata model, the path lo expreed a [n db] L a PL ( Urban) = 69, log, ( f ) 3, 8log( hb ) a( h ) + ( 44, 9 6, 55log( h )) log( d ) m ( h ) = (,log( f ) 0,7) h,56 log( f ) + 0, 8 m m, b, ()

2 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING ( Rural) = LPL ( Urban) 4,78( log( f )) + 8,33log( f ) 40, 94 LPL, () d dtance between BS and MS n km, h b heght of BS (tranmtter) and h m heght of MS (recever), both n m. The range of parameter over Hata model vald under the followng condton 50 h m f [ MHz] hb [ m] [ m] (3). Medum and mall cale propagaton model Moble rado envelope r(t), llutrated n Fg., compoed of m(t) and r(t) () t m() t r() t =.. (4) Raylegh dtrbuton n a cae of large number of obtacle and there are domnant reflected wave (NLoS envronment Non Lne of Sght). NLoS propagaton alway ext n cte or bultup envronment. Raylegh dtrbuton defned a a p ( a) = exp, (6) σ. σ where a gnal ampltude and σ varance of the gnal dtrbuton [db ]. In a tuaton where the dtance between the tranmtter and the recever mall and the envronment tatc, there a fxed patal pattern of maxma and mnma. Motly there a domnant tatonary (nonfandng) gnal component. Th a cae of LoS (Lne of Sght) propagaton path. The LoS propagaton model gven by the Rcan dtrbuton [4, 5, and 0] a ( ) ( a + ) a. p a = exp I 0, (7) σ. σ σ where I 0 (.) modfed Beel functon of the frt knd and zeroth order, the peak value of the pecular rado gnal, varable a gnal ampltude and σ varance of Rcean dtrbuton. Fg.. A moble rado gnal fadng repreentaton. The component m(t) called longterm fadng or lognormal fadng and t varaton due to terran contour between bae taton and moble taton. It repreent a low varaton n the mean envelope over a dtance. Medumcale varaton take on Gauan tattc when the gnal expreed n db. The Gauan or normal denty functon take the form ( a μ) p ( a) = exp, (5) πσ σ where a gnal level [db], σ varance of the gnal dtrbuton [db], and μ the mean gnal level tated [db]. Smallcale propagaton model are characterzed by the fat varaton of receved gnal trength over a hort dtance on the order of a few wavelength or over hort tme duraton on the order of econd. The econd component repreent hortterm fadng or multpath fadng. Varaton of th fadng due to wave reflecton from the urroundng buldng and other tructure [, 4, and 5]. Channel wth a large number of path can be modelled a a Raylegh channel. The gnal ampltude 3. Sytem model We aume the ytem model a followng: The number of BS N, Sgnal from N BS are meaured at MS, Receved Sgnal Strength from each BS ndependent to each other. The ervce area cont of 7 cell a hown Fg.. All cell n the ytem are deployed wth omn drectonal antenna. The cell radu 000m. Fg.. Confguraton of cell arrangement. Smulaton are realzed n two dfferent envronment, urban and rural. For each envronment

3 RADIOENGINEERING, VOL. 4, NO., APRIL ued proper Hata model, for urban envronment () and for rural envronment (). In urban envronment we conder NLoS propagaton and n rural envronment we conder LoS propagaton. 4. meaurement model In th ecton, we ntroduce the propoed algorthm for baed moble potonng. Fg. 3. meaurement model. x ( L + L L ) = T +, (8) LS MS where receved gnal trength, T x tranmtted gnal trength. Followng parameter nfluence gnal attenuaton: L LS gnal degradaton, caued by largecale propagaton, L MS gnal degradaton, caued by medumcale propagaton and fnally L SS gnal degradaton, caued by mallcale propagaton. All of the parameter are n [db]. It eay to defne dtance between MS and BS from meaurement at the MS from th BS. For mplfcaton we conder the locaton n a twodmenonal (D) plane. Let the true locaton of MS [x,y ] T (recever) and the coordnate of the th BS [x,y ] T (ource), =,,,N. The dtance between MS and the th BS, denoted by d, gven by d ( x x ) + ( y y ), =,,..., N SS =. (9) In the preence of dturbance we denote a meaured dtance r r = d + n = ( x x ) + ( y y ) + n,, (0) =,,..., N where n the noe or range error at the th BS. For the mplfcaton we aume that meaurement error {n } are zero mean Gauan varable wth known varance σ. The dtance r determne radu of crcle. If we ue at leat three BS to reolve ambgute, poton of MS gven by the nterecton of crcle. The crcle are gven by equaton ( x x ) + ( y y ) = r, =, N. (),..., In general, two approache can be taken for olvng MS locaton on the ba of gnal trength meaurement []. The traghtforward approach to ue a geometrc nterpretaton of the meaurement and compute the nterecton of the lne of poton (n th cae t mean crcle). The econd approach tattcal approach. 5. Moble locaton algorthm 5. Geometrc algorthm GA The functon of uggeted algorthm etmaton of the MS locaton pont (wth the hghet probablty). In deal cae, the crcle are nterected n one pont, there MS locaton defned unequvocally. In a real envronment we can t aume prevou cae. In th cae there are three relevant nterecton and algorthm ha to calculate one pont (MS locaton). Thee three pont and crcle crcumcrbe Regon of Poble Poton (Fg. 4). Fg. 4. The Regon of Poble Poton formed by the Interecton of Crcle. The bet calculaton of poton would be to evaluate the center of gravty of the Regon of Poble Poton [8]. A mple and farly traghtforward etmate of th to determne the mean poton of the trangle corner pont (formng the Regon of Poble Poton). Th done n a mple twotage proce. Set of all the nterecton of crcle par calculated at frt. Method for fndng the two nterecton (two et of value for x and y) from thee equaton requre conderable amount of algebrac manpulaton. The proce for fndng the two nterecton (between two crcle) decrbed at the followng. At frt calculated dtance between center of crcle x = x + x, =, horzontal dtance between center, () y = y + y vertcal dtance between center, (3) c = x + y center dtance. (4) We adjut angle β for proper quadrant wth repect to coordnate ytem

4 4 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING y β = arctan. (5) x For further decrpton we have to defne varable α: c + r + r + α = arcco. (6) cr ( β α ) x = r co center th crcle to t nterecton, horzontal (7) ( β α ) y = r n center th crcle to t nterecton, vertcal (8) ( β + α ) x + = r co center th crcle to nd nterecton, horzontal (9) ( β α) y + = r n center th crcle to nd nterecton, vertcal (0) Fnally, coordnate of crcle nterecton are: x = x + x t nterecton coordnate, () y = y + y x y = x = y x + y nd nterecton coordnate. () After the frt tep we know coordnate of nterecton [ x ; y ], j =,,..., N I =. (3) j j Secondly a ubet of nteror nterecton created n the followng way. If an nterecton pont of a par of crcle nde of all the other crcle, then t defned a pont from ubet of nteror nterecton. Otherwe, t not ncluded n the ubet of nteror nterecton I [ x ; y ], j =, N =. (4) INTER j j,..., Our algorthm ue three crcle for locaton calculaton, t mean that N=3. There are known coordnate of crcle center and crcle radue. From thee parameter t poble to determne nterecton of crcle. After frt tep, there are known x nterecton a, b, c, d, e and f, but only three of them belong to nteror nterecton (a hown n Fgure 3). The algorthm ha to chooe thee three nterecton. After econd tep, there are known three pont (b, c and a) and conequently we have to calculate mean value of thee correct pont. The mean of thee pont dentcal wth locaton etmaton of th algorthm. where R =x +y ; r the meaured dtance between the ource and the th recever. By mean of new varable defnton K =x +y, we rewrte (5) through a et of lnear expreon x x + y y R = K r, =,,..., N. (6) Equaton (6) can be expreed n a matrx form GZ = h, (7) where x y G x y = M M M, x N y N x Z = y, (8) R K r K r h =. M K N r N The poton can be etmated ung the tandard leat quare a Z = G h. (9) 6. Smulaton reult and comparon Preented numercal mulaton compare the performance of the propoed geometrc algorthm and the tandard LS method. Smulaton are done n two cae. In the frt cae we aume urban envronment. In econd cae we aume rural envronment. Thee condton are mportant for correct choong envronment properte. If we conder urban envronment, fgure 4, 5, 6, 7, how the gnal trength receved at the MS n urban envronment. The gnal can be decompoed to partcular part longterm fadng (path lo and hadowng) and hortterm fadng. 5. LS algorthm r = = R ( x x ) + ( y y ) x x y y ( + x + y ), =,,..., N (5)

5 RADIOENGINEERING, VOL. 4, NO., APRIL Fg. 4. Sgnal trength of moble rado gnal n urban envronment. Fg. 7. Shortterm (Raylegh) fadng n urban envronment. The tuaton for the econd cae (rural envronment) dfferent (ee Fg. 8.). Fg. 5. Path Lo n urban envronment accordng to (). Fg. 8. Moble rado gnal n rural envronment. Envronment Urban Rural Fadng Dtrbuton Shadowng Log normal Short term Raylegh Shadowng Log normal Short term Rcean σ [db] 4 6 μ [db] 0,5 0 Fg. 6. Shadowng n urban envronment. Tab.. Table of partcular envronment ther parameter and dtrbuton ued for decrpton. We aume that there are even tranmtter (BS), and the recever are cloe to each other. Ther poton are [0, 0] m, [000, 0] m, [000,000] m, [000, 000] m, [000, 0] m, [000, 000] m, and [000, 000] m. Recever (MS) move randomly n the quare 000 m x, y 000 m. (30)

6 6 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING Smulaton are performed ung three tranmtter (wth the hortet dtance between tranmtter and recever, dependng on the gnal trength). All reult were baed on 5000 ndependent run. The accuracy of both method compared by Root Mean Square Error (RMSE) ( X x) + ( Y y) RMSE = [m], (3) where [X,Y] are coordnate of true locaton and [x,y] are coordnate of etmated locaton. At frt t neceary to determne the nfluence of fadng to locaton accuracy. The problem of fadng partally elmnated by etmatng Local Average Power. It calculated by equaton (3) N = N = 0, (3) where N number of ample. Comparng of reult hown n the followng table. Envronment Urban Rural N S =0 N S = N S =0 N S = RMSE [km] GA 0,398 0,866 0,05 0,395 RMSE [km] LS 0,468,5946 0,937 0,5 Tab.. Comparng of reult for both algorthm wth condton defned n the table. For the next experment we conder ung of algorthm wth Local Average Power (N = 0 ample). Fg. 9 and 0 how the dtrbuton of the MS poton etmate obtaned by the GA and LS, for dfferent envronment. Fg. 0. Etmated poton of MS for urban envronment. In the fg. 9 a 0 we llutrate envronment mpact on potonng accuracy. Both method work jut relably n the rural envronment (ee fg. 9). Condton for potonng n the urban envronment are much more complcated and therefore the dtrbuton of MS poton larger. Thee reult are numercally expreed n the table.. From the table (and fg. 9 and 0) we can ee that the geometrc algorthm more utable (n comparon wth tandard LS method) for etmaton of poton n the preence of NLoS propagaton envronment. 7. Concluon Propoed locaton algorthm reduce the nduced error n the preence of NLoS propagaton. We compare the propoed geometrc algorthm wth tandard LS method. Accordng to thee reult, the performance of the propoed algorthm better n comparon to the conventonal method. Acknowledgement Reearch decrbed n the paper wa upported by the tate programme of Slovak republc, No. 003 SP 5/ / Communcaton Network and Servce of New Generaton. Th paper wa upported by the grant VEGA /040/03 Effectve rado reource management method n next generaton of moble communcaton network. Fg. 9. Etmated poton of MS for rural envronment. Reference [] CAFFERY, J. J. Jr. Wrele Locaton n CDMA Cellular Rado Sytem, Kluwer Academc Publher, 000. [] RAPPAPORT, T. S. Wrele Communcaton: Prncple and Practe, Prentce Hall PTR, 996. [3] HATA, M. Emprcal formula for propagaton lo n land moble rado ervce, IEEE Tranacton on Vehcular Technology, vol. VT 9, no. 3,pp. 3735, Augut 980. [4] PRASAD, RAMJEE. Unveral Wrele Peronal Communcaton, Artech Houe, 998.

7 RADIOENGINEERING, VOL. 4, NO., APRIL [5] SIWIAK, K. Radowave Propagaton and Antenna for Peronal Communcaton nd ed. Artech Houe, 998. [6] WANG, S., WANG, F., DEVABHAKTUNI, V. K., ZHANG, Q.J. A hybrd neural and crcutbaed model tructure for mcrowave modelng. In Proceedng of the 9 th European Mcrowave Conference. Munch (Germany), 999, p [7] WANG, X., WANG, Z., O DEA, B. A TOAbaed locaton algorthm reducng the error due to nonlneofght (NLOS) propagaton. IEEE Tranacton on Vehcular Technology, 003, vol. 5, no., p. 6. [8] SPRATT, M. An Overvew of Potonng by Dffuon, Moble Sytem and Servce Laboratore, HPL0007, 00. [9] CHEUNG, K. W., SO, H. C., MA, W.K., CHAN, Y. T. Leat Square Algorthm for TmeofArrvalBaed Moble Locaton. IEEE Tranacton on Sgnal Proceng, 004, vol. 5, no. 4, p. 8. [0] GARG, V. K., WILKES, J. E. Wrele and peronal communcaton ytem, Prentce Hall, 996. [] DOBOŠ, Ľ., DÚHA, J., MARCHEVSKÝ, S., WIESER, V.: Moblné rádové ete, EDIS, Žlnká unverzta, Žlna, 00 About Author... Peter Brída wa born n Bojnce, Slovaka, n 979. He graduated from Unverty of Žlna n 00, then he tarted Ph.D. tudy at the Department of Telecommuncaton, Unverty of Žlna. H work nclude wrele potonng n cellular rado ytem and atellte navgaton ytem. Peter Čepel wa born n Martn, Slovaka, n 979. He graduated from Unverty of Žlna n 003, then he tarted Ph.D. tudy at the Department of Telecommuncaton, Unverty of Žlna. H work nclude mart antenna ytem and ther ung for nterference cancellaton. Ján Dúha graduated from Mocow Electrcal Inttute for Communcaton n 963 n Mocow and Ph.D. degree n Telecommuncaton from Unverty of Žlna n 98. From 987 he the aocate profeor at the Department Telecommuncaton n Unverty of Žlna. H reearch nteret nclude moble network, rado relay network and televon technology.