Geometric Algorithm for Received Signal Strength Based Mobile Positioning

Transcription

1 RADIOENGINEERING, VOL. 4, NO., JUNE 005 Geometrc Algorthm for Receved Sgnal Strength Baed Moble Potonng Peter BRÍDA, Peter ČEPEL, Ján DÚHA 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 gnal trength (), Leat quare (LS), Nonlneofght (NLoS), Lneofght (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), angleofarrval (AOA) meaurement determned from the MS gnal receved at the BS [7, ]. In th correpondence, we focu on moble potonng ung the nformaton. The advantage of the technque n farly low cot nce power meaurement are already made by handet (part of the handoff algorthm). If a 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 ecton. 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 a gnal path lo wth a dtance []. Therefore t utable to defne bac parameter neceary for locaton method. Rado channel generally hotle n nature. It very dffcult to predct t behavor. Therefore, rado channel modeled n a tattcal way ung real propagaton meaurement data. In general, the gnal fadng n a rado envronment between a tranmtter and a 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).. LargeScale 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 a path lo n macrocell on expermental reult of Okumura []. The model expree 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, ( Rural) = LPL ( Urban) 4,78( log( + 8,33log( f ) 40, 94 PL f )) L b, () ()

2 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING where d the dtance between BS and MS n km, h b the heght of BS (tranmtter), and h m the heght of MS (recever), both n m. The range of parameter over Hata model vald under the followng condton 50 h m f [ MHz] 500, 30 hb [ ] [ m] 0. m 00,. (3). Medum and Small Scale Propagaton Model The moble rado envelope r(t), llutrated n Fg., compoed of m(t) and r(t) ( t) = m( t) r( t).. (4) The component m(t) called a longterm fadng or a lognormal fadng and t varaton due to a terran contour between a bae taton and a 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 p ( a) = πσ exp ( a µ ) σ where a the gnal level [db], σ the varance of the gnal dtrbuton [db], and µ the mean gnal level tated [db]. (5) p ( a) a a exp, (6) σ. σ = where a the gnal ampltude and σ the varance of the gnal dtrbuton [db ]. In a tuaton where the dtance between the tranmtter and recever mall and the envronment tatc, there a fxed patal pattern of maxma and mnma. Motly there a domnant tatonary (nonfadng) 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 the gnal ampltude and σ the varance of Rcean dtrbuton. 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 n Fg.. All cell n the ytem are deployed wth omn drectonal antenna. The cell radu 000 m. Fg.. A moble rado gnal fadng repreentaton. Smallcale propagaton model are characterzed by the fat varaton of the 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 a hortterm fadng or a multpath fadng. Varaton of th fadng due to a wave reflecton from urroundng buldng and other tructure [, 4, 5]. A channel wth a large number of path can be modeled a a Raylegh channel. The gnal ampltude 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 Fg.. Confguraton of cell arrangement. Smulaton are done n two dfferent envronment, urban and rural. For each envronment proper Hata model ued, 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:

3 RADIOENGINEERING, VOL. 4, NO., JUNE x ( LLS + LMS LSS = T + ), (8) where the receved gnal trength, T x the tranmtted gnal trength. Followng parameter nfluence gnal attenuaton: L LS the gnal degradaton, caued by a largecale propagaton, L MS the gnal degradaton, caued by a medumcale propagaton, and fnally L SS the gnal degradaton, caued by a mallcale propagaton. All of the parameter are n [db]. to calculate pont (MS locaton). Thee 3 pont and crcle crcumcrbe the Regon of Poble Poton (Fg. 4). Fg. 3. meaurement model. It eay to defne the dtance between MS and BS from meaurement at the MS from the th BS. For mplfcaton we conder the locaton n a D plane. Let the true locaton of MS [x,y ] T (recever) and the coordnate of the th T BS [x,y ] (ource), =,,, N. The dtance th between MS and the BS, denoted by d, gven by d ( x x ) + ( y y ), =,,..., N = In preence of dturbance a meaured dtance r ( x x ) + ( y y ). (9) r = d + n = + 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 the radu of a crcle. If we ue at leat three BS to reolve ambgute, the poton of a 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 a tattcal approach. 5. Moble Locaton Algorthm 5. Geometrc Algorthm GA The functon of the uggeted algorthm an etmaton of the MS locaton pont (wth the hghet probablty). In the deal cae the crcle are nterected n one pont, the MS locaton defned unequvocally. In a real envronment we can t aume the prevou cae. In th cae there are 3 relevant nterecton and the algorthm ha Fg. 4. The Regon of Poble Poton formed by the Interecton of Crcle. The bet calculaton of the 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. The et 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 the dtance between center of crcle calculated x = x + x, =, the horzontal dtance, () y = + y y the vertcal dtance, (3) = the center dtance. (4) c x + y We adjut the angle β for the proper quadrant wth repect to the coordnate ytem y β = arctan. (5) x For further decrpton we have to defne the varable α: c + r + r α = arcco cr x = r co( β α ) +. (6) the center th crcle to nterecton, horzontal, (7) y = r n( β α ) the center th crcle to nterecton, vertcal, (8) ( ) x + = r co β + α the center th crcle to nterecton, horzontal, (9) ( ) y + = r n β α the center th crcle to nd nterecton, vertcal. (0) Fnally, the coordnate of crcle nterecton are: t t nd

4 4 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING x = x + x the t nterecton coordnate, () y = y + y x + + the nd nterecton coordnate. () y = x = y + x + y After the frt tep we know nterecton coordnate [ 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 a ubet of nteror nterecton. Otherwe, t not ncluded n the ubet of nteror nterecton I [ x ; y ], j =, N INTER = j j,...,. (4) Our algorthm ue three crcle for the 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 the frt tep, x nterecton a, b, c, d, e and f are known, but only three of them belong to nteror nterecton (a hown n Fgure 3). The algorthm ha to chooe thee 3 nterecton. After the econd tep, three pont (b, c and a) are known and conequently we have to calculate the mean value of the correct pont. The mean of thee pont dentcal wth the locaton etmaton of th algorthm. 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 the econd cae we aume rural envronment. Thee condton are mportant for correct choong of envronment properte. Fg. 4. Sgnal trength of moble rado gnal n urban envronment. 5. LS Algorthm r = = ( x x ) + ( y y ) R x x y y ( + x =,,..., N + y ), (5) where R =x +y ; r the meaured dtance between the th ource and the recever. By mean of the 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 where x y = x y G M M x N y N Z =, M T [ x y R ] (7), (8) [ K r K r ] T h = L K N r N. The poton can be etmated ung tandard leat quare Z = G h. (9) Fg. 5. Path Lo n urban envronment accordng to (). Fg. 6. Shadowng n urban envronment.

5 RADIOENGINEERING, VOL. 4, NO., JUNE Conderng urban envronment, Fg. 4 to 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. 000 m x, y 000 m. (30) Smulaton are performed ung three tranmtter (wth the hortet dtance between the tranmtter and the 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) RMSE = ( X x) + ( Y y) [m], (3) where [X,Y] are the coordnate of the true locaton and [x,y] are the coordnate of the etmated locaton. At frt t neceary to determne the nfluence of fadng to the locaton accuracy. The problem of fadng partally elmnated by etmatng Local Average Power. It calculated by equaton (3) Fg. 7. Shortterm (Raylegh) fadng n urban envronment. The tuaton for the econd cae (rural envronment) dfferent (ee Fg. 8.). N = N = 0 where N the number of ample., (3) Comparng of the reult hown n the table. Envronment Urban Rural N =0 S N = S N S =0 N S = RMSE [km] GA 0,398 RMSE [km] LS 0,468,5946 0,866 0,05 0,395 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 the 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. 8. Moble rado gnal n rural envronment. Envronment Fadng Dtrbuton Urban Shadowng Log normal Short term Raylegh Rural Shadowng Log normal Short term Rcean σ [db] 4 6 µ [db] 0,5 0 Tab.. Table of partcular envronment, ther parameter and dtrbuton ued for the 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. The recever (MS) move randomly n the quare Fg. 9. Etmated poton of MS for rural envronment. In Fg. 9 a 0 we llutrate an envronment mpact on the potonng accuracy. Both method work jut relably n the rural envronment (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 Tab.. From Tab. (and Fg. 9, 0) we can ee that the geometrc algorthm more utable (n comparon wth tandard LS method) for

6 6 P. BRÍDA, P. ČEPEL, J. DÚHA, GEOMETRIC ALGORITHM FOR RECEIVED SIGNAL STRENGTH BASED MOBILE POSITIONING the etmaton of a poton n the preence of NLoS propagaton envronment. Fg. 0. Etmated poton of MS for urban envronment. 7. Concluon The propoed locaton algorthm reduce the nduced error n the preence of NLoS propagaton. We compare the propoed geometrc algorthm wth the tandard LS method. Accordng to thee reult, the performance of the propoed algorthm better n comparon to the conventonal method. Acknowledgement The reearch decrbed n the paper wa upported by the tate programme of the 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. Reference [] CAFFERY, J. J. Jr. Wrele Locaton n CDMA Cellular Rado Sytem. Kluwer Academc Publher, 000. [] RAPPAPORT, T. S. Wrele Communcaton: Prncple and Practce. Prentce Hall PTR, 996. [3] HATA, M. Emprcal formula for propagaton lo n land moble rado ervce. IEEE Tranacton on Vehcular Technology, 980, vol. VT9, no. 3, pp [4] PRASAD, RAMJEE. Unveral Wrele Peronal Communcaton. Artech Houe, 998. [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 European Mcrowave Conference. th 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 quare 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 Sytem. 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 the Unverty of Žlna n 00, then he tarted h Ph.D. tudy at the Dept. 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 the Unverty of Žlna n 003, then he tarted h Ph.D. tudy at the Dept. of Telecommuncaton, Unverty of Žlna. H work nclude mart antenna ytem and ther ung for nterference cancellaton. Ján DÚHA graduated from the Mocow Electrcal Inttute for Communcaton n 963 n Mocow and receved h Ph.D. degree n Telecommuncaton from the Unverty of Žlna n 98. Snce 987 he ha been the aocate profeor at the Dept. of Telecommuncaton, Unverty of Žlna. H reearch nteret nclude moble network, rado relay network and televon technology.