Wireless Signal Map Matching for NLOS error mitigation in mobile phone positioning

Transcription

1 Internatonal Global Navgaton Satellte Systems Socety IGNSS Symposum 006 Holday Inn Surfers Paradse, Australa 17 1 July 006 Wreless Sgnal Map Matchng for NLOS error mtgaton n moble phone postonng Bnghao L, Andrew G. Dempster, Chrs Rzos, Joel Barnes School of surveyng and spatal nformaton system, UNSW, Australa Tel: Fax: Emal: bnghao.l@student.unsw.edu.au Hyung Keun Lee School of Electroncs, Telecommuncaton & Computer Engneerng, Hankuk Avaton Unversty, Korea Presenter Andrew G. Dempster ABSTRACT Angle of arrval (AOA), tme of arrval (TOA) and tme dfference of arrval (TDOA) are wdely used for moble phone postonng. However, these measurements experence degradaton of locaton accuracy due to localsed non-lne-of-sght (NLOS) sgnal propagaton, especally n urban or suburban area. NLOS error s well known to be a major source of error n moble phone postonng and s smply caused by buldngs blockng the lne-of-sght propagaton of the RF sgnal. Hence moble staton (MS) appears further away from the base transcever staton than t actually s. Ths sgnfcantly ncreases the postonng error. To mtgate the effects of NLOS error n terrestral wreless locaton systems, a wreless sgnal mapmatchng (WSMM) concept was recently ntroduced. WSMM s based on usng a database method to generate the NLOS error correcton map, and then use the correcton map to correct the measurements. Therefore, a more accurate MS locaton can be estmated. Furthermore, WSMM can automatcally extract the relatonshp between an electronc map representng the deal world and the fully-populated anonymous user dstrbuton representng dstorted world. After the concept was verfed by smulaton, an experment was carred out n a typcal suburban area. The

2 test result shows the proposed database method based on unversal krgng can mprove the accuracy of poston estmate usng the TDOA technque f the reference ponts can be dentfed. KEYWORDS: moble phone postonng, TDOA, NLOS error, database 1. INTRODUCTION Utlzng moble phone networks for postonng has been a hot research topc snce the end of 1990 s. It s well known that the basc Cell ID technque has been deployed around the world, but the method does not meet most of the requrements for applcatons n locaton-based servces (LBS). Much attenton has been focused on the sgnal tme delay and angle of arrval measurements. Generally, approaches based on sgnal tme delay (tme-of-arrval (TOA) or tme-dfference-of-arrval (TDOA) etc.) and angle-of-arrval (AOA) measurement can greatly mprove the accuracy of poston determnaton. Unfortunately the man shortcomng of these methods s that they requre lne-of-sght (LOS) propagaton for accurate locaton estmates. However, non-lne-of-sght (NLOS) error s the domnant error n locaton estmaton (Caffery and Stüber, 1998) n urban or suburban area where people are more nterested n the moble user s (MU) locaton. Fgure 1 shows how the NLOS error problem occurs. When drect sgnal paths between handset and base transcever staton (BTS) are mostly obstructed by buldngs and other structures, alternate, reflected paths domnate. These paths are longer, affectng TDOA and TOA methods, and arrve from a dfferent drecton, affectng AOA. TDOA and TOA NLOS errors are always postve,.e. the path s longer, but range from a small number to thousands of meters (Slventonen and Rantalanen, 1996; Woo et al., 000), dependng on the propagaton envronment. L (1998) studed the effect of NLOS error on the performance of AOA technque n poston estmaton. The study shows when a NLOS condton s presented for only one BTS, the estmaton error of AOA technque ncreases 10 tmes or so. Handset (MU) LOS path NLOS path LOS path (abstracted by buldng) Handset (MU) BTS Fgure 1 LOS path and NLOS path, how NLOS error occurs To mtgate poston estmates from NLOS error corrupton, dfferent approaches have been nvestgated. In (Morley and Grover, 1995), the authors used an algorthm based on the probablty densty functon (pdf) model to reduce the NLOS error. However, t s dffcult to formulate the pdf, and ths functon should vary wth the changng envronment. A general method use to mtgate the NLOS error s error dentfcaton and reconstructon. Wyle and Holtzman (1996) explaned, by usng the tme hstory of the range measurements n a smple

3 hypothess test, and explotng the knowledge of the standard devaton of the standard measurement nose, one can determne f the measurements correspond to a LOS or NLOS envronment. A two-step LOS reconstructon was proposed. Frst the data was smoothed by N th order polynomal ft, then the knowledge of the standard measurement nose was utlzed to correct the NLOS error. Smlarly, Woo et al. (000) dentfy the NLOS from the range characterstc and reconstruct the LOS rangng usng a Kalman flter. Whle n (Cong and Zhuang, 001), the NLOS BTS detecton was based on an assumpton that f a large NLOS error exsts for a partcular BTS, on the average the resdual wll be large n magntude. Ths requres redundant measurements. Furthermore, n (Cong and Zhuang, 004), two approaches were proposed to detect the NLOS error dependng on how much a pror nformaton s avalable. An NLOS State Estmaton algorthm could be used wth some pror nformaton on NLOS errors avalable from an emprcal database. In the case wth no knowledge of NLOS, an mproved resdual algorthm could be appled to detect a small number of NLOS BSs (treatng NLOS corrupted measurements as outlers and rely solely on the knowledge of Gaussan measurement nose). Another approach conssts of explotng the redundant nformaton present n the measurements to detect and reject the NLOS errors. The man contrbuton n ths drecton was presented n (Chen, 1999) where the problem was formulated n terms of hypotheses, where each hypothess corresponded to a set of BS consdered under NLOS scenaros. The algorthm presented there was based on a weghted combnaton of the partal poston estmates assocated to each hypothess. A well-known category of NLOS error mtgaton method s constraned optmzaton method. Ths method s to explot the property that the NLOS errors are always postve errors, then to search the true poston by addng some constrants such as penalty functon n (Caffery and Stuber, 1998). In (Wang et al., 003), mathematcal programmng s used to fnd the ML (maxmumlkelhood) estmate of the source poston n the restrcted doman defned by the nequaltes nduced due to NLOS propagaton. Unfortunately, none of these methods can solve the NLOS problem adequately, snce too many elements affect the sgnal propagaton, and the propagaton envronment vares from place to place. Especally n urban or suburban areas, NLOS propagaton s common for rado frequency (RF) sgnal. Often, only 1 or, even none of the sgnals from BTSs (or MS) can propagate n LOS scenaro. The NLOS error mtgaton s a classc problem, whch could be solved usng a basc database method. In ths method, the NLOS error can be drectly extracted from the reference measurements at the reference ponts, and logged n a database for further usage. Jayaraman et al. (000) descrbe methods for collectng data to create the database. But the data collecton and database mantenance s qute a costly and laborous process. To solve ths problem and effectvely mtgate the NLOS error, a wreless sgnal map-matchng (WSMM) concept was recently ntroduced. WSMM can automatcally extract the relatonshp between an electronc map representng the deal world and the fully populated anonymous user dstrbuton representng dstorted world. Then a NLOS error correcton map can be generated based on the spatal correlaton. The correcton map can be used to correct the measurements. Therefore, a more accurate MS locaton can be estmated. As usng TDOA measurement for postonng has many advantages, the WSMM wll be dscussed here base on t.. HYPERBOLIC POSITIONING ALGORITHMS TDOA measurement multplyng speed of lght gves the range dfference measurement. The range dfference measurement determnes a hyperbola wth the two BTSs as foc. Generally,

4 two TDOA measurements, whch need at least three BTSs, can determne the transmtter s locaton, that s, the ntersecton of the two hyperbolas. Assume that there are M BTSs dstrbuted arbtrarly n a -D plane. Consder the TDOAs wth respect to the frst BTS whch s the one communcatng wth the handset and normally (but not necessarly) s the closest one to the handset. τ, 1 = τ τ 1 =,3, K, M (1) Let τ = [τ 1, τ 31,, τ M1 ] T be the estmated TDOA vector. TDOA between recevers and j are computed from τ j = τ 1 τ j1, =,3, K, M () Let the source (handset) be at unknown poston (x, y). The BTSs locatons (x, y ) are known. The dstance between source and BTS s r = ( x x) + ( y y) = x + y x x y y + x + y, =,3, K, M (3) f c s the speed of lght, then, r 1 = cτ 1 = r r 1 = ( x x) + ( y y) ( x1 x) + ( y1 y ), =,3, K, M (4) defne a set of nonlnear equatons whose soluton gves the locaton of the source (x, y). However, solvng the nonlnear equatons (4) s not trval. A substantal amount of work has been done n solvng ths problem. The wdely used algorthms are the Taylor-seres method, Fang s method and Chan s method. Taylor-seres method was ntroduced n (Foy, 1976). It s an teratve method, starts wth an ntal guess, and mproves the estmate at each step usng least-squares (LS). Ths method can provde a precse poston estmate at reasonable nose levels and has been commonly employed. The dsadvantage of ths method s the rsk of dvergence durng the processng, and the computaton burden. Fang s method (Fang, 1990) gves an exact soluton when the number of TDOA measurements s equal to the number of unknowns, but t cannot use redundant measurements. Chan s method (Chan and Ho, 1994) provdes the exact soluton and also takes advantage of redundant measurements. Furthermore t approaches the CRLB (Cramer-Rao lower bound). However, both Fang s method and Chan s method occasonally suffer from the ambgutes problem (there are results, but only one s the reasonable estmate, dscussed n detal later), and f the TDOA measurements are contamnated by nose or other errors (say NLOS error), these methods have some dffcultes to provde the locaton. It has been evdenced by our smulaton and experment that the Taylor-seres method can work well when TDOA measurements are serously contamnated by NLOS error and nose. Further more, Taylor-seres method s more flexble comparng wth other methods. As the PC s becomng more and more powerful, the computaton burden s no longer a serous problem. Hence, Taylor-seres method was chosen to estmate the MS s poston n our research.

5 3. WIRELESS SIGNAL MAP MATCHING Snce terrestral wreless locaton systems enables a large amount of samplng wth respect to multple users at dfferent locatons, fully populated user dstrbuton, though dstorted by the NLOS error, has become practcally possble. The key dea of WSMM s to extract NLOSnduced poston error and each measurement s NLOS error by comparng the geometrc features of the dstorted user dstrbuton wth those of the deal map. As a result, the proposed WSMM has two attractve advantages n mtgatng NLOS error. One s that t does not requre addtonal network element nstallaton and the other s that t elmnates human effort for surveyng feld data wth specal nstruments. The purpose of WSMM s to create a correcton map (CMAP) whch can be used to correct the NLOS error. The whole procedure of WSMM s shown n Fgure. start Read measurement database (MDB) Flter out nvald measurements n MDB Compute each poston & relate t to MDB Identfy reference measurements (RMs) & RPs Buld correcton map (CMAP) based on RMs & RPs Apply CMAP to MDB Re-compute each poston & check user dstrbuton Broadcast porton of CMAP upon request Update CMAP? Fgure Block dagram for the whole procedure of WSMM 3.1 Measurement Database The most mportant prerequste for the proposed WSMM s the constructon of measurement database (MDB). The MDB can be constructed by samplng the measurements from a handset wthn the area of nterest by core network nfrastructure shown n Fgure 3. The functon of WSMM server could be also accomplshed by GMLC (Gateway Moble Locaton Centre). The sampled measurements are flled nto a data structure that s desgned for effcent MDB management. Fgure 4 shows a typcal data structure for MDB constructon. The data felds are categorzed nto user ndex, handset model, tme ndex, locaton-related network measurements, and any LBS-related varables for whch a spatal-temporal or a statstcal surface map s desred. The locaton-related network measurements may comprse one or more of TDOA, TOA, AOA, transmtted sgnal strength (TSS), frequency-of-arrval (FOA), receved sgnal strength (RSS), and sgnal-to-nose rato (SNR) etc.

6 MSC/VLR LMU RNC BTS/LMU RNC MSC/VLR GMLC RNC MSC/VLR BTS/LMU BTS/LMU LMU: Locaton Measurement Unt RNC: Rado Network Controller MSC: Moble Servces Swtchng Centre VLR: Vstor Locaton Regster GMLC: Gateway Moble Locaton Centre WSMM server Fgure 3 Core network nfrastructure for terrestral wreless locaton systems Alas for prvacy (arbtrary ndex number) I(1) I() Handset model Tme ndex TDOA(1:Nb-1) TOA(1:Nb) AOA(1:Nb) TSS(1:Nb) RSS(1:Nb) SNR(1:Nb) Varables to be analyzed on ether dstorted or corrected spatal-temporal doman Temporary Results... I(Nb) Fgure 4 Data structure for measurement database 3. Reference Measurement Extracton Reference measurement extracton s obvously the key aspect of WSMM. Acqurng the references automatcally can greatly support the database method (L et al., 005). The uncompensated NLOS errors n sampled measurements generate based poston estmates whch consttute dstorted user dstrbuton. Fgure 5 shows an example n typcal Manhattan-lke urban envronment. To recover the dstorted dstrbuton to the deal dstrbuton, some form of reference nformaton s requred. In WSMM, the reference nformaton s formed by two technques. One s measurement characterstc classfcaton and the other s map feature extracton. The utlzaton of measurement characterstc classfcaton s relatvely smple. For ths purpose, sgnal strength (SS) value of each MDB

7 element s checked compared to a pre-defned threshold value. Accordng to the Hata- Okumura model (Hata, 1980), SS value descrbes the dstance between any transmtter and recever wth good accuracy f they are suffcently adjacent so that there s no obstructon for the LOS condton. Thus, the measurement set whch has the maxmum SS wth respect to one BTS means that they are sampled near that BTS. In these measurement sets, the effects of NLOS error would be small and ther sampled poston would approxmately equal that of the correspondng BTS. 0m BTS3 100m 100m 0m BTS BTS1 a b c Fgure 5 (a) Manhattan-lke urban envronment, (b) Ideal MU poston dstrbuton and (c) dstorted MU poston dstrbuton Usually, the amount of reference nformaton provded by the measurement characterstc classfcaton would be not suffcent for NLOS error mtgaton. To provde a suffcent amount of reference nformaton, map features should be extracted. If we consder a smple map that conssts of nodes and lnks, any feasble map-matchng technques can be appled wth respect to nodes, lnks, and node-lnk combned geometry (Whte, 000). Dense urban areas are mostly composed of road junctons, road segments, and buldngs, where road junctons are stored as nodes and road segments are stored as lnks. Though any map feature s useful as reference nformaton, a road juncton s the easest feature for map matchng. To extract reference measurements by map features, two maps are utlzed, an deal map (IMAP) and a feature map (FMAP). The IMAP s used as the reference nformaton for WSMM. Thus, t should accurately represent the real world and usually ncludes the coordnates of BTSs, buldngs, and geometrc features such as road junctons and lnks (refer to Fgure 5). The FMAP s a 3-dmensonal surface map based on dstorted user dstrbuton computed by the MDB. The z-values (e.g. the heght) of FMAP represent the degree of confdence of ther correspondng xy-postons as feature areas. For example, the hgher the z- value s, the more possble ts xy-poston corresponds to a map feature (Lee et al, 005). Many canddates may be utlzed as the FMAP, ncludng a populaton surface (refer to Fgure 6), a DOP surface utlzng user ponts wthn a specfc radus, and any possble measure surface that expresses the smlarty between local user dstrbutons wth feature area patterns. In Fgure 6, a typcal FMAP representng a smoothed populaton surface s llustrated where the z-values correspondng to the dstorted road juncton locatons show local maxma. By comparng the xy-postons of road junctons stored n the IMAP and the xy-postons wth local maxmum z-values n the FMAP, the dstorted postons of road junctons are dentfed. For each dentfed xy-poston of the FMAP, several measurement sets n the MDB can be found that corresponds to ts neghbourhood.

8 Fgure 6 A typcal FMAP representng smoothed populaton surface In ths way, the reference ponts can be found automatcally and the NLOS errors of the reference ponts can be extracted (Lee et al, 005). All the reference ponts are used to generate the correcton map. In order to generate the correcton map effcently, unversal krgng s utlzed. Krgng s an estmaton procedure whch was frst used by the mnng ndustry. The basc tool n krgng, the varogram, s used to quantfy spatal correlatons between observatons. As there are many advantages of krgng (Clark, 1979), ts applcaton can be found n very dfferent dscplnes. wthout WSMM wth WSMM Fgure 7 Cumulatve error dstrbuton wth and wthout WSMM (smulaton of the typcal Manhattan-lke area) Based on our smulated data error dstances between estmates and true user postons were computed. As a result, the cumulatve error dstrbuton dagram of Fgure 7 was obtaned. Two lnes n the fgure wth the symbols o and + correspond to the cumulatve error dstrbuton wth and wthout the WSMM respectvely. One can see 85 percent of users are wthn 50 m error dstance wth the WSMM whle 5 percent of users are wthn the same error dstance wthout the WSMM.

9 4. EXPERIMENTS AND RESULTS To verfy the proposed WSMM, an experment was carred out usng a CDMA (Code Dvson Multple Access) network n a typcal suburban envronment n Bejng, Chna. In such an envronment, NLOS propagaton can be expected. The test area s about 1km by km and n total there are 4 BTSs. At least 8 BTSs are located n the adjacent areas. To smplfy the experment, the test area s further dvded nto small areas (partly overlapped), named area A and area B. Fgure 8 shows the map of test area A. In each small area, 3 BTSs are dstrbuted evenly. As we know, a typcal BTS has 3 sectors and each sector has a unque ID. Hence each sector (antenna) can provde a TDOA measurement. However, the 3 sectors are part of one BTS, so they have the same or very smlar locaton. From the trlateraton postonng pont of vew, the 3 sectors can be only used as one base staton because the measurements must come from spatally dverse locatons. The coordnates of these BTS are prerequste. A standard CDMA000 1x handset was used to collect data. A normal GPS recever was used to provde the true locaton of MU. Fgure 8 The map of test area A y (m) BTS User Dstrbuton Dstorted By NLOS Error and Nose (a) BTS TDOA GPS BTS BTS x (m) y (m) BTS User Dstrbuton Dstorted By NLOS Error and Nose (b) BTS TDOA GPS BTS BTS x (m) Fgure 9 User poston dstrbuton along a suburbans street n the presence of dstorted by NLOS error and nose; (a) usng dense test ponts but less measurements at each pont and (b) usng less test ponts but around 30 measurements at each pont We walked along the nearby streets, and several thousands of measurements were taken. The poston provded by GPS was used as the truth reference (because of the blockage of satellte s sgnal by the buldngs, sometmes map matchng was used to correct the offset). Fgure 9 depcts the test results along a man street n test area A. Part (a) s based on data

10 collected at densely dstrbuted test ponts (the average nterval of the test ponts s about 15 m), and at each pont, only measurements were taken (the average of the measurements were utlzed). Part (b) s based on data collected at less densely dstrbuted test ponts (average nterval s about 40 m), but around 30 measurements were acqured at each pont. The results were dstorted serously because of the NLOS error. Part (a) also shows the effect of the nose. However, both of the two dagrams have a smlar pattern. It ndcates that the NLOS error has a fxed pattern along ths street. 100 Ideal test ponts & ntersectons 100 Dstorted dstrbuton of test ponts 1000 BTS BTS3 800 y (m) 600 y (m) BTS x (m) x (m) Fgure 10 The deal map (left) and dstorted map (rght) of test area B. The crcles n deal map ndcate the ntersectons; the dfferent symbols ndcate the test ponts from dfferent streets. After the data along the street n the test area had been collected, a dstorted map was generated. Fgure 10 shows the deal map whch was based on GPS data, and the dstorted map of area B as an example. The deal map was generated usng GPS data. The dfferent symbols n the dstorted map ndcate the dfferent streets. Snce the map has been deformed serously, wthout those symbols, t s hard to fnd the streets. The nose and the rarty of test ponts made t almost mpossble to fnd the ntersectons usng the dstorted map only. Ths s one of the dffcultes n deployng WSMM n a real applcaton. Assumng the ntersectons showng n the deal map (ndcated by crcles) can be found, the proposed method can be utlzed. The NLOS error can be mtgated more or less n that case. Fgure 11 compares the cumulatve dstance error dstrbuton before and after usng the correcton map. The mprovement s consderable. Before applyng the correcton, only 3% of the test ponts wthn 50m-dstance error and close to 60% of the test ponts wthn 100m-dstance error whle after correcton, those percentages ncrease to 49 and 86 respectvely. One thng that must be emphaszed s that only 4 reference ponts (the ntersectons) were utlzed to generate the correcton map. Intutvely, f more reference ponts were used, the result would be better. Smlar mprovements were also found n area A. 5. CONCLUSIONS In ths paper, a new approach for mtgatng NLOS error, the WSMM technque s ntroduced. The man advantage of WSMM s that t can automatcally extract the reference ponts and employ a small number of reference ponts to generate a NLOS error correcton map effcently (based on krgng). From the smulaton and experment results, t has been shown that ths approach can mprove the accuracy of TDOA postonng consderably.

11 From the experment, t s observed that the nose level s much hgher than what antcpated; and t gets serous n the NLOS scenaro. Ths makes the detecton of the reference ponts extremely complex and dffcult. Apparently, ths s the major problem for WSMM. Future work wll focus on nose reducton and reference pont detecton before correcton after correcton cumulatve error dstrbuton probablty (%) error dstance (m) Fgure 11 Cumulatve error dstrbuton before and after applyng the correcton ACKNOWLEDGEMENTS Thanks to Prof. Jngjun Guo, Mr. Baotong Xe of Tsnghua Unversty (P.R. Chna), Mr. Donghang L, and Mr. Bng Qn for the help to collect the data. REFERENCES Caffery J, Stuber, GL (1998) Overvew of radolocaton n CDMA cellular systems, IEEE Communcatons Magazne, vol. 36, no. 4, pp Slventonen MI, Rantalanen T (1996) Moble staton emergency locatng n GSM, IEEE Internatonal Conference on Personal Wreless Communcaton, New Delh, Inda, 19-1 February, pp Woo SS, You HR, Koh JS (000) The NLOS mtgaton technque for poston locaton usng IS-95 CDMA networks, Proc. IEEE VTC, Boston, USA, 4-8 September, vol. 6, pp L X (1998) A selectve model to suppress NLOS sgnals n angle-of-arrval (AOA) locaton estmaton, The Nnth IEEE Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons, Boston, USA, 8-11 September, vol. 1, pp Morley G, Grover W (1995) Improved locaton estmaton wth pulse rangng n presence of shadowng and multpath excess-delay effects, Electron. Lett., vol. 31, no.18, pp Wyle MP and Holtzman J (1996) The non-lne of sght problem n moble locaton estmaton, 5th IEEE Internatonal Conference on Unversal Personal Communcatons, Cambrdge, USA, 9 September- October, vol., pp Cong L, Zhuang W (001) Non-lne-of-sght error mtgaton n TDOA moble locaton, IEEE Global Telecommuncatons Conference, San Antono, USA, 5-9 November, vol. 1, pp

12 Cong L, Zhuang W (004) Non-lne-of-sght error mtgaton n moble locaton, Twenty-thrd AnnualJont Conference of the IEEE Computer and Communcatons Socetes, Hong Kong, 7-11 March, vol. 1, pp Chen P-C (1999) A non-lne-of-sght error mtgaton algorthm n locaton estmaton, IEEE Wreless Communcatons and Networkng Conference, New Orleans, USA, 1-3 September, vol. 1, pp Wang W, Wang Z, O Dea B (003) A TOA-based locaton algorthm reducng the errors due to Non- Lne-of-Sght (NLOS) propagaton, IEEE Trans.Veh. Technol., vol. 5, no. 1, pp Jayaraman S, Wax M, Hlsenrath OA (000) Calbraton table generaton for wreless locaton determnaton, US patent 6,101,390. Foy WH (1976) Poston-Locaton Solutons by Taylor-Seres Estmaton, IEEE Transactons on Aerospace and Electronc Systems, vol. 1, pp Fang BT (1990) Smple Solutons for Hyperbolc and Related Fxes, IEEE Transactons on Aerospace and Electronc Systems, vol. 6, no. 5, pp Chan YT and Ho KC (1994) A smple and effcent estmator for hyperbolc locaton, IEEE Transactons on Sgnal Processng, vol. 4, no. 8, pp L B, Rzos C, Lee HK (005) Utlzng krgng to generate a NLOS correcton map for network based moble postonng, Journal of GPS, vol. 4, no. 1-, pp Hata M (1980) Emprcal formula for propagaton loss n land moble rado servces, IEEE Transactons on Vehcular Technology, vol. 9, no. 3, pp Whte CE, Bernsten D, Kornhauser AL (000) Some map matchng algorthms for personal navgaton assstants, Transportaton Research Part C: Emergng technologes, vol. 8, no. 1-6, pp Lee HK, L B, Rzos C (005) Implementaton procedure of wreless sgnal map matchng for locaton-based servces, 005 IEEE Internatonal Symposum on Sgnal Processng and Informaton Technology (ISSPIT), Athens, Greece, 18-1 December, pp Clark, I. (1979) Practcal geostatstcs, Appled Scence Publshers, London.