GNSS MULTIPATH MITIGATION USING LOW COMPLEXITY ADAPTIVE EQUALIZATION ALGORITHMS

GNSS MULTIPATH MITIGATION USING LOW COMPLEXITY ADAPTIVE EQUALIZATION ALGORITHMS 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo Progrmme Phsilisch-Technische Bundesnstlt (PTB), Brunschweig, Germn 7-9 October 05 Negin Sohndn, Ali Broumndn, nd Gérrd Lchpelle Geomtics Engineering Deprtment, Universit of Clgr, Clgr, Albert, Cnd. Emils: {nsohnd, broumn, lchpel}@uclgr.c ABSTRACT An dptive filter selection nd tuning lgorithm for GNSS receiver is proposed wherein different pttern recognition pproches re emploed to select proper dptive multipth compenstion nd trcing techniques nd corresponding tuning prmeters bsed on the tpe of multipth environment nd receiver motion mode (vehiculr or pedestrin). Two different clssifiction pproches, nmel neurl networs nd support vector mchines, re used for environment nd motion stte identifiction nd the results re compred. Pttern recognition is performed bsed on set of temporl nd spectrl fetures extrcted from the correltion sequence of received signls. The multipth compenstion trcing techniques re selected from set of stochstic-grdient-bsed dptive filters implemented in time nd wvelet domins. The proposed lgorithms re evluted using rel Glileo nd GPS dt collected in n urbn environment vi implementtion in softwre defined GNSS receiver. INTRODUCTION Multipth propgtion poses significnt chllenges to stellite bsed nvigtion sstems nd remins dominnt source of ccurc degrdtion for high precision GNSS pplictions. Without ccurte Line- Of-Sight (LOS) del estimtion in multipth environments, receivers cnnot provide relible position, velocit nd time (PVT) estimtes. Although there re mn lgorithms vilble tht ttempt to mitigte the effects of multipth, its mitigtion remins n issue. The most common del trcing lgorithms include vrints of the trditionl del-loc loop (DLL) method such s the double-delt correltor, strobe correltor nd high resolution correltor techniques. Although these lgorithms re effective when the receiver is subject to few, we multipth reflections, the performnce of these techniques in severe multipth scenrios is still rther limited. The other clss of multipth mitigtion techniques includes the dvnced methods such s the Multipth Estimting Del Loced Loop (MEDLL) [], the Multipth Mitigtion Technique, the Fst Itertive Mximum Lielihood Algorithm (FIMLA) [], Sequentil Mximum Lielihood [3], the Reduced Serch Spce Multipth Lielihood (RSSML) lgorithm [4] nd the deconvolution pproches [5]. This clss of techniques is bsed on Mximum Lielihood (ML) estimtion. These ML-bsed lgorithms introduce lrge computtionl complexities to the receiver s result of exploring lrge serch spces or performing mtrix inversion procedures. At the cost of this complex multicorreltor structure, dvnced estimtion lgorithms introduce multipth mitigtion performnce superior to tht of correltion-bsed techniques. However, in some pplictions, this level of computtionl complexit m be expensive In order to mitigte the effect of multipth distortion on GNSS pseudornge mesurements with prcticll chievble computtionl complexit, this pper proposes n lgorithm for dptive compenstion of the multipth chnnel through utilizing tuned selection of stochstic-grdient-bsed pproches [6], including Lest Men Squres (LMS), Recursive Lest Squres (RLS), Wvelet-bsed LMS (W-LMS) nd Wveletbsed RLS (W-RLS) []. For exmple W-RLS nd RLS re more pproprite thn the other two lgorithms in deling with fst vring chnnels nd W-LMS is more pproprite for slow vring chnnels nd is less complex. Moreover, ech of these lgorithms hs different tuning prmeters tht should be set ccording to the chnnel chrcteristics. In this pper, two pttern recognition lgorithms, nmel Neurl Networs (NN) nd Support Vector Mchines (SVM) re used to utomticll select the pproprite dptive multipthcompenstion-bsed trcing lgorithm nd the corresponding tuning prmeters bsed on the chrcteristics of the multipth chnnel including the tpe of the environment nd tpe of motion of the receiver. The pttern recognition of the chnnel smples is performed bsed on extrcting set of effective temporl nd spectrl fetures from the correltion sequence of the received GNSS signl. An optimum decision bloc is used in the structure of the dptive multipth compenstion methods to produce the control error signl in the decision feedbc loop tht is used to updte the dptive filters coefficients. A set of simultions using GPS nd Glileo signls is first used to produce trining sequence nd test dt 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge of 9

for different multipth environments including urbn, suburbn, indoor nd open s cses. The trined clssifiers re then used in seprte simultion wherein mixture of dt produced under different multipth scenrios is used to evlute the performnce of the dptive selection nd tuning method. The performnces of the dptive selection method for different clssifiers re compred. The proposed scheme is lso tested using rel Glileo nd GPS signls in n urbn environment (downtown Clgr), vi implementtion in softwre defined GNSS receiver. In ll of the rel dt tests, the position solutions computed using the proposed techniques re compred to reference trjectories obtined b tightl coupled integrted GNSS-INS sstem nd to the solutions computed b some of the conventionl del trcing techniques.. Multipth model The received bsebnd signl in multipth chnnel cn be modelled s n M-pth signl composed of direct pth nd (M-) reflected rs plus n Additive White Gussin Noise (AWGN) term n(t) s M j () r t s t h t A s t e n t where st is the trnsmitted spred spectrum signl, ht is the chnnel impulse response, A, nd re the time-vrint mplitude, instntneous phse nd del prmeters corresponding to the th pth. The received signl, fter being down converted, filtered nd smpled, is correlted with replic of the Pseudo- Noise (PN) code. The output of the correltor cn be expressed s M g w 0, T,..., N T where s s, () j Ae is the complex pth coefficient corresponding to the th pth, g is the idel utocorreltion function of the PN code nd w is the noise term t the output of the correltor. Eqution () cn be written in mtrix form s G w, (3) where is the vector of the smples of Tp length of N Ts smpling periods, nd, T p nd with T s being the serch nd... M (4) The vector w with length of N is the vector of noise smples with covrince mtrix of Q, nd G is N M mtrix tht cn be represented s G... M g g g (5) where 0... g g m m g Ts m g N Ts m. The sttisticl distribution of LOS nd multipth prmeters including the complex ttenution coefficients, number of pths nd the del prmeters of different components s well s the temporl vritions of ll of these prmeters re gretl ffected b the tpe of multipth environment (size nd shpe of the reflectors s well s their sptil distribution) nd the tpe of receiver motion. The sttisticl behviour of multipth components determines the pttern of the utocorreltion function of the received GNSS signl nd its temporl vritions. In ddition, different multipth ptterns require different trcing strtegies to chieve optimized trcing performnce, nd consequentl optimized positioning ccurc. Therefore, identifing the tpe of multipth environment nd the stte of the receiver motion from the correltion pttern provides insightful nowledge bout the sttistics of the chnnel which cn be used for djusting the trcing strteg or the trcing prmeters to obtin the best ttinble trcing performnce under vrious signl conditions. In this pper, the chnnel simultion softwre provided in [3] is used to generte received signl ptterns tht tpicll pper in different multipth environments. These generted ptterns re used to trin the clssifiers. For ll of the simultion cses, in the pedestrin motion stte the mximum speed of the receiver is 7 m/h nd in the vehiculr stte the mximum speed is 50 m/h. In generl, for the urbn cse the del spred prmeter of the chnnel tes lrger vlues compred to the suburbn cse. Moreover, the urbn nd sub-urbn chnnels cn be better distinguished under pedestrin motion stte rther thn vehiculr stte.. Multipth pttern recognition The ts of clssifiction module is to lern ptterns from the trining dt set tht help to clssif the observed dt into different clsses of interest. A clssifier should be trined using sufficient set of dt in the trining stge during which set of coefficients is lerned. These coefficients mp input fetures to output clsses. The trining set should include ll the vrieties expected to be cptured b the clssifier. After completing the trining stge, the clssifier cn be used to ssign n output clss to n new dt tht flls into one of the lerned clsses using the coefficients lerned. 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge of 9

The most importnt stge in designing clssifier is selecting proper fetures tht re ble to effectivel cpture ll the properties of dt to distinguish between different clsses. Hving ver smll number of fetures will result in bised clssifier tht represents poor ccurc on both trining nd test dt. However, lerning with too mn fetures in ddition to incresing the computtionl complexit of the sstem, will result in over-fitting the dt tht cuse good performnce on the trining set but poor ccurc on the test dt set. Obviousl, both of the bove cses should be voided using well designed fetures. The following subsections explin the fetures nd clssifiers used herein. Feture Extrction The fetures for multipth clssifiction re extrcted from the correltion sequence of the received GNSS signl rther thn the chnnel prmeters themselves. This method of feture extrction is much more fesible thn direct use of chnnel coefficient since ccurte estimtion of ll the chnnel prmeters requires ver high smpling rtes (hundreds of MHz). Two different sets of fetures, temporl nd spectrl, re extrcted to represent ech chnnel smple. The temporl fetures represent the tpe of chnnel nd re used to clssif the tpe of environment. The spectrl fetures, however, chrcterize the tpe of receiver motion. The correltion del xis is divided into 6 bins. The first 5 bins re equispced nd cover the rnge of dels from zero to hlf of chip. The lst bin represents dels from hlf chip to one chip. Therefore, there re 3 temporl fetures consisting of the mgnitudes nd reltive phses of the correltion function t the centre of ech bin. In order to extrct the spectrl fetures, Fourier trnsform is performed on ever 0 successive trining chnnel smples. Therefore, for ech correltion del bin, 0 timesuccessive smples contribute in computing Fouriertrnsformed sequence from which frequenc-domin fetures re extrcted. The index of the dominnt spectrl pe nd its bndwidth re the two spectrl fetures extrcted for ech bin. Therefore, there re totl of 3 frequenc fetures for ech chnnel smple. After extrcting the fetures mtrix, x, ech column of the mtrix is normlized s xi xi mx men xi x min x i i (6) Therefore fter normliztion, ll the fetures will be between nd -. Clssifiction Bsed on Neurl Networs (NN) The neurl networ considered here consists of three lers s shown in Figure. The first ler is the input ler with 64 nodes which consists of the extrcted fetures for the current input epoch. The second ler is hidden ler with 5 nodes nd the third ler is the output ler with six nodes where ech node represents one of the output clsses nmel vehiculr-urbn, pedestrin-urbn, vehiculr suburbn, pedestrinsuburbn, indoor nd open s. A neurl networ provides nonliner mpping between input fetures nd output lbels. It is one of the most effective nd less computtionll complex clssifiers. In generl, in neurl networ tht consists of L N lers, L N - mtrices contining the required weight coefficients re trined. Ech of these mtrices trnsfers the node vlues of one ler to the corresponding one in the next ler. Before multipling the node vlues of one ler to the corresponding weight mtrix, one bis node with the vlue of unit is dded to the current ler. In Figure the weight mtrices re shown b nd. After multipling the ctivtion vlues of one ler to the corresponding weight mtrix, the resulting vlues re pssed through non-liner function, nmel sigmoid function, to obtin the ctivtion vlues of the next ler. Therefore, if the ctivtions of lers j nd j+ re referred to s j nd j+ respectivel, the reltion between them cn be represented s j sigmoid (7) e j j j j This forwrd propgtion continues until it reches the lst ler. Input Fetures Output Clsses Figure : Feture extrction methodolog for multipth pttern recognition Figure : The rchitecture of neurl networ with one hidden ler 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 3 of 9

Afterwrd, bc propgtion lgorithm is emploed to updte the weight mtrices b flowing the grdient of the following cost function (tht is to be minimized) computed t the output ler ll the w bc to the first ler s J m K i i log h x i i i log -h x n i j m L N sn sn n ij m where K is the number of the output lers, input ler (fetures) for the i th trining epoch, h (8) i x is the is the th i element of the computed output, is the th element of the true output vector for the i th epoch of dt (it is vector contining in the index corresponding to the true clss nd zero elsewhere), m is the totl number of input frmes nd is the regulriztion prmeter which is used to void n over fitting problem. The forwrd nd bcwrd propgtion procedures re itertivel repeted until convergence is obtined (normll fter certin number of itertions). Support Vector Mchines (SVM) Clssifiction Support vector mchines re mong the best lerning lgorithms developed from sttisticl lerning theor [4]. Similr to ll other clssifiction pproches, SVM lerns mpping from input fetures x to n output clss lbel ( x ). In the simplest two-clss clssifiction cse, the clss lbels re defined s either ). The theor behind positive or negtive one ( SVM is bsed on the ide of seprting the positive nd negtive exmples of the trining set with mximized geometric mrgin to the decision boundr (hperplne) s shown in Figure 3. This is equivlent to optimizing the prediction confidence on the trining dt [5]. Since the input dt m be linerl nonseprble in the originl feture spce, it is projected into much higher dimensionl spce R n (n m be infinite) using non-liner mpping function x, x i where x is the mtrix of originl fetures in the R l spce ( l n), nd l is the originl number of fetures for ech trining exmple. Therefore, x is n m b l mtrix whose i th row contins fetures of the i th trining exmple. Figure 3: Mximizing the geometric mrgin in SVM After projecting the trining dt into the new spce, the SVM triner serches for liner discriminnt function f x w x b in the projected feture spce (since trining exmples will be linerl seprble fter projection), nd ptterns re clssified b the sign of f(x). In this cse, the geometric mrgin of the hperplne prmetrized b (w, b) with respect to trining exmple i i x, is defined s T i i w i b w x Given trining set w i i (9) S x, ; i,..., m, the geometric mrgin over the whole set is defined s the smllest of the geometric mrgins on the individul trining exmples. To mximize the geometric mrgin, SVM solves the following optimiztion problem [6]: i T i m H w x b min w C w, b i T i i H0 w x b (0) where C is the regulriztion prmeter, nd H 0 nd H (Hinge loss functions), shown in Figure 4, cn be represented s mx,0, mx,0 H z z H z z () 0 H(z) Figure 4: Hinge loss functions mrgin H0(z) Optimizing the cost function in (0) cn be entirel written in terms of the inner products of x (Burges 998). Thus, one does not need to now the high dimensionl mpping function x to solve the optimiztion problem. Insted, the cost function cn be represented nd optimized onl s function of the dot z i s 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 4 of 9

products of x i s, which is referred to s the ernel. Specificll, the computtion of i j T i T j, i j x K x x x x is much less expensive thn tht of x nd.the ernel function is mesure of similrit between the two exmples. Severl different non-liner ernels hve been introduced nd tested in the literture, including the polnomil ernel, rdil bsis function (RBF) nd sigmoid ernel. Among those the RBF ernel, lso nown s the Gussin ernel, x x K x, x exp, is one of the most prcticl choices (Hsu et l 003) nd will be used here. 3. Test results for the trined clssifier The sme chnnel models used in generting the trining set nd the cross-vlidtion set exmples (chnnel models in [3]) re lso used in n independent simultion to generte the test set. The simultion combines the deled nd ttenuted versions of single pth Glileo signl using the simulted chnnel prmeters to generte correltion function ptterns of the received signl bsed on (). From ech generted pttern, totl of 64 fetures re extrcted bsed on the strteg explined in the previous section. For this test, the trining set contins 0,000 ptterns/clss, nd ech of the cross-vlidtion set nd the test set contins 000 ptterns/clsses. Six different clsses re considered: Urbn-Vehiculr, Urbn-Pedestrin, Suburbn- Vehiculr, Suburbn-Pedestrin, Indoor nd Open S. Tble shows the ccurc of clssifiction for ech clss fter evluting the trined clssifiers on the test dt set. The results in the first column re bsed on the NN clssifiction nd the results in the second column correspond to the SVM clssifiction. Tble : Clssifiction ccurc Clss/Tpe Accurc of NN [%] Accurc of SVM [%] Urbn-Vehiculr 68.9 7. Urbn-Pedestrin 84.8 78.0 Suburbn-Vehiculr 88.3 84. Suburbn-Pedestrin 9.5 87.3 Indoor 00 95.7 Open s 00 00 The results in the tble show tht for most clsses (except the Urbn-Vehiculr cse where the two clssifiers show lmost similr performnces), the NN clssifier shows clssifiction ccurc superior to tht the SVM clssifier, specificll in distinguishing between urbn nd suburbn clsses. The tble shows tht urbn nd suburbn ptterns re more seprble under the pedestrin motion stte rther thn in the cr motion stte. Open s nd indoor ptterns re lmost perfectl distinguished from urbn nd suburbn cses. The number of itertions for NN ws set to 50. 4. Multipth compenstion using stochstic grdient method in time domin Herein, the stochstic-grdient-bsed dptive filtering concept is emploed to compenste for the distortion produced b multipth on the utocorreltion sequence of the received signl. The input to the filter is the vector of the utocorreltion sequence of the received signl ( ) nd its output is the estimte of the utocorreltion function of the LOS signl ( ŷ ). Therefore, the reltion between the input nd output vectors cn be written s ŷ = C () where C is n N b N mtrix of the compenstion coefficients. Thus, the problem of interest is to find n optimum vlue for the mtrix C. In order to find this mtrix, the following men squre error cost function is minimized t the output of the compenstion filter: C d ˆ d C d C J E tr E (3) where d g is the true LOS correltion LOS LOS functions wherein g is the vector of idel correltion LOS functions shifted b LOS. LOS nd LOS re the complex pth gin nd del prmeters ssocited with the LOS signl. There re two recursive solutions for minimizing (3) tht cn be expressed s [7] C C Γ RC (4) C C R Γ RC (5) where R E, Γ E d nd 0 is positive constnt clled step prmeter. These recursive optimistion lgorithms re referred to s grdient descent nd Newton s method nd the require perfect nowledge of the utocorreltion nd cross-correltion mtrices. However, computing the true vlues of these mtrices is not possible for time-vring chnnels. For this reson, stochstic grdient pproches re dopted to provide low-complex solutions cpble of dptive trcing of the estimted prmeters b replcing R nd Γ b their pproximtions. Herein, two stochstic 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 5 of 9

grdient pproches, nmel the Lest Men Squres (LMS) nd Recursive Lest Squres (RLS), will be used to compenste the effect of the multipth chnnel from the correltion smples nd estimte the LOS signl prmeters. The LMS lgorithm is derived b replcing R nd Γ in (5) b their instntneous pproximtions, ˆ R nd ˆ Γ d, which results in the following recursive formul [7]: C C d C (6) where nd - re time indices. The RLS lgorithm is obtined b replcing R in (6) b its exponentill weighted time verge nd results in the following joint recursions [8]: P P P P, P I P C C P d C (8) (7) where P R. In (7), is sclr tht should be selected in the rnge of 0. When vlue smller thn unit is ssigned to, the recent smples re ssocited with lrger weights thn the previous ones. This strteg enbles trcing mechnism for the dptive sstem. The vector d in (6) nd (8) is unnown on the receiver side. Therefore, feedbc technique is developed to solve this problem b dding LOS signl estimtion bloc to the sstem. This bloc provides n estimte of the trnsmitted dt tht is used s substitute for d to updte the coefficients of the compenstion mtrix. Since the output of the dptive compenstion bloc is supposed to be multipth-free in the sted stte, the best estimte of the LOS pe from this dt is the ML estimte under the ssumption of the presence of onl single pth. When using this strteg, the output of the LOS estimtion bloc still hs the form T of d = g ˆt LOS, ˆt in which ˆ LOS, nd ˆ re LOS, LOS, represented b [] nd ˆ ˆ g G LOS, rg mx g G g g G ˆ ˆ LOS, ˆ LOS, g ˆ G g LOS, ˆ LOS, Therefore, in (6) nd (8), d is replced b d. (9) (0) 5. Multipth compenstion in wvelet domin Wvelet Trnsform (WT) is tool for simultneous time nd frequenc nlsis of non-sttionr signls using set of orthonorml wveform series. Discrete Wvelet Trnsform (DWT) cn be used to estimte or equlize the chnnel impulse response through deconvolution in the wvelet domin [9]. In this section, chnnel estimtion through deconvolution in the wvelet domin is first introduced nd then technique for DWT-bsed dptive multipth mitigtion is proposed. Implementing the dptive lgorithms discussed in the previous section in the wvelet domin decreses their computtionl complexit nd provides signl denoising. Both DWT (decomposition) nd IDWT (reconstruction) procedures re implemented vi bn of liner lowpss nd high-pss filters. When orthonorml wvelet bses re used for nlsis nd snthesis filters, there is no net effect of the successive DWT nd IDWT opertions on the convolved output. Therefore, the chnnel filter cn be merged into the DWT portion of the filter bn s shown in Figure 5. For the se of simplicit nd without loss of generlit, onl one level of decomposition is considered here. In this figure, wvelet nlsis nd snthesis opertions re shown for both trnsmitted nd received signls. The dshed line in Figure 5 indictes the loctions in the signl flow of both bloc digrms where the DWT pproximtion coefficients nd detil coefficients re the sme for the two cses nd cn be expressed s FG h F Gh F () l l l F G h F Gh F () d h h h where nd d re the vectors of the pproximtion F nd F h re the mtrices nd detil coefficients of, l of low-pss nd high-pss nlsis filters, F s nd F s re the mtrices of the reconstruction (snthesis) filters. Therefore, either eqution () or () cn be used to estimte h using deconvolution method. However, since the therml noise mostl ppers t the output of the high-pss filter nd bis terms such s multipth pper t the output of the low-pss filter, the pproximtion eqution FG l h F l is used for chnnel estimtion to provide denoising to the sstem. For this reson, in this section, the dptive lgorithms introduced previousl re implemented in the wvelet domin in order to increse the robustness to noise nd decrese the computtion lod of the sstem []. Considering G FG l is the wvelet trnsform of G, the proposed wvelet-bsed LMS (W-LMS) nd wvelet-bsed RLS (W-RLS) lgorithms implement (6), (7) nd (8) b replcing nd d b their wvelet-domin trnsformed versions s 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 6 of 9

G Figure 5: Wvelet-bsed decomposition nd reconstruction of the received signl H C C d C (3) H P P P P P, P H I H (4) C C P d C (5) In the bove equtions ˆ ˆLOS, F l F h F l F h d g where LOS, ˆ LOS, nd ˆ LOS, re computed using (9) nd (0) b replcing ˆ, G nd h h g b their wvelet trnsforms ˆ C, G nd g (columns of G ), respectivel. In ddition to denoising, the dvntge of (3-5) over is of order of L times (6-8) is tht the length of smller thn the length of, ssuming tht L is the level of decomposition. In other words, insted of direct trcing of the correltion function sequence, some of its fetures re trced in the new model. The blocdigrm of the wvelet-bsed dptive sstem is shown in Figure 6. F s F s F s F s 6. Rel dt results In this section, set of GPS L C/A nd Glileo Eb/c results re demonstrted to further compre the performnce of the proposed dptive filter selection nd tuning lgorithms with those of the fixed strteg trcers with live signls. Moreover, the performnce of the proposed lgorithms is compred to the conventionl Nrrow Correltor (NC) technique. The test dt set ws collected in downtown Clgr. A tightl-coupled integrted GPS-INS (Inertil Nvigtion Sstem) on the vehicle ws used to obtin continuous reference position solutions with -m ccurc for the purpose of performnce ssessment; NovAtel ntenn nd SPAN sstem mounted on vehicle were used for this purpose. The smpling frequenc of the front-end digitizer ws 0 MHz. The proposed del estimtion techniques were implemented in softwre receiver. The loop updte rte ws 0 ms nd the PLL nd DLL bndwidths were 5 nd Hz. In the implementtion of nrrow correltors, correltor spcing of 0. chip ws utilized. The prmeters µ (for LMS nd W-LMS) ws set to 0.07 nd λ (for RLS nd W-RLS) ws set to 0.87. For wvelet trnsformtion, Hr wvelet filters with one level of decomposition were used. This choice of wvelet ws selected bsed on the deconvolution-bsed estimtion results presented in [0]. The s plot of the stellites nd the dt collection trjector re shown in Figure 7. Test Trjector Figure 7: S plot of stellites nd dt collection test trjector RF Frontend OSC Bn of Correltors NCO G DWT Approximtion DWT Approximtion Adptive Chnnel Compenstion ˆLOS, ˆ LOS Signl l, Estimtion l, Bloc Figure 6: Bloc digrm of the dptive sstem in wvelet domin - ε z + Loop Filter MSR The two dptive filter selection nd tuning lgorithms (referred to s Mixed NN nd Mixed SVM in the figures) detect the tpe of the multipth environment for ech time snpshot using the trined NN nd SVM clssifiers nd then select the proper trcing strteg. The W-RLS lgorithm ws emploed for three of the scenrios, nmel vehiculr, pedestrin urbn nd vehiculr suburbn. For ech of these cses, the vlue of λ ws selected bsed on the numbers provided in Tble. For the suburbn pedestrin scenrio, the method uses W- LMS with the corresponding vlue of µ provided in Tble (since WLMS is less complex thn WRLS []). 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 7 of 9

RMS [m] Up [m] North [m] Est [m] Tble : Selected vlues of tuning prmeters of dptive lgorithms under different multipth scenrios Scenrio/ Algorithm WRLS/RL S Urbn vehiculr Urbn Pedestrin Suburbn vehiculr Suburbn pedestrin λ = 0.75 λ = 0.8 λ = 0.95 λ = 0.95 WLM/LMS µ = 0.0 µ = 0.0 µ = 0.005 µ = 0.005 The time series of estimted position errors nd ssocited RMS re shown in Figure 8 nd Figure 9. The most importnt observtion from these figures is tht both context-bsed lgorithms outperform the best of the fixed-strteg lgorithms which re bsed on the W-RLS technique. The NN-bsed strteg hs resulted in n improvement of bout 35% in RMSE of the up component nd the SVM-bsed strteg hs resulted in similr improvement in the north component of the position solution. As expected from the results in Tble, the NN-bsed strteg generll shows slightl better performnce compred to the SVM-bsed strteg (except for the North component). Compring the fixed strteg techniques together shows tht, in generl, the lrgest RMSE vlues correspond to the NC lgorithm. However, the performnce difference between NC nd LMS is brel noticeble. RLS shows n improvement of bout 4% to 33% compred to the LMS nd NC. The W-LMS nd W-RLS lgorithms demonstrte importnt improvements compred to their time domin duls. For exmple for the up component, the RMSE vlue is 7 m for W-RLS nd 5 m for RLS lgorithms, which is equivlent to 47% improvement. This improvement is smller for the est nd north components of this trjector. W-LMS shows similr improvements compred to the time domin LMS. Another importnt observtion is tht the performnce of LMS nd RLS is similr in the wvelet domin. 7. CONCLUSIONS An dptive filter selection nd tuning lgorithm for GNSS receivers ws proposed; it uses neurl networs nd SVM clssifiction pproches to identif the tpe of multipth environment bsed on correltion smples of the received signls nd selects nd tunes the receiver s trcing strteg ccordingl. The ccurcies of the trined clssifiers were evluted using test dt set nd the results showed tht the NN-bsed clssifier slightl outperforms the SVM-bsed clssifier for the cse of multipth pttern recognition. The trined clssifiers were used to select nd tune the receiver s trcing strteg. Stochstic-grdient-bsed dptive filters ws tested using set of rel dt including both Glileo nd GPS signls. The test results showed tht the clssifiction-bsed dptive selection nd tuning lgorithms resulted in improvement of 5% to 35% in the estimted position RMS errors. 00 50 0 RLS LMS -50 W-RLS W-LMS -00 NC 0 00 400 600 800 000 00 Time [s] Mixed NN Mixed 00 SVM 50 0-50 -00 0 00 400 600 800 000 00 Time [s] -00 0 00 400 600 800 000 00 Time [s] Figure 8: Position estimtion error time series for downtown trjector 70 60 50 40 30 0 0 0 00 50 0-50 RLS LMS W-RLS W-LMS NC Mixed NN Mixed SVM Positioning RMS Errors Est North Up Figure 9: Comprison of estimtion position RMS errors REFERENCES [] B. Townsend, D. J. R. vn Nee, P. Fenton, nd K. Vn Dierendonc Performnce evlution of the multipth estimting del loc loop, Nvigtion Journl of the Institute of Nvigtion, vol. 4, no.3, pp. 503-54, 995. [] M. Shmoudi, M. G. Amin, Fst Itertive Mximum Lielihood Algorithm for Multipth Mitigtion in the Next Genertion of GNSS Receivers, IEEE Trnsctions on Wireless Communiction, vol. 7, no., pp. 436-4374, November 008. [3] M. Shmoudi, nd M. G. Amin, Robust Trcing of We GPS Signls in Multipth nd Jmming Environments, Signl Processing, Elsevier, vol. 89, no. 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 8 of 9

7, pp. 30-333, Jul 009. [4] M. Zhidul, H. Bhuin nd E. S. Lohn, Multipth Mitigtion Techniques for Stellite-Bsed Positioning Applictions, Globl Nvigtion Stellite Sstems: Signl, Theor nd Applictions, Prof. Shunggen Jin (Ed.), ISBN: 978-953-307-843-4, InTech, 0. [5] D. Sournetou, A. H. Sed, nd E.S. Lohn, Crmer Ro Bounds for Multipth Chnnel Estimtion in GNSS Receivers, Hindwi Interntionl Journl of Nvigtion nd Observtion, IJNO, vol. 0, Article ID 356975, 0. [6] A. H. Sed, Adptive Filters, John Wile & Sons, Inc., Hoboen, New Jerse, 008. [7]S. Hin, Adptive Filter Theor, Prentice Hll, 4th-edition, 00. [8]M. H. Hes, Recursive Lest Squres Sttisticl Digitl Signl Processing nd Modeling. Wile. ISBN 0-47-5943-8, 996. [9] C. Vz, D. G. Dut, Performnce of Discrete Wvelet Trnsform-Bsed Deconvolution Applied to Multipth Chnnel Estimtion, IEEE Srnoof Sposium, Newr NJ, - M 0. [0] C. Vz, D. G. Dut, Effects of Wvelet Choice in fst fding Chnnel Estimtion Using Wvelet Trnsform-Bsed Deconvolution, ISCIT 0, Hngzhou, -4 Oct. 0. [] N. I. Zieden, Pttern Recognition-Bsed Environment Identifiction for Robust Wireless Devices Positioning, Interntionl Journl of Advnced Computer Science nd Applictions (IJACSA), vol. 3, no., pp. 5-3, 0. [] N. Sohndn, A. Broumndn, G. Lchpelleh GNSS Multipth Mitigtion using Low Complexit Adptive Equliztion Algorithms, Proceedings of NAVITEC 04 (Noordwij, Netherlnds, 3-5 Dec), 8 pges [3] A. Lehner, nd A. Steingss. StelliteNvigtion Multipth Chnnel Models. http://www.ns.dlr.de/stnv. [4] V., Vpni, Sttisticl Lerning Theor John Wile, New Yor, 998. [5] BURGES C. J.C. (998) A Tutoril on Support Vector Mchines for Pttern Recognition, Journl of Dt Mining nd Knowledge Discover, Vol., No., P. 67 [6] N. Cristinini, nd J. Shwe-Tlor Support Vector Mchines, Cmbridge: Cmbridge Universit Press, 000. [7] Hsu C.W., Chng C.C., nd Lin C.J. A Prcticl Guide to Support Vector Clssifiction Technicl report, Deprtment of Computer Science, Ntionl Tiwn Universit, 003. http://www.csie.ntu.edu.tw/~cjlin/ppers/guide/guide. pdf. 5 th ESA Interntionl Colloquium Scientific nd Fundmentl Aspects of the Glileo, 7-9 October, Brunschweig, Germn Pge 9 of 9