A Novel GNSS Weak Signal Acquisition Using Wavelet Denoising Method

Transcription

1 A Novel GNSS Weak Sgnal Acquston Usng Wavelet Denosng Method Jn Tan, Lu Yang, BeHang Unversty, P.R.Chna BIOGRAPHY Jn Tan s a post-doctor n School of Electronc and Informaton Engneerng, BeHang Unversty, P.R.Chna. He receved a B.S. and Ph.D. n Computer Scence from BeHang Unversty. Hs research nterests are computer software, software defned rado recever and hgh senstve GNSS recever. Lu Yang s a graduate student n School of Electronc and Informaton Engneerng, BeHang Unversty, P.R.Chna. She majors n communcaton and nformaton system and currently her research feld s manly satellte communcaton. jntan@buaa.edu.cn, mckeybaby003@63.com, Web Ste: ABSTRACT Wth the ncreasng demands of precse postonng n weak sgnal envronment, hgh senstve GNSS recever research and development has been pushed badly n need. Conventonal GNSS sgnal acquston technques are consdered nadequate when the ncomng sgnal s too weak. In ths paper we have manly consder wavelet denosng algorthm applyng n weak GNSS sgnal acquston. Conventonal wavelet de-nosng algorthms nclude regonal scale transformaton method and threshold method. The frst method requres less lmtaton about the nose type, but the latter one s appled only n Gauss nose condtons. Besdes wavelet de-nosng process s done when the sgnal s ndependent n tme sequence, therefore our work has done based on the tradtonal correlaton acquston. When the noncorrelaton or dfferental correlaton has done, the nose dstrbuton and property has been also changed. If the nose pre-processed s Gauss dstrbuted, the postprocessed nose s no longer Gauss whte nose. Under ths crcumstance we conduct statstcs analyss to estmate the dervaton of nose, and assume a new Gauss nose. Then the wavelet de-nosng process s done. Our algorthm contans three key steps. Frstly, correlaton and dfferental correlaton method are used to acqure the very weak sgnal; secondly, nose dervaton s estmated and nose model s establshed; then the wavelet denosng process s appled. The result turns out fne for the sgnal lower than other acquston method. INTRODUCTION There are several weak GPS sgnal acquston methods ntroduced n recent years. Most of them focus on how to ncrease the PIT (Predct Integrated Tme) of the GPS sgnal and how to predct the data bt transt of GPS sgnal. Based on these researches and wavelet de-nosng theory, we wll ntroduce a new weak GPS sgnal acquston method to ncrease at least db the senstvty of GPS acquston. The typcal GPS sgnal arrve at earth s about -60dBW. Typcal GPS algorthm use ms PIT correlaton tme to detect ths GPS sgnal. When n n-door usage, the GPS sgnal could reduce to -80dBW or even lower. By usng coherent/non-coherent combned acquston method and dfferental acquston method, -8dBW GPS sgnal could be detect under 00ms PIT of GPS sgnal. But the weaker GPS sgnal detecton need much longer PIT due to the sgnal square loss and doppler frequency change. So, n ths paper we ntroduce the wavelet de-nosng method to ncrease the senstvty wthout ncreasng PIT tme. We use wavelet de-nosng method to decrease the background nose, thus to ncrease the sgnal peak of weak sgnal acquston. WEAK GPS SIGNAL ACQUISITION. Coherent/Non-coherent (NC) Coherent ntegraton s referred as the regular correlaton between the receved sgnal and local generated replca. Usually there are three methods to do a coherent ntegraton: sequental acquston, parallel phase doman acquston (IFFT) and parallel frequency doman acquston (FFT). For regular GPS receved sgnal a ms coherent ntegraton can contrbute 30dB energy accumulaton, whch s enough to reach the threshold. But that s not the condton of a weak GPS sgnal envronment. Long tme coherent ntegraton s lmted by the unknown message of navgaton data transferrng. For example f the bt edge occurs n the mddle of a data sequence, the total coherent ntegraton can be zero due to two magntude equally ntegraton blocks that have the opposte sgns. To elmnate the effect of navgaton data on ntegraton non-coherent process s used by squarng the n-phase and quad-phase coherent ntegraton results. Ths s called coherent/non-coherent combned method. 303

2 Wth the help of ths method weak sgnal acquston s luckly mproved and to some extent undoubted. But noncoherent also has ts nherent drawback because of two reasons. The frst reason s the Doppler frequency effect on the code length, whch wll be dscussed n detal later on and the second reason s the square loss. Square loss comes when the non-coherent process s done, by squarng the magntude of sgnal s enlarged and at the same tme the magntude of nose s also enlarged. A squarng ntegraton of Gauss Nose s no longer normally dstrbuted, whch brngs dffculty to calculate SNR.. Dfferental (DF) Dfferental correlaton s somewhat lke the coherent/non-coherent method. But n the dfferental case the n-phase and quad-phase are not squared. Supposed that our coherent ntegraton s done sequentally by a fxed tme nterval n a receved sgnal, the dfferental correlaton s then processed by multplyng one tme of n-phase result wth the next tme of n-phase result, and the same calculaton wll be done on the quad-phase result. Then the n-phase and quad-phase are added together to form the fnal determnaton. The advantage of dfferental correlaton s sad that t has better performance dealng wth the nose. Smple speakng t has less energy loss than the non-coherent method. 3. CCMDB The full name of CCMDB method s Crcular Correlaton wth Multple Data Bts [7]. Ths acquston type s based on the basc crcular correlaton of PRN code, usually done n parallel code acquston determnaton. Nevertheless tradtonal GPS acquston nvolves two arguments to be estmated or to further extent be refned, but acquston n ths method extend the arguments from two to four: ncludng estmaton of C/A code ntal phase, Doppler frequency, data combnaton of navgaton and the edge when the data symbol transfers from one to zero or from zero to one. To accomplsh such a more complex acquston procedure, longer data wll be used for energy accumulaton. Besdes the data combnaton and data transferrng edge are guessed by a maxmum accumulaton result method. It s supposed that each edge of ms data may be the rght data transferrng place accordng to equal possblty occurrence. The calculaton wll be tme consumng snce long data process and complex data combnaton possblty enumeratons. Consequently t s encouraged to develop algorthm to reduce less effcent searchng and total calculaton tme can be decreased. 4. MDBZP MDBZP stands for Modfed Double Block Zero Paddng [7]. The DBZP calculates the coherent ntegraton at all of the Doppler bns and all of the code delays at the same tme. Thus t requres less processng compared to the crcular correlaton. In ths method there s no need to multple the receved sgnal wth a local generated carrer whch has a estmated frequency of the receved carrer. Local produced PRN code s dvded nto several blocks as t needs and each of those blocks s padded wth an all zero valued block of the same sde. The new bult block, whch has twce sdes of ts prevous one, correlates wth receved sgnal of the same sde. A maxmum correlaton result wll also be used as a determnaton and select data results for FFT calculaton, whch can be helpful to fnd the estmated Doppler frequency. The problem of DBZP s that only one replca code s used n the correlaton calculaton at all the Doppler bns. The replca code s not compensated by the Doppler effect on the code length. Thus there wll be a dfference n the length between the receved and replca codes. Consequently subsequent ncoherent ntegratons wll be added at dfferent code delays relatve to each other. Ths problem ncreases as the ntegraton length ncreases. Therefore a lmtaton to the maxmum ntegraton length exsts. Ths means there s lmtaton to the mnmum SNR that can be acqured. The MDBZP crcumvents the lmtaton of DBZP by nvtng Doppler frequency compensatng models. WAVELET DE-NOISING. Theory Compared wth the tradtonal de-nose method, the technque of wavelet de-nosng based on the wavelet transform has many dstnctve vrtues. It can reduce the nose of sgnal keepng the sngularty of sgnal. Now wavelet de-nosng s commonly used n vdeo mage denosng. Some reports[3] sad t also can be used n realtme sgnal processng. Because of some key advantages over Fourer analyss, wavelet analyss has become a wdely used tool n sgnal estmaton, classfcaton, and compresson. Wavelet transform tends to concentrate the sgnal energy nto a relatvely small number of large coeffcents. On ths bass, a method called wavelet shrnkage to use threshold n wavelet doman was proposed, and t was shown to be asymptotcally near optmal for a wde range of sgnals corrupted by addtve Gaussan nose []. Commonly steps to reduce hgh frequency nose by wavelet de-nosng are []: A drect wavelet transform s computed from the orgnal mage. Nose level at each wavelet scale s estmated separately. Ths defnes a threshold for zerong wavelet coeffcents. Other wavelet coeffcents are shreked accordng to local dervaton estmaton (Soft threshold). After nverse wavelet transform, the mage s renormalzed. 304

3 y y -Δx -Δx Δx x Δx x Hard threshold Soft threshold Fg Hard threshold and soft threshold Fg Image wavelet de-nosng The sgnal wth Gaussan nose s dvded nto dscrete detaled sgnal and dscrete approached sgnal after wavelet transform. It s proved[6] that the ampltude and dervaton decreased when the scale level decreased. For all wavelet scale levels, the dervaton of whte nose detaled sgnal decreased when the scale ncreased. But the sgnal does not ft the crtera. Accordng to ths method, we could choce a threshold to flter out the Gaussan whte nose to acheve de-nosng effect for orgnal sgnal.. Wavelet method choce The soft and hard threshold could be used for wavelet denosng flter. Assumng Δx s the threshold, for soft threshold: sgn( x) ( x Δx) x > Δx y = 0 else For hard threshold: x x > Δx y = 0 else The hard threshold means value s set to zero when ts abstract value s lower than threshold, and the other data does not changed. The soft threshold shrnks the other data to zero. By comparson, soft threshold does not contan n-contnuous value, whereas hard threshold contan n-contnuous value of ±Δx. Commonly speak, soft threshold s much effectve than hard threshold. Accordng to paper[], the selecton of threshold of addtve Gaussan nose s based on followng four crtera: rgrsure, sqtwolog, heursure and mnmax. We does not dscuss much wth dfferent crtera, n our smulaton we use the thrd crtera as threshold selecton method of our wavelet de-nosng workng. 3. Acquston method choce The NC and DF acquston method s frst used to get a two-dmenson correlaton power grd. In NC method, the test statstcs Y s followng: When code/doppler matched, ΔwTN sn ( ) L Y = A L cos( ΔwTN ) + Δ Z wt ( ) When code/doppler not matched, Y = where, L Z Z = nosel, nosel, T s coherent tme L s dfferental tme N s dfferental number Δw s dfference of estmaton frequency A s power nose rato of GPS sgnal In DF method, the test statstcs Y s followng: When code/doppler matched, ΔwTN sn ( ) L Y = A L cos( ΔwTN) + ΔwT sn ( ) Z When code/doppler not matched, Y = L Z Z = nose nose where, l, l, T s coherent tme L s dfferental tme 305

4 N s dfferental number Δw s dfference of estmaton frequency A s power nose rato of GPS sgnal Reconstruct the acquston grd from the array. Then these wll make t easer to fnd out the peak of doppler and code phase. The probablty dstrbutons of these two methods are: Fg 4 Wavelet de-nosng flow Fg 3 Dstrbuton of NC(rght) and DF(left) method The mean value of correlaton power of NC method s not zero, that mean the nose can not be fltered by wavelet de-nosng. On contrary, the mean value of correlaton power of DF method s zero and the probablty dstrbute s smlar as addtve whte gauss nose. So, we can use wavelet de-nosng method to decrease the nose level of DF method. Because the peak value has dfferent dstrbuton as nose level, the sgnal nose rato of peak wll be ncreased after the nose s fltered by wavelet. The probablty dstrbuton of DF method s smlar to addtve gauss nose. In order to get the probablty densty of test statstcs Y, we should frstly get the probablty densty of nose Z. Though Z s not exactly ft the Gaussan dstrbuton. But for convenent, we assume t s an Gaussan dstrbuton, 4 the average s zero and dervaton s L Z 4LN σ. Furthermore, s also assumed to be a Gaussan 4 dstrbuton wth zero average and 8LN σ dervaton. Two hypothess testng are H0(Sgnal not detected) and H(Sgnal detected). So, f(y H0) and f(y H) are both Gaussan dstrbuton wth dfferent dervaton. Thus we can use wavelet de-nosng method to flter out Gaussan nose n Y. 4. De-nosng method Smlar as mage wavelet de-nosng, the sgnal wavelet de-nosng method contans followng steps: Frst transform the -D acquston grd to -D acquston array. A drect wavelet transform s computed from the orgnal acquston array. Soft threshold s used for zerong wavelet coeffcents. After nverse wavelet transform, the acquston array s renormalzed and the SNR of peak ncreased. For example, when the sampler s MHz and 00ms PIT data (5x4ms correlaton) s used by DF method for acquston. Because the correlaton tme s 4ms, the doppler step wll be 5Hz. Assumng the doppler s lmted n +/-5KHz, the total search span wll be 8. The acquston grd has 8*000 (97000) values. We frst transform the -D acquston grd nto -D acquston array. Fve-layer wavelet transform s done, and then use soft threshold wavelet method to flter out the nose. After that, we wll use nverse wavelet transform to rebuld the acquston array. There are two wavelet de-nosng methods to process the non-coherent result. The frst s to flter out the nose of each 4ms correlaton result, and then add 5 de-nosng data blocks together. The second s to add the acquston grd frstly, then use wavelet de-nosng method to flter out the nose. Because the wavelet de-nosng functon s a lnear system, so n fact, these two methods wll get the same result. By comparson, the second method wll use fewer computaton tme. All these procedures had been tested upon MATLAB Wavelet Toolbox. EXPERIMENT The actual GPS sgnal s sampled n BeHang Unversty campus (N:39.979, E: 6.344, Alt:98m) at Nov, 6th, 007. The sgnal strength covers -60dBW to -80dBW. Satellte 7 s tryng to be searched n our research.. Comparson of NC and DF Accordng to paper [4], the DF method has about.db senstvty ncreased compared to NC method. In our experment, wth 00ms PIT tme, the senstvty of NC and DF method are: Sample Bt NC Senstvty DF Senstvty MHz bt -77dBW -78dBW MHz bt -79dBW -80dBW 4MHz bt -8dBW -8dBW Based on DF method, the wavelet de-nosng could stll ncrease the senstvty by db. That means the senstvty wll reach -83dBW when usng 4MHz sample and bt quantzaton. We select two sgnal streams from sampled sgnal, n whch strong GPS sgnal power s about - 60dBW, and weak GPS sgnal power s about -75dBW. 306

5 The NC and DF acquston grds wthout wavelet denosng over a strong sgnal are: Fg 8 NC method for Weak Sgnal Fg 5 NC method for Strong Sgnal Fg 9 DF method for Weak Sgnal Fg 6 DF method for Strong Sgnal The antenna poston of weak sgnal s: The antenna poston of strong sgnal s: Fg 0 Weak Sgnal Sample Fg 7 Strong Sgnal Sample. De-nosng effect of NC strong sgnal The NC and DF acquston grds wthout wavelet denosng over a weak sgnal are: Fg Strong NC Sgnal before de-nosng 307

6 Fg Strong NC Sgnal after de-nosng Fg 5 Strong DF Sgnal after de-nosng Fg 3 Strong NC Sgnal wavelet de-nosng procedure The SNR of orgnal sgnal s 9.46 (45.7dB), and the SNR of de-nosed sgnal s 9.85 (45.0dB). The mean level of nose level s same. That means the wavelet denosng method does not decrease the average nose when the nose s not a gauss nose. So wavelet de-nosng method could be used on NC method. Fg 6 Strong DF Sgnal wavelet de-nosng procedure The SNR of orgnal sgnal s (60.78dB), and the SNR of de-nosed sgnal s (65.40dB). In strong sgnal envronment, the wavelet de-nose can archve about 5dB ncrease to sgnal power. 4. De-nosng effect of DF weak sgnal 3. De-nosng effect of DF strong sgnal Fg 7 Weak DF Sgnal before de-nosng Fg 4 Strong DF Sgnal before de-nosng Fg 8 Weak DF Sgnal after de-nosng 308

7 [4] We Yu, Bo Zheng, Rob Watson, Gerard Lachapelle, Dfferental combnng for acqurng weak GPS sgnals, Sgnal Processng(007) [5] Ba XaoHu, L JnHa, ChenJe. Unaded Indoor GPS Acquston Algorthm, Applcaton of Electronc Technque, vol.9, 006. [6] D.L.Donoho. De-nosng by soft-thresholdng, IEEE Transactons on Informaton Theory.995, 4(3): [7] N. I. Zedan. GNSS Recevers for Weak Sgnals, Artech House Publshers. Fg 9 Weak DF Sgnal wavelet de-nosng procedure The SNR of orgnal sgnal s 4.7 (3.89dB), and the SNR of de-nosed sgnal s (35.dB). In weak sgnal envronment, the wavelet de-nose can archve about 3dB ncrease to sgnal power. Furthermore, from prevous fgure, the hgh frequency part (d coeffcent) does not contan peak power. So, wavelet de-nosng method could use d coeffcent to determnate the nose level as threshold, and then flter out the gauss nose. CONCLUSION The result shows that the wavelet de-nosng method could be used to help acquston of weak GPS and GNSS sgnal. Under strong sgnal envronment, the peak wll ncrease about 5dB after de-nosed. And under weak sgnal envronment, the peak wll ncrease about 3dB after de-nosed. Ths wll ncrease the probablty of detecton of weak sgnal and reduce the false alarm rato. FUTURE WORK Future work wll focus on how to de-nosng the sgnal whch could not be detected under CF or NC method. We wll consder on how to de-nose the nose wthout decrease the orgnal sgnal. Then ths method wll help to ncrease the sensbltes of GNSS recever rather than ncrease the probablty of detecton. REFERENCE [] Zhang JQ, Gao ZM, Guo DF, Applcaton of Wavelet De-nosng to Spectrum-Codng Transmsson, Acta Electronca Snca, Vol, 0, 000. [] Wavelet Denosng. [3] XIA Ru MENG Ke QIAN Feng WANG ZhenLe, Onlne Wavelet Denosng va a Movng Wndow, Vol. 33, No. 9 ACTA AUTOMATICA SINICA September,