SETIT 009 5th Internatonal Conference: Scences of Electronc, Technologes of Informaton and Telecommuncatons March -6, 009 TUNISIA Multpath Mtgaton n GPS/Galleo Recevers wth Dfferent Sgnal Processng Technques K.BENACHENHOU, E. SARI and M.HAMMADOUCHE Aeronautc department of BLIDA aerokamb@ yahoo.fr kahnasar@yahoo.fr hamadouche_mhamed@yahoo.fr Abstract: It s well known that multpath error s one of the major error sources affectng the postonal accuracy of Global Postonng System (GPS). Multpath effect can be reduced by several methods essentally by sgnal processng technques whch can be realzed at the correlator level, by usng new sgnals (BOC or MBOC) or wth adaptve technques. The man motvaton of ths paper s to provde these methods for assessng multpath performance, frst we mplement each approach separately than we propose to combne them, concern adaptve technques we choce an NLMS algorthm. The obtaned results are presented and analyzed through multpath errors envelope. Key words: GPS, Galleo, multpath mtgaton, NLMS, DLL. 1. State-of-the-art As the domnant error source n hgh-accuracy GPS applcatons, multpath was the subject of several research work for ths last years. A number of sgnal processng technques have been proposed to detect and mtgate multpath errors on both range and phase measurements. Many of those are based on the trackng loop dscrmnator, n ths context the narrow correlator was proposed by Van Derendonck and al []. The narrow correlator employs a DLL wth very small chp spacng between Early and Late code local replcas. Strobe and Edge Correlators [], Hgh Resoluton Correlator (HRC) [8], double delta correlator [4] or the Gated Correlator [9], are proposed, they acheve smlar performance wth narrow correlator. Waveform optmzaton was another approach to mprove trackng performance n multpath. A new sgnals based on new modulaton scheme are proposed n modern navgaton satellte system. Bnary offset carrer (BOC) spreadng modulatons [5] are one way to accomplsh ths, and a BOC(1,1) spreadng modulaton was selected as the baselne for the future GALILEO L1 OS and GPS L1C sgnals. Betz and J.W [5] show that BOC sgnal provde better performance than C/A code. MBOC waveforms provde typcally smaller average errors than BOC(1,1) waveform [7]. Another waveform optons, TMBOC(6,1,4/33), shows an average error less than those of any other opton for all delays [1]. Another category of technques reles on an estmaton of the parameters (ampltude, delay and phase) of the lne-of-sght (LOS) sgnal along wth those of all the multpath components. It ncludes a multpath estmaton technque (MET) proposed by Townsend and Fenton [4], based on the slope of the autocorrelaton functon to estmate the code phase offset delay of the drect sgnal, ths technque has been utlzed to reduce only code-phase error n DLL and the effect of PLL carrer-phase error s not consdered. From these reasons, van Nee and R.D [14] employed a multpath estmaton delay lock loop (MEDLL) to estmate multpath sgnals and mtgate code and carrer-phase errors. Mnam and Morkawa [10] propose an RLS adaptve flter based multpath mtgaton technque. An adaptve flterng process s used for estmatng a multpath delay profle wtch s used for subtractng the estmated multpath effects from the measured autocorrelaton value of GPS sgnal. In ths paper, we wll at frst analyze multpath performance based on waveform optmzaton; comparson based on multpath error envelope wll be presented. Than, we propose to use narrow and double-delta correlator, the subject s to dentfy the best combnaton between sgnal and correlator that wll be used next. Second, we propose an adaptve flterng approach to multpath mtgaton based on NLMS algorthm. We wll estmate the drect plus multpath sgnal parameters to separates them and - 1 -
SETIT 009. subtract ths later sgnal from the measured autocorrelaton value of receved sgnal. Fnally, we propose to assocate all ths methods, smulaton results are presented to compare the performance of the proposed methods.. Introducton Global Postonng System (GPS) s a satelltebased navgaton system desgned and developed by US Department of Defence (DoD) to provde nstantaneous 3D poston, velocty and tme nformaton almost anywhere on or above the surface of the earth at any tme, and n any weather. The GPS receves rght-hand, crcularly polarzed sgnals from a number of satelltes. The crcularly polarzed sgnals facltate the rejecton of multpath sgnals. The current GPS recevers operate at L1 (1575.4 MHz) and L (17.6 MHz). The postonal accuracy provded by GPS s lmted by varous errors. Also, the GPS pseudorange obtaned by ether carrer-phase or code-phase measurements are affected by several types of random errors and bases (systematc errors). These errors can be classfed as those orgnatng at the satelltes, those orgnatng at the recever and those that are due to sgnal propagaton, we can note orbtal errors, satellte clock errors, and multpath errors. Wth the use of dfferental technques t s possble to remove many of the common-mode error sources, but the error effects of multpath have proven much more dffcult to mtgate. Multpath s when the lne-of-sght frst comes to the recever and the same sgnal, a lttle bt weaker, comes agan as a delay. Ths delayed sgnal s created when the lne-of-sght sgnals has bounced on buldngs, mountans, trees or the ground before reachng the recever. Multpath sgnals are characterzed by four parameters and all are relatve to the drect lne-of-sght sgnals. These are ampltude, tme delay, phase and phase rate change. Multpath can be mtgated at three dfferent levels: antenna, sgnal processng and navgaton. In our work we focus on the sgnal processng level whch can be decomposed n two knds: ones that attempt to mtgate t wthout estmatng t, here we wll study the nfluence of multpath on dfferent sgnals and also dfferent correlators and ones that estmate the multpath, here we wll develop an adaptve method NLMS algorthm based. 3. Multpath effect To demodulate the navgaton data successfully an exact carrer wave and code replcas has to be generated. To do that a Costas Loop s often used assocated to DLL loop, we focus at frst on DLL. The goal for a code trackng loop s to keep track of the code phase of a specfc code n the sgnal, the output of such trackng loop s a perfectly algned replca of the code. The code trackng loop n the GPS recever s a delay lock loop (DLL) called an Early-Late trackng loop, the dea s to correlate the nput sgnal wth three local replcas of the code, Prompt, Early and Late separated wth précsed chp spacng and than tracks the zeros-crossng of the dscrmnator response. In presence of multpath (we suppose a sngle reflecto the receved GPS sgnal can be expressed as: s t A dt c t cosf t 0 0 LOS sgnal drect t c t cosf t bt A1 d 1 f 1 I 1 reflected sgnal f 0 I 0 (1) When we develop the dscrmnator response of ths composte sgnal we can obtan Fg.1 wtch shows the effect of the multpath n case of a coherent Early-Late DLL, t can be seen that the dscrmnator zeros-crossng s shfted, thus ntroducng an error n the estmated code delay. FIGURE 1. Code delay error n the presence of multpath In order to assess and study multpath effect and ts related mtgaton technques, t s useful to smulate multpath error envelope whch assume a sngle reflecton of LOS sgnal, then the delay of ths reflected sgnal s swept through a range of values to evaluate the code delay errors n the code trackng loop. The use of such error envelopes s a good and comprehensve way to compare the multpath performance of dfferent sgnal wth respect to each other. In the case of C/A code used n actual GPS sgnal, where the correlaton functon presented n Fg.3 and f we use a coherent Early- Late dscrmnator we can show that the theoretcal error envelope s gven mathematcally as: 1 1 g 0 g 0 3 Tc 1 () 34 Tc - -
SETIT 009. 1 1 g g 3 Tc 1 (3) 34 Tc Wth A / A 1 s the reflecton coeffcent and correspond to the chp spacng. Another nterestng sgnal n BOC famly s the so called MBOC. The European approach to the MBOC mplementaton conssts n addng n tme a BOC(1,1) and a BOC(6,1), defned as composte BOC modulaton, such a sgnal structure allows the recevers to obtan hgh performance n terms of multpath rejecton and trackng, Ths s manly due to a hgher transton rate brought by the BOC(6,1) on top of the BOC(1,1). The notaton ntroduced n [9] s MBOC(6,1,1/11), where the term (6,1) refers to the BOC(6,1), and the rato 1/11 represents the power splt between the BOC(1,1) and BOC(6,1) spectrum components as gven by: G 10 1 f ) GBoc( 1,1) ( f ) GBoc(6,1 ( f ) (6) 11 11 MBoc ( ) FIGURE. C/A code multpath errors envelope These are called envelopes snce only the worst cases are consdered, when the relatve multpath phase s 0 radans, the multpath component s n phase and wth radans, the multpath component s out of phase. In the framework of the modernzaton plans of Global Navgaton Satellte Systems (GNSS) a new modulaton has been proposed as a possble Sgnal- In-Space (SIS) wth mproved performance wth respect to the robustness aganst external sources of degradaton, manly multpath. We speak about Bnary Offset Carrer (BOC: Bnary Offset Carrer) modulaton. A BOC(n,m) modulaton has a CDMA spreadng code clocked at frequency m.f C/A multpled by a bnary valued (1 or -1) square wave at frequency n.f C/A (the offset carrer), where f C/A s a fundamental frequency unt used n satellte navgaton, 1.03MHz. In ths case the satellte transmtted sgnal s gven as follows: S( t) A. d( t). CA( t). Sboc ( t).cos( L1. t ) (4) wth: S ( t) sgn(sn(.. f. t)) (5) boc sc Fg.3 shows the autocorrelaton functon of Boc(1,1) sgnal. Comparng wth C/A code autocorrelaton functon, we observe a narrower peak for Boc than C/A code. where GBOC(m,(f) s the unt-power spectrum densty of a sne-phased BOC modulaton as defned n [10]. The normalzed autocorrelaton functon of the MBOC(6,1,1/11) spread spectrum tme seres, computed over nfnte bandwdth and wth deal spreadng codes, s llustrated n Fg.3, along wth the autocorrelaton functon for C/A and BOC(1,1) codes. Observe that MBOC(6,1,1/11) s correlaton functon peak s narrower than that of BOC(1,1), but the wdths at values of 0.5 and at the zero crossng are vrtually the same. Also we observe the apparton of undulatons that certanly nfluences on the multpath error envelop shape. FIGURE 3. Autocorrelaton functon of C/A, BOC(1,1) and MBOC(6,1,1/11) codes The Fg.4 llustrate the C/A code error envelope showng maxmum and mnmum trackng error for each delay n case of standard early-late correlator wth chp spacng d=0.5 chp for dfferent values of reflecton coeffcent =0., 0.5 and 0.8. We observe that the error nduced by multpath s proportonal to ths coeffcent. Next we determne the multpath error envelope for Galleo BOC(1,1). - 3 -
SETIT 009. senstve for multpath sgnals wth a relatve path delay up to 300 m. as an example, The resultng range errors n case of BOC(1,1) at 50m multpath delay wth 0. 5 s about 4 m, but n case of C/A code s about 60m. Ths demonstrates that BOC(1,1) sgnals are better to handle multpath sgnals than C/A code sgnals. In Fg.6 MBOC(6,1,1/11) error envelope s presented, we remark that ths sgnal provde an error envelopes that are smaller than both C/A and BOC(1,1) sgnal for the small values of path length delays. FIGURE 4. C/A code multpath error envelope, E-L standard dscrmnator, d=0.5 chps FIGURE 5. BOC(1,1) multpath error envelope, E-L standard dscrmnator, d=0.5 chps 4. Mnmsaton by usng dfferent correlators The presented results are obtaned n the case of a wde correlator/standard correlator, that use one correlator at 0.5 chps before the assumed punctual top of the peak and another delayed wth 0.5 chps, ths s for dfferent types of sgnal. In multpath mtgaton context at sgnal processng level we can use another types of correlators, n ths paper we have study a narrow correlator and double dfference correlator. 4.1. Narrow correlator To avod bg parts of the nfluence of multpath, the narrow correlator concept was developed. The narrow correlaton technque has been frst proposed n 199 [3] and ntroduced to GPS recever by NovAtel. Instead of usng a standard correlator wth chp spacng of 1 chp between the Early and Late replcas, the chp spacng of a narrow correlator s less than 1chp, usually 0.1 chp s used to buld up the dscrmnator functon. Ths prncple s presented n Fg.7 bellow. FIGURE 7. Narrow correlator FIGURE 6. MBOC(6,1,1/11) multpath error envelope, E-L standard dscrmnator, d=0.5 chps The result s plotted n Fg.5. Comparng Fg.4 and 5 for standard correlator spacng (d=0.5) we see that the C/A code multpath error envelop s 4.. Hgh resoluton correlator Ths type of correlator s n the famly of double dfference correlators whch use two correlator pars nstead of only one n ther code dscrmnator functons. To provde multpath mtgaton ths type of correlator employ two correlators n parallel as llustrated n Fg.8, the wde par has exactly double the chp spacng of the narrow par. The narrow par generally has a chp spacng of 0.1chps; the wde correlator has a chp spacng of 0.. Code dscrmnators s based on lnear combnaton of - 4 -
SETIT 009. two early mnus late dscrmnators, the frst one s made up of an early E 1, prompt P 1, and late L 1, the second s made up of an early E, prompt P, and late L. In ths work we choose as a lnear combnaton: or C/A codes. At longer path length delay values, the MBOC waveforms provde lower average delays. D HRC 1 E1 L E L (7) FIGURE 8. Hgh resoluton correlator FIGURE 9. C/A code multpath error envelope, E-L narrow correlator, d=0.1 chps Lke early-late processng, double-delta multpath mtgaton processng s a known processng technque that was desgned for BPSK- R spreadng modulatons, but may be appled to more advanced modulatons as well. Smaller multpath error envelopes may be obtaned when we appled narrow or double delta correlator. Fg.9 shows the multpath errors resultng from a narrow correlator processng wth the same multpath propagaton model used prevously for dfferent value of reflecton coeffcent. In ths fgure, we can easly remark the sgnfcant mprovement gven by ths correlator. The multpath error envelopes has a maxmum value of 10 m for =0.8 and 8 m for =0.5 comparng wth Fg.4 whch we have a maxmum of 10 m for =0.8 and 70 m for =0.5. FIGURE 10. C/A code multpath error envelope, double dfference correlator, d=0.1 chps Fg.10 shows the multpath errors resultng from narrow correlator and double delta processng. In ths fgure, for narrow correlator the chp spacng s =0.1 chps, n case of double delta correlator the outer early-late spacng s 0.1 chps and nner earlylate spacng s 0.05 chps. We observe that the multpath error envelopes for the narrow correlator optons are nearly the same as those for double delta correlator. Fg.11 shows the multpath errors envelopes wth a narrow correlator for both C/A, BOC(1,1) and MBOC(6,1,1/11) codes. We observe that MBOC(6,1,1/11) waveforms provde typcally smaller average errors than ether BOC(1,1) or C/A waveforms. An mportant feature of MBOC waveforms s that the error envelope dmnshes at smaller path length delay values than for BOC(1,1) FIGURE 11. Multpath error envelope of C/A,BOC(1,1) and MBOC(6,1,1/11) codes - 5 -
SETIT 009. 5. Adaptve Multpath Mtgaton The block dagram of the multpath mtgaton system s shown n Fg.1. Receved sgnal s processed n RF flter then down converted and sampled to a dgtal IF sgnal by an A/D converter. The trackng module composed of DLL and PLL receve a GPS IF sgnal and generate a local code and carrer replcas. FIGURE 13. Proposed NLMS based algorthm The system equatons used by the NLMS flter to determne the error and output of the flter are lsted below. In the presence of multpath, dgtal IF sgnal,.e. output sgnal at the A/D converter can be wrtten as: FIGURE 1. Adaptve multpath mtgaton method Multpath estmator s an adaptve flter NLMS based wth IF sgnal as reference, he estmate a delay profle of multpath. The estmated sgnal parameters are used n the correlaton extractor to determne a correlaton value of delayed sgnal. The detaled process of the multpath estmator, the correlaton value extractor, and the multpath cancellaton wll be presented as follows. 5.1. Multpath Estmator The task of multpath estmator s to estmate the multpath delay profle by the use of adaptve flter. There are many algorthms that could be used n ths context; most are varatons of the least mean squared (LMS) algorthm. Some varatons nclude normalzed LMS (NLMS) and the recursve least squares algorthm (RLS). The NLMS algorthm was chosen because t s the most commonly used algorthm n adaptve flterng applcatons, he s powerful enough to accomplsh the system s requrements and s also relatvely smple compared to the other algorthms. The NLMS algorthm uses relatvely few calculatons, whch makes t sutable for the speeds of the DSP s avalable today. The NLMS algorthm n our case study seeks to mnmze the excess MSE between the composte (LOS plus multpath) IF sgnal and a sgnal local replca at the output of trackng module as a reference sgnal. The communcaton network n Fg.13 has the necessary sgnals that are requred by the LMS algorthm. yˆ ( Mˆ 0 Aˆ g( n ˆ ) cos( wn ˆ ) ( (8) Where A, and are the ampltude, the code delay, and the carrer phase of m th delayed sgnal. M s the number of multpath component, g s spreadspectrum code, and ω s IF frequency and n s dscrete tme. The 0 th delayed sgnal corresponds to the drect sgnal. The parameter wth the symbol denoted the estmated parameter. Because the parameters are mpossble to be determned drectly wthout any assumpton about multpath sgnals, we utlze reference sgnals n estmaton process. A reference sgnal s a replca of code and carrer obtaned from output of DLL and PLL, and s wrtten as: K y( w. x ( ( (9) 0 ( ) Where w A ˆ j m m e, the adjustable weght whch s used to mnmze the least squares crtera defned by usng (8) and (9) as: y( yˆ(. y( yˆ( L E (10) where E[.] s a expectaton operator, and the mark * represents complex conjugate. The error sgnal e( s created from the subtracton of the desred sgnal from the output of the adaptve flter: e( y( yˆ( (11) * - 6 -
SETIT 009. The adaptve LMS equaton s gven by: w( n 1) w(. e(. x( (15) The reference sgnal x( generated at the output of the trackng module s used as an nput to the adaptve flter so that the adaptve NLMS flter s response approxmates the multpath system s frequency response. The error sgnal s feedback to the adaptve flter and s used as an nput wth the orgnal nput sgnal to update the NLMS adaptve flter. After several teratons, we can obtan estmated delay profle from flter taps and delay element, consequently multpath sgnal can be estmated. The parameter determnes the convergence or dvergence speed and precson of the adaptve flter coeffcents. If s large, the flter wll converge fast, but could dverge f s too large. When s large, the adaptaton s quck, but there wll be an ncrease n the average excess MSE. Ths excess MSE may be undesrable result. If s small, the flter wll converge slowly, whch s equvalent to the algorthm havng long memory, an undesrable qualty. 5.. Correlaton Extractor After obtanng the estmated delay profle, we separate multpath sgnals from drect sgnal, ths s done trough the subtracton of delayed sgnals correlaton from that of receved sgnal. We assume that the frst peak of ampltude of the estmated delay profle s the drect sgnal, and the remanders are delayed sgnals. The component of the delayed sgnals s, then, used to compute the correlaton value of delayed sgnals. The followng equaton represents the correlaton value of one estmated delayed sgnal wth ampltude carrer phaseˆ m : R Â m, delay ˆ m and ) Aˆ R( ) exp j( ˆ ˆ ) (16) M ( m m p m sgnal R M ( ), and the mproved correlaton value Rc ( ) s obtaned: R ( ) R ( ) R ( ) (19) c M L Snce trackng errors caused by multpath n DLL and PLL manly come from dstorton of the correlaton functon of receved sgnal, the subtracton of RL ( ) provdes multpath mtgaton n the trackng loop. Therefore, the use of R c ( ) enables the trackng loops to track drect sgnal more accurately. Although above processes (.e. estmaton, extracton, and elmnaton process) can reduce the effects of multpath on the autocorrelaton of receved sgnal, trackng errors n DLL and PLL are not elmnated completely. Because the reference sgnal used n multpath estmator contans multpath error, and estmated delay profle does not reflect correctly that of real multpath. To approach obtanng deal delay profle of multpath, we apply the above processes recursvely. 5.4. Smulatons and results As prevously, we wll buld up the multpath error envelop assocated to our proposed NLMS method, we note that a dampng factor 0. 7 and bandwdth w 170 Hz has been used at PLL level. We consder a multpath wth ampltude A=0.5 and a phase equal to zero degree than to p for several delays. Fg.14 shows smulaton results n code and carrer phase error mtgaton wth NLMS method comparng wth narrow correlator obtaned result n case of C/A code. Smulaton results show that by usng adaptve multpath mtgaton technque, multpath s consderably reduced. We observe that DLL wth a narrow correlator has an error code phase of ± 8 meters n presence of multpath sgnal, on the other hand, usng multpath mtgaton wth NLMS adaptve method ths error s reduced at 1 meter. Where RM ( ) s the auto-correlaton functon of GPS sgnal: R ( ) E[ p( p( n )] (17) Therefore, the correlaton value of all estmated delayed sgnal R ( ) s obtaned as follows: Mˆ m p d R d ( ) R m ( ) (18) 5.3. Multpath Elmnaton The correlaton value of delayed sgnal y(t) s subtracted from the correlaton value of receved - 7 - FIGURE 14. Smulaton results wth NLMS based mtgaton technque for C/A code
SETIT 009. [3] B. W. Parknson and J. J. Splker (Eds.), Global Postonng System: Theory and Applcatons, Vol. 1, pp. 45-407, AIAA Inc., 1996. [4] B. Townsend, P. Fenton, and K. J. van Derendonck, L1 Carrer Phase Multpath Error Reducton Usng MEDLL Technology, Proc. ION GPS-95, 1995. [5] Betz. J.W, Bnary Offset Carrer modulatons for rado navgaton, Journal of the Insttute of Navgaton, 1996. Vol 48, No4, Wnter 001. FIGURE 15. Smulaton results wth NLMS based mtgaton technque for Boc(1,1) code In the case of BOC(1,1) code, multpath mtgaton performances summarzed by the multpath error envelop are presented n Fg.15. We observe that the error don t exceed 0.5 meters n the range 150-300 meters, ths error s smaller than the case gven by fgures 11&14. 6. Conclusons In ths paper, a several multpath mtgaton sgnal processng methods have been proposed for Galleo and GPS sgnals. We have evaluate the multpath error envelop for each presented case to llustrate and analyze the multpath nfluence on a trackng loop. As a frst concluson, we can say that BOC code s better than C/A code. Narrow correlator s a best choce for both C/A and BOC codes, however smulatons revealed ths correlator combned wth BOC or MBOC codes are more attractve. By performng a normalzed least squares algorthm, we observe that the multpath s successfully cancelled and we can make a reconstructon of the orgnal sgnal. The obtaned results confrm that the NLMS algorthm s a very powerful and smple tool for multpath mtgaton for both GPS and Galleo recever. The paper concluded that the adaptve methods are very promsng as a soluton to multpath mtgaton ssues n future GNSS recevers. 7. References [1] A. J. van Derendonck and M. S. Brash, Evaluaton of GNSS Recever Correlaton Processng Technques for Multpath and Nose Mtgaton, Proc. ION Natonal Techncal Meetng, pp. 07-15, 1997. [] A. J. van Derendonck, P. Fenton, and T. Ford, Theory and Performance of Narrow Correlator Spacng n a GPS Recever, Journal of the ION, Vol.39, No.3, pp.65-8,199. [6] B. Townsend, R. D. J. van Nee, P. Fenton, and K. J. van Derendonck, Performance Evaluaton of the Multpath Estmatng Delay Lock Loop, Proc. ION Natonal Techncal Meetng, 1995. [7] E. D. Kaplan, Understandng GPS: Prncples and Applcatons, Artech House, 1996. [8] G.A. McGraw and M. Braasch. GNSS multpath mtgaton usng hgh resoluton correlator concepts. In Proc. of ION Natonal Techncal Meetng, pages 333 34, San Dego, CA, Jan 1999. [9] McGraw, G. A., Braasch M. S, GNSS Multpath Mtgaton Usng Gated and Hgh Resoluton Correlator Concepts, Proceedngs of he ION Natonal Techncal Meetng, pp 333-34, 1999 [10] Masateru Mnam, Hroyuk Morkawa, and Tomonor Aoyama, An Adaptve Multpath Mtgaton Technque for GPS Sgnal Recepton, School of Engneerng, The Unversty of Tokyo. [11] Phelts, R. E., Enge, P. K., The Case For Narrowband Recevers, ION Natonal Techncal Meetng, San Dego, CA, January 000. [1] Phelts, R. E., Stone, J. M., Enge, P. K., Powell, J. D., Software-based Multpath Mtgaton: Samplng for Multpath Invarance, Program and Proceedngs of the 4th Internatonal Symposum on Satellte Navgaton Technology and Applcatons, Sesson 3, 1999. [13] R. D. J. van Nee, The Multpath Estmatng Delay Lock Loop, Proc. IEEE Second Symposum on Spread Spectrum Technques and Applcatons, pp.39-4, 199. [14] R. D. J. van Nee, The Multpath Estmatng Delay Lock Loop: Approachng Theoretcal Accuracy Lmts, Proc. IEEE Poston Locaton and Navgaton Symposum, pp. 46-51, 1994. [15] R. D. J. van Nee, Method of Estmatng a Lne of Sght Sgnal Propagaton Tme Usng Reduced-Multparh Correlaton Functon, Unted States Patent, No.56153, 1997. [16] S. Haykn, Adaptve Flter Theory, Prentce Hall, 1996. - 8 -