An Efficient Method for GPS Multipath Mitigation Using the Teager-Kaiser-Operator-Based MEDLL

Transcription

1 YI HU, AOZHONG SONG, BIN ENG, XIAOYU DANG, AN EFFICIENT ETHOD FOR GPS ULTIPATH ITIGATION USING An Effent ethod for GPS ultpath tgaton Usng the Teager-Kaser-Operator-Based EDLL Y HU, aozhong SONG,, Bn ENG, Xaoyu DANG College of Eletron & Informaton Engneerng, Nanjng Unversty of Aeronauts & Astronauts, Nanjng, Chna The Aademy of Satellte Applaton, Bejng, Chna hystarom@63.om, smz8@nuaa.edu.n, mengb@63.om, dang@nuaa.edu.n Abstrat. An effent method for GPS multpath mtgaton s proposed. The motvaton for ths proposed method s to ntegrate the Teager-Kaser Operator (TKO) wth the ultpath Estmatng Delay Lok Loop (EDLL) module to mtgate the GPS multpath effently. The general mplementaton proess of the proposed method s that we frst utlze the TKO to operate on the reeved sgnal s Auto-Correlaton Funton (ACF) to get an ntal estmate of the multpaths. Then we transfer the ntal estmated results to the EDLL module for a further estmaton. Fnally, wth a few teratons whh are less than those of the orgnal EDLL algorthm, we an get a more aurate estmate of the Lne-Of-Sght (LOS) sgnal, and thus the goal of the GPS multpath mtgaton s aheved. The smulaton results show that ompared to the orgnal EDLL algorthm, the proposed method an redue the omputaton load and the hardware and/or software onsumpton of the EDLL module, meanwhle, wthout dereasng the algorthm auray. Keywords GPS, multpath mtgaton, TKO-EDLL, LOS tme delay estmaton.. Introduton The fators that affet modern Global Postonng System (GPS) reevers to aheve hgh aurate pseudorange measurement have been greatly mproved. These fators nlude the frequeny drft of the satellte atom lok and that of the reever osllator, tme delay error aused by the onosphere and the troposphere, and the phase enter devaton of the reever antenna and so on. But for the multpaths whh orgnate from the refleton or dffraton of the surroundngs around the reever, t s hard to anel or remove them by the mathematal modelng or by the Dfferental GPS (DGPS) method [], sne the surroundngs may hange qukly and unpredtably. At the same tme, the multpath may ause a sgnfant dstorton to the ACF s shape, whh wll aordngly affet the LOS sgnal tme delay estmaton and hene the pseudo-range measurement []. For these reasons, now t has beome a farly mportant work to mtgate the multpath of the reever as muh as possble. In order to mtgate the GPS multpath effently, many new approahes have now been presented, and some of them have got wdely used n GPS reevers. At the reevng end, aordng to the plae where the multpath s mtgated, the GPS multpath mtgaton methods an be roughly ategorzed nto two types: the front-end methods and the bak-end methods. For the frst type, the multpaths are mtgated at the reever s antenna. The tehnques suh as the hoke rng antenna [3] and the mult-antenna array [4] are typal of ths knd. For the seond type, the multpaths are mtgated by proessng on the reeved sgnal s ACF n the reever. Based on the number of the orrelators used n the reever, ths type an be further lassfed nto two knds [5]: the onventonal tehnques suh as the narrow Early-nus-Late (nel) estmator [6], [7], the Double Delta estmator ( ) [8] nludng the Hgh Resoluton Correlator (HRC) [9], [] and the ultple Gate Delay (GD) estmator [], [] and so on; the advaned tehnques suh as the ultpath Estmatng Delay Lok Loop (EDLL) tehnque [5],[3], the Fast Iteratve axmum Lkelhood Algorthm (FILA) [4], the TKO [5], [6] and so on. For ths knd of, they often use more orrelators than those n. Besdes the tehnques mentoned above, the post-proessng tehnques are also now beomng an mportant part of the GPS multpath mtgaton methods, and these tehnques nlude Wavelet Flter (WF) [7], Adaptve Flter (AF) [8] and so on. Among the tehnques mentoned above, the EDLL an often get hgher auray ompared wth the other tehnques, and now has been appled nto some advaned GPS reevers [9]. But ts hgh omputaton load and more hardware and/or software onsumpton have lmted ts further applatons n onventonal GPS reevers [5], []. Contrarly, for the TKO, t an offer a smple and effent estmaton of the GPS multpath, moreover, t does not requre a hgh hardware and/or software onsumpton as the EDLL does [], but the Sgnal-to-Nose Rato (SNR) and the lmted bandwdth are the two lmtng fators for ts estmate auray [7].

2 RADIOENGINEERING, VOL., NO. 4, DECEBER 3 3 The proposed GPS multpath mtgaton method, whh ntegrates the Teager-Kaser Operator wth the EDLL algorthm (TKO-EDLL), s just for redung the hgh omputaton load and the resoures onsumpton of the EDLL algorthm, meanwhle, wthout dereasng the algorthm auray. The general mplementaton proess of the TKO-EDLL s that frst we utlze the TKO to get an ntal estmate of the multpaths nludng the path numbers, the tme delays, and the ampltudes and so on. Then we transfer these ntal estmated results to the EDLL module for a further estmaton. Fnally, wth a few teratons whh are less than those of the orgnal EDLL algorthm, we an get a more aurate estmate of the LOS sgnal, and thus the goal of GPS multpath mtgaton s aheved. The rest of ths paper s organzed as follows. In Seton, a reeved sgnal model s gven. In Seton 3, the TKO and the EDLL algorthm are brefly desrbed. Seton 4 presents the prnple of the proposed TKO- EDLL and ts detaled algorthm mplementaton, followed by the performane smulatons and omparsons of the TKO-EDLL and the EDLL n Seton 5. Fnally, the paper s onluded n Seton 6.. Sgnal odel The reeved sgnal of the GPS reever after downonverson an be wrtten as j fif t () rt () adt ( ) t ( ) e nt () where the subsrpt denotes the LOS sgnal, and denote the Non-LOS (NLOS) sgnals, a, and are the th multpath normalzed ampltude, tme delay and arrer phase respetvely, dt () s the navgaton data bt and t () s the GPS Coarse/Aquston (C/A) ode wth the value of + or -, f IF s the ntermedate frequeny (IF) ontanng the Doppler frequeny shft, and nt () s supposed to be the addtve nose norporatng all soures of nterferenes over the hannel. In (), sne the data bt dt (), and ts duraton ( ms) s far longer than that of C/A ode (977.5 ns), ts effet on the reeved sgnal an be attrbuted to, thus we an neglet dt () n (). At the same tme, we an orrelate rt () wth the loal repla t ( ) e, suppose j fif t that rt () s traked perfetly by the Phase Loked Loop (PLL) of the reever and that the ntal phase of loal generated arrer equals, then the reeved sgnal s ACF an be wrtten as j Rx( ) ar( ) e N( ) () where s the loal C/A ode tme delay or phase, LT j fif t N( ) n( t) ( t) e dt LT C s the orrelaton funton of C/A ode wth the nose, R( ) LT ( t ) ( ) t dt LT C s the normalzed ACF of C/A ode, and ts deal result s, T R( ) T (3), elsewhere where T s the C/A ode nterval and L s the aumulaton tme expressed n the multples of T. In (), the estmate of the reeved sgnal s ACF orrespondng to Rx ( ) s j R ( ) ar( ) e. (4) For the onvenene of our study, we make two hypotheses on (4) as follows. () The propagaton tme of the NLOS sgnal s longer than that of the LOS sgnal, that s, for all,,,. () The ampltude attenuaton of the NLOS sgnal s heaver than that of the LOS sgnal. Though n some speal oasons suh as ndoors or n an LOS sgnal sheltered envronment, ths result may get reversed, but for these speal ases, the multpath mtgaton annot be solved solely by the algorthm, t needs some other means for assstane, and t s out of the sope of ths paper. Based on ths pont, f we set a, we an get a for all,,,. 3. TKO and EDLL Algorthm 3. TKO TKO s a non-lnear quadrat operator ntally used for measurng the nstantaneous-varyng sgnal s energy, and t an also be used for the GPS multpath mtgaton [5]. For a ontnuous-tme omplex sgnal x(t), ts TKO an be wrtten as [] where x () t d x() t x () t dx() t dx () t dt xt () dt dt d x () t xt () dt s the omplex onjugate of x() t. (5)

3 4 YI HU, AOZHONG SONG, BIN ENG, XIAOYU DANG, AN EFFICIENT ETHOD FOR GPS ULTIPATH ITIGATION USING The dsrete-tme TKO of (5) an be wrtten as [] xn ( ) x( n) xn ( ) xnx ( ) ( n). xn ( ) x( n) In (5), f we replae x() t wth Rx ( ) gven n (4), then we an obtan [ Rx( )] a os( ) sgn( ) (, T) T (7) a sn( ) sgn( ) (, T) j Rx( ) a( ) e n ( ) T j Rx( ) a( ) e where sgn( t ) s the sgn funton, () t s the mpulse Dra funton, n ( ) s the result of ψ (٠) operatng on the omponent n ( ), and (, tt ) s the retangle pulse funton wth tme nterval T. From (7) we an see that the TKO of Rx ( ) s senstve to the tme delay of the multpath omponent, besdes, t an also offer us a good estmaton of the multpath ampltude whh has a moderate or hgh strength when SNR s hgh, as an be learly seen n Fg.. 3. EDLL Algorthm The EDLL algorthm s a ost-lkelhood (L) estmaton method for GPS multpath mtgaton. For Rx ( ) gven n (), the estmates of the th multpath based on the EDLL algorthm an be gven as [3] ˆ ˆ ˆ (6) N j ˆ ˆ m j max Rx( ) amr( m) e e, m (8) m aˆ R ˆ aˆ R ˆ ˆ e e N j ˆ ˆ m j x( ) m ( m), (9) m m ˆ ˆ ˆ ˆ ˆ N j ˆ m arg Rx( ) amr( m) e. () m m where N s the estmated multpath numbers, and the notaton (٠) means to take the real part of a omplex value. The general steps of the EDLL algorthm are as follows [3]. Fnd the hghest peak of R x (τ) and regard t as the peak of the LOS ACF, then estmate the peak parameters and get the estmated ACF of the LOS. Remove the estmated LOS ACF from R x (τ) and fnd the hghest peak of the resdual sgnal and take t as the seond path peak, then estmate ts orrespondng parameters and get the estmated ACF of the seond path. () Repeat the proess smlarly as n step untl all N NLOS paths are estmated or a termnaton ondton s met. (d) Based on the estmates of N NLOS paths, remove them from R x (τ) and utlze the resdual of R x (τ) to estmate the LOS agan as n. In most ases, the whole proess above may need many tmes of teratons so that a more aurate estmaton of eah multpath an fnally be got. Normalzed ACF Normalzed ACF.5.5 TK TKthreshold - - Tme delay [T ].5.5 TK TKthreshold - - Tme delay [T ] Fg.. Smulaton results of the TKO on the reeved sgnal s ACF wth dfferent SNR. The normalzed ampltudes and the respetve tme delays of the multpaths are set to [,.6,.3] and [,.3,.5]T, ther ndent angles are all set to. The aumulaton tme of ACF s set to ms and the SNR n eah smulaton s set to SNR = - db, and SNR = db. The TKthreshold n the fgure s a threshold used for lmtng the effet of the nose on the TKO estmaton. 4. TKO-EDLL Algorthm 4. Prnple of the TKO-EDLL From the mplementaton of the EDLL algorthm

4 RADIOENGINEERING, VOL., NO. 4, DECEBER 3 5 we an see that t s an extremely tme and resoures onsumng proess, beause there s not any pror knowledge of the multpath omponents. On the other hand, f we an offer some pror nformaton of the multpaths suh as the path numbers, the ntal ampltude estmates and/or the ntal tme delay estmates for the algorthm, then we an speed up the teraton proess and mprove the algorthm s effeny. rt () xer Correlator E t ( T s ) t ( ) EDLL e P R ( T ) x C/A ode Generator j fif t s Rx ( ) R ( T ) x L t ( T s ) s TKO Dgtal Sgnal Proessor N, aˆ, ˆ, ˆ Carrer Generator aˆ,, ˆ r r r Fg.. Prnple blok dagram of the TKO-EDLL. The E, P and L denote the Early orrelator, the Prompt orrelator and the Late orrelator respetvely, and T s s the sample nterval. Gven ths onsderaton, the proposed TKO-EDLL algorthm s just to utlze the TKO to get an ntal estmate of the path numbers N and the orrespondng estmates ˆ ( aˆ, ˆ, ) of eah multpath (the detaled meanng of the supersrpt and subsrpt an be referred to n the subsequent Subseton 4.). Then these ntal estmated results are transferred to the subsequent EDLL module so that a further estmaton of the aqured multpaths an be got. Fnally after several teratons, more aurate estmates r r ( ˆ ˆ r a,, ) of the LOS sgnal an be obtaned from the fnal estmated results. The prnple blok dagram of the proposed TKO-EDLL s shown n Fg.. 4. Implementaton of the TKO-EDLL Algorthm Aordng to Fg., a detaled mplementaton proess of the proposed TKO-EDLL algorthm an be gven as follows. Step. Frst n (6), substtute x(n) wth the dsrete ACF R x (n) to get an ntal estmate of eah multpath. In ˆ ˆ fat, a and are just the ampltude and the orrespondng tme delay of the ompettve peak of TKO operatng on R x (n) [7], so we an obtan them by fndng the ompettve peak of TKO operatng result; for, after we get a ˆ ˆ and ˆ, t an be dretly obtaned by (), here ˆ for the LOS sgnal s regarded as. Then, from the estmated results, hoose those whose ampltudes exeed the preset TKO threshold. After that, sort the hosen multpaths n desendng order and selet the frst N ompettve peaks for the subsequent further estmaton, here N s the number preset n advane. If N s larger than the atual path numbers got by the TKO, let N equal the atual path numbers. Step. Take the ampltudes, the tme delays and the arrer phases of the N estmated multpaths nto (4) to get ther respetve estmated ACFs. Then the estmated ACF of the th multpath an be wrtten as ˆ R ( ) aˆ R( ˆ )exp( j ) () where the subsrpt denotes the th estmated multpath,,,,, N. Here s for the LOS sgnal and N are for the NLOS sgnals. The supersrpt denotes the teraton tmes, and t means the ntal TKO estmaton when ts value equals. Step 3. Transfer the ntal TKO estmated results to the EDLL module to perform a more aurate estmaton on eah path. For the th multpath, ts prmary EDLL estmates an be wrtten as follows based on (8) to (), ˆ ˆ aˆ ( ˆ R )exp( j ), ˆ arg[ ( ˆ R )]. ˆ max R ( )exp( j ), () Due to the parameters n () ouplng eah other, t s hard to get ther analytal results, and ther pratal mplementatons are often got by the teraton method whh an be gven as follows. Based on the prevous estmated multpaths ( N ), get the resdual sgnal of Rx ( ) and ts energy aordng to the followng formulas: ˆ ˆ ˆ Rx Rk Rx akr k j k k k ( ) ( ) ( ) ( ) ( )exp( ), E (3) ( ) d. T (4) T Based on the ( ) gven n (3), get the estmates of tme delay, phase and ampltude of the th multpath aordng to the formulas gven as follows [3]: ˆ max ( ) ( ), ( ˆ ) f ˆ ( ˆ ) ( ˆ ) f ˆ ( ˆ ) ˆ ˆ and ˆ ˆ and atan, ( ) ˆ atan, ( ), f ( ) ( ), f ( ) ( ), (5) (6)

5 6 YI HU, AOZHONG SONG, BIN ENG, XIAOYU DANG, AN EFFICIENT ETHOD FOR GPS ULTIPATH ITIGATION USING ˆ aˆ ( ˆ )exp( j ) (7) where atan( t ) s the artangent funton, and the notaton (٠) means to take the mage part of a omplex value. () Remove the phase rotaton from ( ), that s, ˆ ˆ ( ) ( ) os ( ) sn. (8) Then for a gven peak delay, the normalzed C/A ode phase dsrmnatng funton an be gven as [], [3] d d ( ) ( ) D( ) (9) d d ( ) ( ) where d s the orrelator spang of E and L of the EDLL dsrmnator, D( ) s a funton of the dsrmnatng error and t takes the monoton part of the rght term of (9) around. Based on the ˆ gven n (5), we an get ( ˆ d ) and ( ˆ d ) from (8), where ˆ and s the deal or theoretal value of ˆ. Take them nto (9), we an get the orrespondng result D( ). (d) Sne D( ) n (9) s a monoton funton, we an get from the nverse funton of D( ), that s, we an get by the value D( ). Then the tme delay of the th multpath an be updated as ˆ. () (e) Realulate the resdual sgnal and the resdual energy of Rx ( ) as n for the subsequent (+)th multpath estmaton. Step 4. Repeat the proess of Step 3 untl all the N multpaths are estmated. At the same tme, ompare E N wth the preset energy resdual E th to determne whether the proess s termnated. If E N Eth, take the N estmated results above nto the EDLL module agan for the next teraton as n Step 3. Repeat ths teraton proess untl the fnal termnaton ondton E r N Eth ( r ) s met, here r s the teraton tmes. Step 5. Choose the frst multpath estmated results r r ( ˆr r r r aˆ ˆ,,, ) or ( ˆ ˆ r a,, ) as the estmates of the LOS sgnal and output them for the further GPS rangng or for other purposes. 5. Smulaton Results and the Dsussons To verfy the performane of the proposed method, smulatons of the TKO-EDLL algorthm and the orrespondng EDLL algorthm used for omparson are onduted. In Subseton 5., smulatons wth dfferent multpath setups are offered. In Subseton 5., smulatons on the LOS tme delay estmaton wth the varyng seond path tme delay are provded. In Subseton 5.3, smulatons on the LOS tme delay estmaton wth the varyng SNR are suppled. The ommon parameter setups used n followng smulatons are as follows. TKO threshold s set to.5 (normalzed) aordng to the referene [7] for the GPS BPSK modulaton. The number of ompettve peaks s hosen to be 5 [7]. C/A ode aumulaton tme s set to 5 ms for ganng a hgher SNR. Sample frequeny f s = /T s s set to Hz. The orrelator spang of E and L s set to. T. The vald tme range of the reeved sgnal s ACF s lmted to [-, ] T, whh takes the deal LOS tme delay as the enter. Here T. s the C/A ode nterval and T.= /.3 μs ns. Based on the setups gven above, f we take the start of the ACF vald tme range as the tme orgn, we an easly get the deal LOS tme delay relatve to the tme orgn s T, or expressed n samples. We wll take ths theoretal value as the performane omparson rteron n the followng smulatons. 5. Performane Smulatons wth Dfferent ultpath Setups For smplty, here we only present two senaros for verfaton. Aordng to the setups gven n Tab., the smulaton results of the TKO-EDLL and the orrespondng EDLL are shown n Fgs. 3 and 4. In the smulatons, for the onvenene of omparson, we gve the estmated LOS tme delay expressed n samples. Paths Ampltudes (normalzed) Tme delays (n hp) Indent angles (n rad) [,.5 ] [,.3 ] [, 4 ] 3 [,.6,.4 ] [,.,.5 ] [, 6, 5 ] Tab.. ultpath setups for dfferent senaros.

6 RADIOENGINEERING, VOL., NO. 4, DECEBER 3 7 Estmated LOS delay [n sample] Estmated LOS delay [n sample] SNR = -5dB SNR = -db SNR = -5dB Theory 5 5 Number of Iteratons SNR = -5dB SNR = -db SNR = -5dB Theory 5 5 Number of Iteratons Fg. 3. Smulaton results of paths senaro of EDLL and TKO-EDLL under the ondtons of dfferent SNR. Based on the smulaton results shown n Fgs. 3 and 4, we an get ponts. () The teratons of the EDLL algorthm before onvergng to the fnal stable value wll nrease wth the nreasng of the multpath omponents. For example, n Fg. 3, there are about 8 teratons, whle for the 3 paths senaro shown n Fg.4, the teratons wll nrease to about 35. At the same tme, when there are more multpaths wth the smlar strength, there may gve rse to a slght osllaton before the algorthm onverges to the fnal stable LOS tme delay, as an be seen n Fg. 4. Whle for the TKO-EDLL algorthm, as shown n Fgs. 3 and 4, t needs only about teratons at most before onvergng to the stable LOS tme delay estmate, the effeny of the TKO-EDLL mproves about 4 tmes than that of the EDLL n the ase of 3 paths. () The auray of both algorthms wll derease wth the dereasng of SNR, as an also be seen n Fgs. 3 and 4. Ths s beause that at low SNR, the reeved sgnal s ACF beomes more rregular and ths wll derease the estmate auray of the multpath. But there s also a lmtaton on the TKO-EDLL just as that mentoned n Subseton 3., t s senstve to the SNR, the fnal result of the TKO-EDLL s slghtly less aurate than that of the EDLL when SNR s low, as an be seen n both Fgs. 3 and 4. For ths problem, t an be mproved by nreasng the aumulaton tme of the nomng sgnal s ACF. Estmated LOS delay [n sample] Estmated LOS delay [n sample] SNR = -5dB SNR = -db SNR = -5dB Theory Number of Iteratons SNR = -5dB SNR = -db SNR = -5dB Theory 5 5 Number of Iteratons Fg. 4. Smulaton results of 3 paths senaro of EDLL and TKO-EDLL under the ondtons of dfferent SNR. 5. Effet of the Seond Path Tme Delay on the LOS Tme Delay Estmaton The smulaton setup for ths sheme s that we hange the seond path tme delay wthn the sope of one hp to alulate the Root-ean-Square dsrmnatng error (RSE) of the LOS tme delay estmate. Besdes, we arry out the smulatons aordng to the dfferent SNR and the dfferent seond multpath ampltude, and we repeat the smulaton tmes at eah gven seond path tme delay. For smplty, here we only present two ases of the smulaton results orrespondng to SNR = -5 db and SNR = -5 db whh are shown as n Fg. 5. RSE of LOS delay estmate [n meter] EDLL:a=.3,= TKO-EDLL:a=.3,= EDLL:a=.6,= TKO-EDLL:a=.6,= Seond path delay [T ]

7 8 YI HU, AOZHONG SONG, BIN ENG, XIAOYU DANG, AN EFFICIENT ETHOD FOR GPS ULTIPATH ITIGATION USING RSE of LOS delay estmate [n meter] EDLL:a=.3,=45 TKO-EDLL:a=.3,=45 EDLL:a=.6,=45 TKO-EDLL:a=.6,= Seond path delay [T ] Fg. 5. RSE smulatons of the LOS tme delay estmaton wth the varyng seond path tme delay. The value of a n the legend box s the normalzed seond path ampltude, and the followed t s the orrespondng ndent angle. The orrelaotr spang of E and L n both smulatons s set to.t, and the SNR s set to SNR = -5 db, and SNR = -5 db, respetvely. From the smulaton results we an get 3 ponts. () For the same SNR and the same seond multpath ampltude, the TKO-EDLL shows a more superor performane n mtgatng the short tme delay multpath than that of the EDLL under the same ondtons. For example, n Fg. 5, for a.3, the performane of the TKO-EDLL outperforms that of the EDLL about 4 tmes for the maxmum RSE and ths result beomes about 6 tmes when a.6, there are also the smlar results n Fg. 5. When the tme delay of the seond multpath s more than about.6t, both algorthms almost have the same performane, as an be seen ether n Fg. 5 or n Fg. 5. () For the same SNR, the RSE performanes of both algorthms wll deterorate wth the nreasng of the seond multpath ampltude. But for the TKO-EDLL, the effet of the seond multpath ampltude s not as dramat as that of the EDLL for the short tme delay multpath. For example, n Fg. 5, when a hanges from.3 to.6, the maxmum RSE of TKO- EDLL almost remans unhanged, whle for the EDLL, ts maxmum RSE nearly doubles, n Fg. 5 we an also get the smlar results. When the seond multpath tme delay s more than about.6t, both algorthms are not senstve to the seond multpath ampltude. (3) The SNR also has an mportant effet on both algorthms, as wll be shown n detal n the followng Subseton Effet of SNR on the LOS Tme Delay Estmaton The smulaton setup for ths sheme s that we fx the seond path tme delay and hange the SNR wthn a gven sope to alulate the RSE of the LOS tme delay estmate. Besdes, we hange the seond path ampltude for more evaluatons and repeat the smulaton tmes at eah gven SNR. For the same reason of smplty, we only present two ases of the smulaton results orrespondng to the seond path tme delay τ =.4 T and τ =.6 T. The smulaton results are shown as n Fg. 6. RSE of LOS delay estmate [n meter] RSE of LOS delay estmate [n meter] EDLL:a=.3 TKO-EDLL:a=.3 EDLL:a=.7 TKO-EDLL:a= SNR [db] EDLL:a=.3 TKO-EDLL:a=.3 EDLL:a=.7 TKO-EDLL:a= SNR [db] Fg. 6. RSE smulatons of the LOS tme delay estmaton wth the varyng SNR. The value of a n the legend box s the normalzed ampltude of the seond path. The orrelaotr spang of E and L n both smulatons s set to.t, and the seond path tme delay s set to.4t, and.6t, respetvely. From the smulaton results we an also get 3 ponts. () For both the TKO-EDLL and the EDLL, the LOS tme delay estmate wll beome more aurate wth the nreasng of SNR, as an be learly seen from Fg. 6. () For both the TKO-EDLL and the EDLL, the RSE of the LOS tme delay estmate wll rse wth the nreasng of the seond multpath ampltude, but the effet of the seond multpath ampltude on the TKO-EDLL s not as dramat as t on the EDLL, as an also be seen n Fgs. 6. (3) Under the ondtons of the same SNR and the same a, for the short tme delay multpath, as shown n Fg. 6, the TKO-EDLL wll outperform the EDLL when SNR s hgh, but for the low SNR, for example, SNR s under - db, the result wll be reversed. Whle for the medum or long tme delay multpath, as shown n Fg. 6, the TKO-EDLL has approxmately the same performane as the EDLL when SNR s hgh. Conversely, when SNR s low, the TKO-EDLL wll show a poor performane, espeally when a s relatvely small, and ths an be explaned by that the TKO s more suseptble to the nose when SNR s low.

8 RADIOENGINEERING, VOL., NO. 4, DECEBER Conlusons In ths paper we present an mproved EDLL algorthm by ntegratng wth the TKO to mtgate the GPS multpath effently. By the omparsons of the two algorthms n omputaton effeny and RSE performane of LOS tme delay estmate, we an get that the proposed TKO-EDLL outperforms the EDLL when SNR s hgh. In fat, we an gan a hgher SNR by nreasng the oherent and non-oherent aumulaton tme of the reeved sgnal s ACF as long as possble. Based on these results, we an onlude that the TKO-EDLL s more preferable to the EDLL n GPS multpath mtgaton applatons. Aknowledgements Ths work was supported by the Open Researh Fund of the Aademy of Satellte Applaton under grant 5 and the Natonal Nature Sene Foundaton of Chna under grant The authors would also lke to aknowledge the anonymous revewers for ther helpful omments. Referenes [] KAPLAN, E. D., HEGARTY, C. J. Understandng GPS: Prnples and Applatons. nd ed. Norwood: Arteh House, 6. [] CHEN, H. H., JIA, W.., YAO,. L. Cross-orrelatonfunton-based multpath mtgaton method for Sne-BOC sgnals. Radoengneerng,, vol., no., p [3] TRANQUILLA, J.., CARR, J. P., AI-RIZZO, H.. Analyss of a hoke rng ground plane for multpath ontrol n global postonng system applatons. IEEE Transatons on Antennas and Propagaton, 994, vol. 4, no. 7, p [4] DANESHAND, S., BROUANDAN, A., NIELSEN, J, LACHAPELLE, G. Interferene and multpath mtgaton utlsng a two-stage beamformer for global navgaton satellte systems applatons. IET Radar, Sonar and Navgaton, 3, vol. 7, no., p [5] BHUIYAN,. Z. H., LOHAN, E. S. Advaned multpath mtgaton tehnques for satellte-based postonng applatons. Internatonal Journal of Navgaton and Observaton,, artle ID 4393, p [6] VAN DIERENDONCK, K. J., FENTON, P. C., FORD, T. J. Theory and performane of narrow orrelator spang n a GPS reever. Journal of the Insttute of Navgaton, 99, vol. 39, no. 3, p [7] BHUIYAN,. Z. H., LOHAN, E. S., RENFORS,. Code trakng algorthms for mtgatng multpath effets n fadng hannels for satellte-based postonng. EURASIP Journal on Advanes n Sgnal Proessng, 8, artle ID 86369, p. -7. [8] IRSIGLER,., EISSFELLER, B. Comparson of multpath mtgaton tehnques wth onsderaton of future sgnal strutures. In Proeedngs of the 6 th Internatonal Tehnal eetng of the Insttute of Navgaton. Portland (USA), 3, p [9] CGRAW, A., BRAASCH,. GNSS multpath mtgaton usng gated and hgh resoluton orrelator onepts. In Proeedngs of the 999 Natonal Tehnal eetng of the Insttute of Navgaton. San Dego (USA), 999, p [] ROUABAH, K., CHIKOUCHE, D., BOUTTOUT, F., HARBA, R., RAVIER, P. GPS/Galleo multpath mtgaton usng the frst sde peak of double delta orrelator. Wreless Personal Communatons., p [] BELLO, P. A., FANTE, R. L. Code trakng performane for novel unambguous -ode tme dsrmnators. In Proeedngs of the 5 Natonal Tehnal eetng of the Insttute of Navgaton, San Dego (USA), 5, p [] BHUIYAN,. Z. H., ZHANG, J., LOHAN, E. S. Analyss of multpath mtgaton tehnques wth land moble satellte hannel model. Radoengneerng,, vol., no. 4, p [3] VAN NEE, R. D. J., SIEREVELD, J., FENTON, P. C., TOWNSEND, B. R. The multpath estmatng delay lok loop: approahng theoretal auray lmts. In Proeedngs of the 994 IEEE Poston Loaton and Navgaton Symposum. Las Vegas (USA), 994, vol., p [4] SAHOUDI,., AIN,. G. Fast teratve maxmumlkelhood algorthm (FILA) for multpath mtgaton n next generaton of GNSS reevers. IEEE Transatons on Wreless Communatons, 8, vol. 7, no., p [5] HAILA, R., RENFORS,. Nonlnear operator for multpath hannel estmaton n GPS reevers. In The 7 th IEEE Internatonal Conferene on Eletrons, Cruts and Systems,. Jouneh (Lebanon),, p [6] SHASI, K. R., YANG, D., SIDDIQUI, A. A. Expermental evaluaton of Teager-Kaser dsrmnator under multpath envronment for GPS sgnal. In The 6 th IEEE Internatonal Conferene on Industral Eletrons and Applatons,. Bejng (Chna),, p [7] ZHONG, P., DING, X. L., ZHENG, D. W., CHEN, W., HUANG, D. F. Adaptve wavelet transform based on ross-valdaton method and ts applaton to GPS multpath mtgaton. GPS Solutons, 8, vol., no., p [8] YEDUKONDALU, K., SARA, A. D., SATYA SRINIVAS, V. Estmaton and mtgaton of GPS multpath nterferene usng adaptve flterng. Journal of Progress n Eletromagnets Researh-,, vol., p [9] TOWNSEND, B. R., FENTON, P. C., VAN DIERENDONCK, K. J., VAN NEE, R. D. J. Performane evaluaton of the multpath estmatng delay lok loop. Navgaton, Journal of the Insttute of Navgaton, 995, vol. 4, no. 3, p [] REN, J. W., CHEN, H. H., JIA, W.., YAO,. L. Lnearombned-ode-based unambguous ode dsrmnator desgn for multpath mtgaton n GNSS reevers. Radoengneerng,, vol., no. 4, p [] LOHAN, E. S., HAILA, R., LAKHZOURI, A., RENFORS,. Hghly effent tehnques for mtgatng the effets of multpath propagaton n DS-CDA delay estmaton. IEEE Transatons on Wreless Communatons, 5, vol. 4, no., p [] HAILA, R., ASTOLA, J., ALAYA CHEIKH, F., GABBOUJ,., RENFORS,. Teager energy and the ambguty funton. IEEE Transatons on Sgnal Proessng, 999, vol. 47, no., p [3] VAN NEE, R. D. J. ethod of estmatng a lne of sght sgnal propagaton tme usng a redued multpath orrelaton funton. U.S. Patent, no. 5653, arh 5, 997.

9 YI HU, AOZHONG SONG, BIN ENG, XIAOYU DANG, AN EFFICIENT ETHOD FOR GPS ULTIPATH ITIGATION USING About Authors Y HU was born n Lu an, Chna, n 974. He s urrently pursung the dotor degree n Communaton Engneerng n Nanjng Unversty of Aeronauts & Astronauts (NUAA). Hs researh nterests nlude satellte navgaton sgnal proessng and Sat-CO. aozhong SONG was born n Shexan, Chna, n 96. He s a professor n the College of Eletron & Informaton Engneerng, NUAA. Hs urrent researh nterests nlude satellte navgaton sgnal proessng, Sat-CO and ommunaton measurng and ontrollng tehnques. Bn ENG was born n Bejng, Chna, n 98. He s an engneer n the Aademy of Satellte Applaton, Bejng, Chna. Hs man researh nterest s satellte navgaton sgnal proessng. Xaoyu DANG was born n Wux, Chna, n 973. He s an assoate professor n the College of Eletron & Informaton Engneerng, NUAA. Hs urrent researh nterests nlude Communaton sgnal proessng and Sat-CO.