An Advanced GPS Carrier Tracking Loop Based on Neural Networks Algorithm

Transcription

1 Iteratioal Joural of Egieerig ad Alied Scieces (IJEAS ISSN: , Volume-3, Issue-9, Setember 06 A Advaced GPS Carrier Tracig Loo Based o Neural Networs Algorithm Jichu She, Shuai Che, Chaghui Jiag, Yumig Bo Abstract The GPS (Global Positioig Systems is the mai tool to rovide the PVT (ositio, velocity ad time service i our daily life. However, there are some drawbacs eeded to be overcome for the wider alicatios of GPS. It is hard for a oular GPS receiver to ositio i a high dyamic/wea sigal eviromet without outer aidig. O the basis of aalyzig the reaso ad the error sources of the tracig loo, a eural etwors algorithm is used to adust the arameters of the fusio of the rd FLL ad 3rd PLL. A udge factor is selected to reset the hase errors of the loo. A oliear fuctio betwee a udge factor ad fusio arameters is costructed by the eural etwor algorithm. The method essetially chages the badwidth of the tracig loo by chagig the loo gai, which is usually igored. The algorithm is imlemeted ad tested i a Matlab software receiver. The exerimets show the modified tracig loo ca wor well i higher dyamic eviromets comared with stadard tracig loo. Idex Terms GPS, tracig, eural etwors, high dyamic. I. INTRODUCTION Sice the Global Positioig System develoed by the Uited States Deartmet of Defese, the GPS has bee widely used as a low-cost equimet to rovide recise ositio iformatio ad velocity iformatio ad time. GPS is a satellite-based all-weather avigatio system. For the Global Positioig System, the satellites broadcast avigatio sigal to all the earth. Ad the users receiver get the sigal from the satellites []. Therefore, oly the receiver is i the direct lie to the satellite, the receiver ca get the correct sigals which ca be alied to avigatio. However, the system caot rovide cotiues avigatio iformatio i high dyamic eviromet. The traditioal tacig loo caot tolerate the dyamic stress. For the commoly used GPS receivers, the tracig loos are comosed of frequecy loced loo (FLL ad hase loced loo (PLL. The FLL discrimiators roduce the frequecy error of the icomig sigal ad relica sigal. The PLL discrimiators roduce the hase error of the icomig sigal ad the relica sigal. The FLL usually erforms better tha PLL i high dyamic eviromet. Fig is the bloc diagram of a geeral GPS receiver tracig loo. Carrier re-detectio itegratio, the loo Jichu She, School of Automatio, Naig Uiversity of Sciece ad Techology, Naig, Chia, ( Shuai Che, School of Automatio, Naig Uiversity of Sciece ad Techology, Naig, Chia, ( Chaghui Jiag, School of Automatio, Naig Uiversity of Sciece ad Techology, Naig, Chia, ( Yumig Bo, School of Automatio, Naig Uiversity of Sciece ad Techology, Naig, Chia. discrimiators ad the loo filter are the ey three comoets of the tracig loo []. The discrimiator oututs are the frequecy/hase errors of the icomig sigal ad the local relica sigal, which is the iuts of the loo filter. They are the most imortat factors which affect the thermal oise ad the LOS (lie of sight dyamic stress threshold. I fact, the thermal oise ad the dyamics stress are a aradox, the arrow loo filter badwidth brigs reduced thermal oise ad the dyamic stress eeds wide badwidth []. I ractice, a comromise must be made to desig a receiver or give u the loo filter with a brad ew filter. I recet decades, with the raid develomet of moder comuter techology i the software ad hardware, artificial eural etwors (ANNs have bee alied to a wide variety of comlicated roblems [3]. It origis from the research of the riciles of the huma brai euro etwor. The ANN is oe of the artificial itelligece algorithms which has the ability to lear ad uderstad. It is the abstractio from the iformatio rocessig of huma brai euro etwor, ad establish some simle model, accordig to the differet comositio of differet etwor coectios. Neural etwor is a comutig model, by a large umber of odes (or euros. Each ode reresets a secific outut fuctio which is called activatio fuctio (activatio fuctio. Each coectio betwee two odes reresets a weighted value for the coectio sigal, ow as a weight, which is equivalet memory artificial eural etwor. The outut of the etwor deeds o the etwor coectio, ad the differet weights ad differet excitatio fuctios. Due to the ability to solve comlex roblems, the algorithm has bee used to solve roblems i guidace ad avigatio ad cotrol. Dah-Jig Jwo [4] alied bac-roagatio eural etwors to GDOP aroximatio ad exlored the erformace ad comutatioal beefit of eural etwor-based GDOP aroximatio. Kai-Wei Chiag [5] develoed a itelliget avigator to rovide reliable avigatio iformatio durig the GPS outages. The research strogly idicate the otetial of the itelliget avigator. Naser EI-Sheimy [6] utilize eural etwor for multisesor system itegratio i avigatio ad ositioig istrumets. I all revious cases, the eural etwors has ever bee used i tracig loos. I this aer, a bac roagatio eural etwor is icororated with traditioal FLL-assisted-PLL tracig loo to solve the aradox of thermal oise ad dyamic stress. A oliear fuctios of PLL hase error udge idicators ad the arameters of the loo filter iuts. 9

2 A Advaced GPS Carrier Tracig Loo Based o Neural Networs Algorithm IF Sigal COS relica COS SIN relica SIN Itegrate Itegrate Promt relica code Carrier loo discrimiator Carrier loo filter Fig.. Structure of geeric GPS receiver tracig loo The rest of the aer is orgaized as follows. The secod sectio of the aer is the itroductio of the system desig ad details of the alied bac-roagatio artificial eural etwors. The ext is the erformace evaluatio of the algorithm ad the coclusios. II. DESIGN OF THE PROPOSED CARRIER TRACKING LOOP A. Structure of the Tracig Loo Geerally, the traditioal tracig loos are comosed of frequecy loced loo (FLL ad hase loced loo (PLL. The FLL discrimiators roduce the frequecy error of the icomig sigal ad relica sigal. The PLL discrimiators roduce the hase error of the icomig sigal ad the relica sigal. Whe the tracig loo locs well, the hase error is ear to zero. The value of the hase error reflects the quality of the tracig loo. A idicator factor is selected to udge the quality of the tracig loo. IP QP E cos( I Q Accordig to the characteristics of FLL ad PLL, the PLL is sesitive to the dyamic stress, but it ca rovide more accurate velocity measuremets comared with FLL. The FLL erforms better i high dyamic eviromet. I order to desig a robust receiver tracig loo, the FLL should oerate at wide badwidth ad the PLL oerate at arrow badwidth. A Bac-roagatio eural etwors is alied to costruct the oliear fuctios of the idicator factor ad the fusio arameters. The fusio arameters are adusted accordig to the values of the idicator factor, which maes the tacig loo to tolerate the thermal oise ad the dyamic stress. The Fig detailed the desig ad the structure of the system. The bac-roagatio artificial etwors algorithm was emloyed i the desig. IF Sigal COS relica COS SIN relica SIN Itegrate Itegrate Carrier loo filter P Promt relica code P PLL discrimiator FLL discrimiator Idicator Factor BPNN Fig.. Scheme of the advaced tracig loo. B. The Bac-roagatio Neural Networs Neural etwors (NN are traiable ad have the ability to lear ad uderstad, which ca be used to the iut-outut fuctios. They have bee alied to solve a wide variety of comlicated roblems which caot be rocessed with covetioal theory. Because the NNs ca be used as a Blac Box ad do t eed to describe the mathematics model. The most imortat is the way how a euro is imlemeted ad how they are coected. The bac-roagatio is the oe of the most ractical learig algorithms which lear ad uderstad iut-outut fuctios from selected samles. The BPNN is a suervised algorithm which calculated the values of the gradiet i the oosite directio of the flow of each ode outut [7]. Whe you submit your fial versio, after your aer has bee acceted, reare it i two-colum format, icludig figures ad tables. BP eural etwor cosists of a iut layer ad a outut layer ad oe or more hidde layers, which are ideedet of each other. Iut sigals from the iut euros i tur through the various hidde layer euros, the fial outut to the outut euros (Fig3. The iut is the values of the idicator factor ad the outut is the fusio arameter of the loo filter (Fig. The essece of BP algorithm is to fid the miimum value of the error fuctio. I this algorithm, the weighted coefficiet of the egative gradiet directio of the error fuctio is modified by the steeest descet method i oliear rogrammig. BP uses a fuctio called active fuctio to describe the relatioshi betwee the outut of the differet layers, thus simulatig the iteractio betwee the layers. So the more commoly used active fuctio is called S tye [7]: f( x ( ex( x This fuctio is smooth ad cotiuous ad differetiable. f ( x x( x Where: x (,, ad f( x (0,. The coectio weights of the etwor are chaged costatly uder the stimulatio of the exteral iut samle, which is the dyamic adustmet of the weights of the coectios. The core is the weight adustmet rules, which is the adustmets rules i the rocess of chagig the coectio weights of each euro of the layers. Fig. 3. A three-layer of bac-roagatio eural etwor The oliear fuctio of the two variables is built by traiig the bac-roagatio eural etwors based o the iut samles ad the outut samles. Ad the it ca be used as a Blac Box i the desig. The traiig rocedures ca be exlaied as followig stes [7]: Ste Oe: Set the iitial values of w i, w, b, b. 0

3 Ste Two: Iut the traiig iut samles ad the desired oututs. x _ iut ( x, x, x3,..., x m d _ ouut ( d, d, d3,..., d Ste Three: Calculate the iuts ad oututs for the th hidde euro: m h _ iut w x hidde _ b i i i h _ outut f ( h _ iut Ste Four: Calculate the iuts ad oututs for the th outut euro: y _ iut w h _ outut ouut _ b y _ outut f ( y _ iut Ste Five: Calculate the error of the th outut euro. ( d y _ outut f ( y _ iut y _ outut ( y _ outut ( d y _ outut Ste Six: Calculate the error of the th hidde euro. f ( h _ iut w h _ iut ( h _ iut w Ste Seve: Correct the coect weights ad thresholds betwee iut layer, hidde layer ad outut layer. w h _ outut outut _ b wi xi hidde _ b Udate Udate w ad outut _ b : w w w, outut _ b outut _ b outut _ b w i ad _ outut b : wi wi wi, outut _ b hidde _ b hidde_ b Calculate the error cost fuctio: error _ cos t ( y _ oututi d _ oututi i Iteratioal Joural of Egieerig ad Alied Scieces (IJEAS ISSN: , Volume-3, Issue-9, Setember 06 Iut vector of outut layer: y iut y iut y iut y iut _ ( _, _,..., _ Outut vector of outut layer: y _ outut ( y _ outut, y _ outut,..., y _ outut Learig rate: The coectio weights of the iut layer euros ad the outut layer euros: w i The coectio weights of the hidde layer euros ad the outut layer euros: w Thresholds of the hidde layer euro: b Thresholds of the outut layer euro: b Error fuctio: error _ cos t ( y _ oututi d _ oututi i III. TEST AND SIMULATION Fially, a test latform ad tool is ecessary for the evaluatio of the algorithm. A software desiged receiver is a low-cost ad flexible tool to oerate ad evaluate the erformace of the roosed scheme. A. GPS IF Sigal Collector A hardware GPS sigal simulator is ecessary for the test of the roosed algorithm. Because it is the hard to verify the algorithm i real high dyamic eviromet. The algorithm is imlemeted ad tested i a Matlab GNSS software receiver develoed by our lab research grou. Fig5 shows the details of GPS IF data collectig equimet. Several high dyamic scearios are desiged ad simulated i the hardware sigal simulator. The GPS IF data are collected by the IF sigal collector after the sigal assig through the atea due to the comuter caot directly rocess the GPS high-frequecy sigal data. The samlig frequecy of the collected GPS L sigal is 6.369MHz ad the itermediate frequecy is 3.996MHz, the data tye is it. Sigal Simulator Atea GPS L IF Sigal Collector PC Reeat the stes util the cost fuctio reaches to a desired rage. Where m is the umber of the iut layer euros ad is the umber of the hidde layer euros ad is the umber of the outut layer euros. Iut samles vector: x _ iut ( x, x, x3,..., x m Fig. 4. The flow chart of the collected GPS L sigal Desired outut samles vector: d outut d d d3 d Iut vector of hidde layer: _ (,,,..., h _ iut ( h _ iut, h _ iut,..., h _ iut Outut vector of hidde layer: i h _ outut ( h _ outut, h _ outut,..., h _ outut i Fig. 5. 3D lot of the selected traectory

4 A Advaced GPS Carrier Tracig Loo Based o Neural Networs Algorithm Fig. 6. Velocity Fig. 9. Outut of the PLL discrimiator Fig. 7. Acceleratio Fig. 0. Outut of the PLL discrimiator Fig. 8. Jer IV. RESULTS Two differet tracig schemes are emloyed for GNSS sigals tracig of the same high dyamic traectory. They iclude FLL-assisted-PLL (40Hz, 5Hz ad the FLL-assisted-PLL based o BPNN (FBPPLL. Tracig erformace of the two schemes are evaluated accordig to the hase error of the hase discrimiator ad the I ad Q values i the same high dyamic traectory. A. Performace Evaluatio The mai urose of the tracig loo is to tracig the avigatio sigal ad relica it. The hase errors is the outut of the PLL discrimiator which ca be a ractical idex to measurig the tracig erformace. Fig9, Fig0, Fig ad Fig shows the calculated hase errors of four differet tracig chaels for the same high dyamic traectory. The FBPPLL hase error is much smaller tha the covetioal tracig algorithm (40Hz FLL ad 5Hz PLL PIT ms. Fig3, Fig4, Fig5ad Fig6 shows the I ad Q values of the tracig loo. Whe the tracig loo wors well. The I is comosed of the avigatio data ad the Q is ust oise. Fig8 shows the Q values of the FBPPLL is much smaller tha the covetioal tracig loos. Fig.. Outut of the PLL discrimiator Fig.. Outut of the PLL discrimiator

5 Iteratioal Joural of Egieerig ad Alied Scieces (IJEAS ISSN: , Volume-3, Issue-9, Setember 06 costructed betwee the idicator factor ad the fusio arameters. The method solves the badwidth aradox of the thermal oise ad dyamic stress ad mae the loo wor well i high dyamic. Fig. 3. Outut of the corrector Fig. 4. Outut of the corrector ACKNOWLEDGMENT This wor was suorted by Natioal Natural Sciece Foudatio of Chia (Grat No.U33033, the Fudametal Research Fuds for the Cetral Uiversities (No , Jiagsu Plaed Proects for Postdoctoral Research Fuds (50050B, ad the Chia Postdoctoral Sciece Foudatio (05M This wor also got the secial grade of the fiacial suort from the Chia Postdoctoral Sciece Foudatio (06T9046. REFERENCES [] Kala, E.D (006 Uderstadig GPS: Priciles ad alicatios, Secod Ed., Artech House, INC., Norwood, MA 006 [] Ward, P. (998 Performace Comarisios Betwee FLL, PLL ad a Novel FLL-Assisted-PLL Carrier Tracig Loo Uder RF Iterferece Coditios. Proceedigs of the th Iteratioal Techial Meetig of The Satellite Divisio of The Istitude of Navigatio, Setember 998, Nashville, TN, [3] Poggie, T. ad Girosi, F. Networs for aroximatio ad learig. Proc. of the IEEE 78(9, , 990. [4] Dah-Jig Jwo. Alyig Bac-roagatio Neural Networs to GDOP Aroximatio. THE JOURNAL ONAVIGATION, vol.55, [5] Kai-Wei Chiag. A itelliget avigator for seamless INS/GPS itegrated lad vehicle avigatio alicatios. Alied Comutig, vol.8, 7-733, 007. [6] Naser El-Sheimy. The Utilizatio of Artificial Neural Networs for Multisesor System Itegratio i Navigatio ad Positioig Istrumets. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUEMNT, vol. 55 (o.5, 005. [7] Hayi, S. Neural Networs: A Comrehesive Foudatio. Pretice-Hall, 990. Jichu She is ow ursuig his bachelor degree i Cotrol Sciece ad Egieerig from Naig Uiversity of Sciece ad Techology. His research ow focuses o GNSS/SINS deely couled avigatio system. Fig. 5. Outut of the corrector Chaghui Jiag is ow ursuig his Ph. D i Cotrol Sciece ad Egieerig from Naig Uiversity of Sciece ad Techology. He received his B.E from Soochow Uiversity i 04. His research ow focuses o GNSS/SINS deely couled avigatio system. Fig. 6. Outut of the corrector Yumig Bo received his M.Sc. degree i Cotrol Sciece ad Egieerig at Naig Uiversity of Sciece ad Techology, Chia, i 987. He received his Ph.D. degree i Cotrol Sciece ad Egieerig at Naig Uiversity of Sciece ad Techology, Chia, i 005. He is curretly a Professor i School of Automatio at Naig Uiversity of Sciece ad Techology, Chia. His research iterests iclude iformatio rocessig, avigatio, guidace, cotrol theory ad alicatio. V. CONCLUSION I this aer the BPNN algorithm has bee alied to the tracig loo which is uique ad distict from ay other tracig loos. A oliear fuctio has bee 3