Improvement in DGPS Accuracy Using Recurrent S_CMAC_GBF

Transcription

1 World Academy of Scence, Engneerng and Technology 31 9 Improvement n DGPS Accuracy Ung Recurrent S_CMAC_GBF Chng-Tan Chang, Jh-Sheng Hu, and Cha-Yen Heh Abtract GPS ytem offer two knd of ue to peoplean accurate navgaton ytem and delverng tme wth unprecedented accuracy. Th paper preent the Recurrent S_CMAC_GBF n DGPS to ncreae for accurate potonng. A low cot commercal module (Trmble-Laen IQ) employed to repreent the mprovement of Recurrent S_CMAC_GBF n DGPS ytem and another expenve commercal module () recever ued for further upgradng. The propoed project collected utable for DGPS ytem ampled at dfferent rate: between receved poton and real poton. The mulaton reult wth real data and predcted data were performed that poton component RMS error are le than.5 meter after of Recurrent S_CMAC_GBF predcton. Keyword DGPS, Recurrent S_CMAC_GBF, predcton, mprovement I. INTRODUCTION PS ytem tructure contan three part: the atellte Gytem n pace, the uer recever at the ground and the ground control taton. There are 4 atellte n x orbtal dtrbuton of around 19 km n dtance from the Earth. All of the uer recever can receve atellte gnal any tme, any weather. Satellte gnal contan lattude, longtude, tme and peed. Mot recever can ue uch nformaton for potonng. The atellte nceantly tranmt on two type frequence: L1 (1575.4MHz) and L (17.6MHz). The role of frequency to be provded to the ground control taton and recever to potonng. There are two level of potonng accuracy are provded, Standard Potonng Servce (SPS) ung mxed wth the Coare/Acquton (C/A) code of only L1 gnal and Prece Potonng Servce (PPS) ung mxed wth the Prece (P) code of L1 and L. The accurace of SPS are: flat about 1m, atttude about 156m (95% authentc). The accurace of PPS are: flat about m, and atttude about.7m (95% authentc). The Peudo Random Noe code (PRN) can be mplcaton of GPS accuracy a Selectve Avalablty (S/A) and Ant-Spoofng (A/S). However, there are everal effect lke clock naccurace, onophere, atmopherc effect, mult-path effect, noe, tropophere delay, etc. In order to have advancement of potonng accuracy, the dfferental GPS (DGPS) wa developed to mprove navgaton accuracy n a local area. The gnal pang through the DGPS can decreae t error from +/- 1 meter to +/- 5 meter, even le. The approach of the Neural Network (NN) provde a promng and very well actual capacty. They have been appled to rch n varety of problem. In the GPS communty, applcaton of neural network oluton n navgaton proceng, o far ha not been wdely dcued. In th reearch, the Recurrent S_CMAC_GBF for predcton of the DGPS correcton wa propoed. And two GPS recever are employed to collect real data, before and after S/A turned off, one the expenve recever () and another one cheap recever (Trmble-Laen IQ). The tructure, output mathematc formula and learnng rule of Recurrent CMAC_GBF wll be ntroduced n ecton II. In ecton III, the Recurrent S_CMAC_GBF for predcton of DGPS correcton wa propoed. And the reult wll be mulated n ecton IV. Fnally, a concluon ummarzed n ecton V. II. RECURRENT S_CMAC_GBF The addre mappng of Recurrent S_CMAC_GBF the ame a S_CMAC_GBF that how n fgure 1. The output or recall proce the um of the weght (content n memory) of layer (hypercube). C. T. Chang wth the Department of Electrcal Engneerng Department, Chng Yun Unverty, Jung-L, Tawan 3, R.O.C. (correpondng author to provde phone: ext. 3; fax: ; e-mal: ctchang@cyu.edu.tw). Jh-Sheng Hu, and Cha-Yen Heh are wth the Department of Electrcal Engneerng Department, Chng Yun Unverty, Jung-L, Tawan 3, R.O.C. (e-mal: amfona@gmal.com, m9614@gm.cyu.edu.tw). Fg. 1 Block dvon of S_CMAC_GBF for two-varable cae 418

2 World Academy of Scence, Engneerng and Technology 31 9 The tructure of recurrent for one hypercube hown n fgure, and t known that the output of every ngle hypercube wll be feedback to telf. The output alo equal to the um of thoe hypercube. x,1 x, x, N v Fg. Recurrent tructure for one hypercube of S_CMAC_GBF The output addreng technque of Recurrent S_CMAC_GBF the ame a that of S_CMAC_GBF. The dfference that the ba functon no longer a mple functon of x, t nclude the output value of prevou temporal equence functon. The th hypercube value can be expreed a w ( x ) vb, ( x 1, h 1, ). Where v the weght, 1, the prevou tate matrx of ba functon output value, h 1, the weght vector of feedback. Then, y can be derved a: y Ne x a, v b, (1) Ne Nv a, v j ( x, j 1, j h 1, j ) j1 Where, every element n the hypercube electon vector a equal to 1. The learnng rule of Recurrent S_CMAC_GBF to mnmze one error functon. Aume the learnng adopt N tranng data, and the targeted output value of a nput tate x ŷ, then the error functon defned a 1 1 T E yˆ ˆ y y a w x, () And the learnng rule of v v E v N v Where v N Nv h,1 h, h, N v j1 e e yˆ, j,1,,nv ( x, j z -1 z -1 1, j T a w x a (3) z -1 v the learnng rate. h, 1, j ) w v Smlarly, the parameter of a Gauan functon: average value m j, varance j and the weghtng of feedback h 1, j, they all can be learned. The learnng rule the ame a n [1]. III. THE RECURRENT S_CMAC_GBF FOR PREDICTION OF DGPS CORRECTIONS The purpoe of the mprovement to reduce the error of GPS recever to cloe to reference poton. One of the problem that we met hown n fgure 3. The blue lne how the reference poton, green lne, and red lne repreent Trmble-Laen IQ. It clearly to be dcovered of wth hgher prce but ha better tablty, and Trmble-Laen IQ cheaper but how a large dfference to reference poton. Th tudy amed at utlzng the olvng ablte to dynamc ytem and tme relatve problem of the Recurrent S_CMAC_GBF to mprove and develop the accuracy of the GPS recever. The predcton tructure and experment procedure hown n the followng. X [m] -,997,85 -,997,83 -,997,835 -,997,84 -,997,845 -,997,85 Trmble-Laen IQ -,997,855 4,949,3 4,949,95 4,949,9 Trmble-Laen IQ Y [m] Z [m] 4,949,85 4,949,8 4,949,75 4,949,7 4,949,65 4,949,6 4,949,55,674,36,674,355 Trmble-Laen IQ,674,35,674,345,674,34,674,335,674,33 Fg. 3 The data from GPS recever wth SA = off and reference poton The error predcton tructure for DGPS Recurrent S_CMAC_GBF ha uperor n generalzaton and predcton; therefore t a very utable for predctng the error of the DGPS. In Fg. 4, the Recurrent S_CMAC_GBF tructure provded for DGPS predcton; t contan an antenna, a GPS recever ( and Trmble-Laen IQ), a recognzable reference poton and three module of Recurrent S_CMAC_GBF. 419

3 World Academy of Scence, Engneerng and Technology 31 9 Frt of all, the atellte data are collected by pang through the antenna, then a program tranform the geodetc coordnate nto geocentrc coordnate. Every Recurrent S_CMAC_GBF equpped wth two nput, one output and one target. A hown n fgure 4, GPS recever ( and Trmble-Laen IQ) put at the known reference poton Pt ( xp, yp, zp) to collect data. Therefore, the geocentrc coordnate Rt ( xr, yr, zr ) at tme t obtaned. The error on each tme tep between the reference poton and the GPS recever a follow: Et Pt Rt. The geocentrc coordnate error at tme t, Dx(t)Dy(t) and Dz(t), are obtaned. For Dx(t) after 1 t delay and nd delay can be obtaned Dx(t-1) and Dx(t-). Both delay data are nput to the propoed Recurrent S_CMAC_GBF, and Dx(t) et to be the target, then the output predcted Dx(t). The Dy(t) and Dz(t) are n the ame way. The propoed Recurrent S_CMAC_GBF ued to predct the error. The parameter are choen a layer=3, varance=.8, v=.3, mean=.3, var=.3, h=.3. In fgure 5, the blue lne how the error between Trmble-Laen IQ and reference poton. The green lne how the predcted error after the learnng of the Recurrent S_CMAC_GBF. It oberved of n a wde range of m error, the target tll traceable. In the followng, th predcton error a the ba ued to mprove GPS recever accuracy Predcted Data Predcted Data Predcted Data Fg. 4 Recurrent S_CMAC_GBF tructure for DGPS error predcton IV. SIMULATION RESULTS The mulaton amed at two knd of GPS recever (Trmble-Laen IQ and ) to make the error predcton and the poton mprovement. Fg. 5 The error predcton by ung Recurrent S_CMAC_GBF n Trmble-Laen IQ cae B. Ung predcton error to mprove the accuracy In fgure 6, the tructure how the uage of predcton error that are predcted by Recurrent S_CMAC_GB to adjut the orgnal data. The propoed method at the ame tme to compenate the output real value of the recever. The mprovement of Trmble-Laen IQ A. Propoed Recurrent S_CMAC_GBF to predcted error The procedure ha et the GPS recever on a recognzed reference poton (X= , Y= , Z= ). The data acceed per econd, 36 data can be collected n one hour. Among thee data, the wort evere ampltude of 1 data are retreved and hown n fgure 3. Fg. 6 The tructure for GPS recever output data compenaton 4

4 World Academy of Scence, Engneerng and Technology 31 9 After the mprovement on the cheap GPS recever for the problem of t poton urpae real value, the effcacy of the cheap GPS could be better than an expenve GPS recever. Therefore, the man purpoe of th reearch acheved. A hown n fgure 7, green lne the real value of ; red lne the after mprovement reult of Trmble-Laen IQ. Accordng to fgure 7, t clearly hown that the cheap GPS recever reult after mprovement perform better than the expenve GPS recever. The error between orgnal Trmble-Laen IQ and the reference poton ha been greatly mproved by Recurrent S_CMAC_GBF, the mproved coordnate data are controlled at the vcnty of the reference poton. X [m] -,997,846 -,997,848 -,997,85 -,997,85 -,997,854 -,997,856 4,949,85 4,949,8 Trmble-Laen IQ Y [m] 4,949,75 4,949,7 4,949,65 4,949,6 Trmble-Laen IQ 4,949,55,674,355,674,35 Trmble-Laen IQ Dx Reult -3 3 Dy Reult Dz Reult Fg. 8 The error to the reference poton after mprovement for Trmble-Laen IQ Table 1 how the mproved error (the dfference between the mproved and the real value) tattcal gnfcance charactertc for 1 real value, SA wa turned off. Z [m],674,345,674,34,674,335,674,33 Fg. 7 The mprovement of Trmble-Laen IQ by ung Recurrent S_CMAC_GBF The error to the reference poton after mprovement are hown n fgure 8. The experment proved Recurrent S_CMAC_GBF can greatly ncreae the accuracy of the GPS recever, t enable cheap GPS recever to have good tablty or even better than expenve GPS recever. To compare mulaton reult and reference poton, t found that the orgnal data error a large a 7m can be fxed to be wthn m by accurate predcton. TABLE 1IMPROVEMENT ERRORS STATISTICAL SIGNIFICANCE CHARACTERISTICS FOR TRIMBLE-LASSEN IQ (SA OFF) Parameter X Component Y Component Z Component Orgnal Adjuted Orgnal Adjuted Orgnal Adjuted MAX MIN RMS Average Varance Standard Devaton A how n table 1, the total RMS error of the Trmble-Laen IQ real data reduced to le than.3m by ung propoed Recurrent S_CMAC_GBF for predcton of DGPS correcton. The mprovement of A. Propoed Recurrent S_CMAC_GBF to predcted error The mplementaton the ame a Trmble-Laen IQ, the data of need to be ynchronou a Trmble-Laen IQ, whch mean the wort ampltude 1 41

5 World Academy of Scence, Engneerng and Technology 31 9 data that hown n fgure 3, and ung Recurrent S_CMAC_GBF to predct error. Becaue of the dfferent tructure of the predctng waveform, the parameter of Recurrent S_CMAC_GBF are elected of layer=3, varance=.5, v=., mean=., var=., h=.. In fgure 9, blue lne the error between and reference poton. Green lne the predcton error by ung Recurrent S_CMAC_GBF. It obvou that thee two value are very cloe whch mean the excellent predcton performance Predcted Data X [m] -,997,85.5 -,997, ,997,85.6 -,997, ,997,85.7 4,949,76. 4,949,76 Y [m] 4,949,75.8 4,949, ,949, Predcted Data Z [m] 4,949,75.,674,345.7,674,345.6,674,345.5,674,345.4,674, Predcted Data Fg. 9 The error predcton by ung Recurrent S_CMAC_GBF n cae B. Ung predcton error to mprove accuracy Although the potonng of the expenve GPS recever more table and accurate than the cheaper one, t accuracy tll can be ncreaed through the experment. The tructure the ame a fgure 6. The un-mproved output of hown n fgure 3. At the ame tme tep, calculate the predcton data and adjut the orgnal data, then the mproved data can be obtaned. A n fgure 1, blue lne how the reference poton and green lne the mproved data of. It obvouly that the tablzed error between recever and the reference poton can be mproved by Recurrent S_CMAC_GBF. And the mproved coordnate are controlled n the vcnty of the reference poton.,674,345. Fg. 1 The mprovement of by ung Recurrent S_CMAC_GBF It found that the orgnal data varaton gettng tablzed. Becaue of the good predcton ablty of Recurrent S_CMAC_GBF, the orgnal data error a large a 17m can be fxed to be wthn.5m..5 Dx Reult Dy Reult

6 World Academy of Scence, Engneerng and Technology Dz Reult -.5 Fg. 11 The error to the reference poton after mprovement for Table how the mprovement error (the dfference between the mproved and the real value) tattcal gnfcance charactertc for 1 real value, SA wa turned off. TABLE.II IMPROVEMENT ERRORS STATISTICAL SIGNIFICANCE CHARACTERISTICS FOR TRIMBLE-57 (SA OFF) Parameter X Component Y Component Z Component Orgnal Adjuted Orgnal Adjuted Orgnal Adjuted MAX MIN RMS Average Varance Standard Devaton Meaurement, and Control, Tranacton of ASME, p.-7, September [3] Albu, J. S., "Data Storage n the Cerebellar Model Artculaton Controller (CMAC)," Journal of Dynamc Sytem, Meaurement, and Control, Tranacton of ASME, p.8-33, September [4] C. S. Ln and C. T. Chang, "Learnng Convergence of CMAC Technque," IEEE Tranacton on Neural Network, Vol. 8, No. 6, pp , Nov [5] Albu, J. S., "A New Approach to Manpulator Control: The Cerebellar Model Artculaton Controller (CMAC)," Journal of Dynamc Sytem, Meaurement, and Control, Tranacton of ASME, p.-7, September [6] C. S. Ln and C. T. Chang, "Learnng Convergence of CMAC Technque," IEEE Tranacton on Neural Network, Vol. 8, No. 6, pp , Nov [7] Chng-Tan Chang, Tung-Sheng Chang, and Chen-Kuo L,1-13 Oct. 4, A Smple and Converged Structure of Addreng Technque for CMAC_GBF, 4 IEEE Internatonal Conference on Sytem, Man and Cybernetc, pp. 697~611. [8] Chng-Tan Chang, Chao-Mng Chong, June 5, Hardware Implementaton of A Smple Structure of Addreng Technque for CMAC_GBF, 5 IEEE Internatonal Sympoum on Indutral Electronc, A4-13. [9] M. R. Moav, A Comparatve Study between Performance of Recurrent Neural Network and Kalman Flter for DGPS Correcton Predcton, The 7th IEEE Conference on Sgnal Proceng, September4. [1] Y. Igun, H. Saka, and H. Tokumaru, A Real Tme Learnng Algorthm for a Multlayered Neural Network Baed on the Extended Kalman Flter, IEEE Tranacton on Sgnal Proceng, vol. 4, pp , Aprl 199. A how n table, the total RMS error of reduced to be le than.6m ung propoed Recurrent S_CMAC_GBF predcton. V. CONCLUSION Th reearch propoed a method to mprove DGPS accuracy by ung Recurrent S_CMAC_GBF. The data beng ued were the error between reference poton and dfferent pecfcaton GPS recever. In the procedure, Recurrent S_CMAC_GBF utlze tme tep error data to predct the followng tme tep error, and the predcted error calculated and adjut the real data of the GPS recever. It found that the compenated data perform excellent accuracy than the orgnal data to the recognzed reference poton. Through mulaton, t proved that Recurrent S_CMAC_GBF uable to predct the DGPS error and perform excellent achevement. In the future, the dynamc predcton and hardware mplementaton of the GPS wll be tuded. It hope to co-develop commercal product wth ndutre of th reearch method to mprove the n-accuracy problem of current commercal GPS product, and to further mprove the relablty and accuracy of GPS for more applcaton. REFERENCES [1] Chng-Tan Chang, Yu-Bn Ln, and Cha-Yen Heh, Hardware mplementaton of Recurrent S_CMAC_GBF baed on FPGA, 8 Internatonal Conference on Machne Learnng and Cybernetc Volume 7, 1-15 July 8 Page(): [] Albu, J. S., "A New Approach to Manpulator Control: The Cerebellar Model Artculaton Controller (CMAC)," Journal of Dynamc Sytem, 43