Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) ehcle Nvton System Interton wth GPS/INS/GSM Jum-Mn Ln Chen-Wen Hun, nd Fon-Lon Ts Insttute of Aeronutcs nd Astronutcs Chun-Hw Unversty Hsn-Chu 3, Twn, R.O.C. Eml jmln@chu.edu.tw Tel 886-586483 Fx 886-58657 Mchel Chn Technoloy nd Enneern Development Secton Mssle & Rocket System Reserch Dvson Chun-Shn Insttute of Scence nd Technoloy Tel : 886-34456536 Fx : 886-347453 Abstrct The purpose of ths pper s to study the performnce of the vehcle nvton system of INS ded wth GPS,.e., the postonn outputs of GPS re tken s the mesurements to clbrte the INS error prmeters n the Klmn flter, such s the nvton error covrnce mtrces of postons, veloctes, hedn nle nd nulr speed, s well s the bses, drft rtes nd scle fctors of the rte yros nd ccelerometers. The nterted system cn preserve the dvntes nd vod the dsdvntes of both systems. Not only the norml opertn but lso the lost trckn condtons of GPS re performed nd nlyzed. Ths s scrcely dscussed n the other ppers. The results show tht the loner the GPS locks, the better the errors of INS re clbrted, thus the nvton system of INS ded wth GPS s better thn those systems wth only GPS or INS. In ddton, the vehcle montorn system s lso relzed by ddn the GSM modems to the vehcle s well s the bse stton, respectvely. Thus the bse stton cn montor the vehcle v GSM modem lnkn s well s mke the cton of Dfferentl GPS (DGPS) correcton to rse the postonn of the vehcle. Keywords: GPS, INS, Klmn Flter, GSM Modem. Introducton The dvnte of the trdtonl Inertl Nvton Systems (INS) s tht the dt rte s hh, but the ccurcy of whch would be derded s the tmes o by []. In enerl, there re two methods to mprove the performnce. The frst one s to ncrese the ccurcy of both the nertl sensors nd the computer. The second one s to clbrte the error prmeters by usn the other nvton nformton [], such tht the dvern rte cn be reduced. The Globl Postonn System (GPS) s one of the nvton methods rht now. The GPS recever cn decode the nvton messes from the stelltes, solve the nvton equtons [3-8] nd provde postonn dt ll over the world. Althouh the dt rte s only Hz, the chrcterstc performnce of whch s lon tme stble [9]. Thus t s ood del to nterte INS wth GPS, the resultn system s not only relble but lso cost-effectve, therefore, t s ppled n ths pper s the centrl prt of the vehcle nvton system. 3
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) The purpose of ths pper s not only to relze nd study the performnce of the vehcle nvton system of INS ded wth GPS, but lso to montor the vehcle by GSM (Globl System for Moble communcton) modem lnkn. The postonn outputs of GPS recever re tken s the mesurements to clbrte the INS error prmeters n the Klmn flter, such s the nvton error covrnce mtrces of postons, veloctes, hedn nle nd nulr speed, s well s the bses, drft rtes nd scle fctors of the rte yros nd ccelerometers. The hrdwre of the system ncludes one notebook PC, one rte yro, two ccelerometers, three A/D converters nd one GPS recever. On the other hnd, the softwre prorm s bsed on TUBRO.C n order to speed up the rel tme snl processn s well s eser for lter-on mntnn. For the prctcl consderton, not only the norml opertn but lso the lost trckn condtons of GPS recever re performed nd nlyzed. Ths s scrcely dscussed n the other ppers [5-8]. The results show tht the loner the GPS recever locks, the better the error prmeters of INS re clbrted, thus the nterted system cn preserve the dvntes nd vod the dsdvntes of both systems,.e., not only the hh postonn rte of INS, but the lon tme stblty of GPS recever re preserved, whle the derded performnce s tmes o by of INS, nd the lower postonn rte of GPS recever re voded. The other dvnte of the proposed system s tht t s modulrzed, nd not senstve to the envronment effect of the vehcle. For exmple, the hedn of the vehcle s obtned by usn the nterted velocty results of GPS / INS (whch s derved n Eq. (9) lter), there s no need of yrocompss. Thus t s not senstve to the mnetc feld dsturbnce effects due to the erth or the envronments. By the wy the wern nd slppn effects of the tre, whch re the dsdvntes of the vehcle nvton systems by usn the odometer [], cn lso be voded.in ddton, the vehcle montorn system s lso relzed by ddn the GSM modems to the vehcle s well s the bse stton, respectvely. Thus the bse stton cn communcte wth the vehcle v GSM modem lnkn, nd mkes the Dfferentl GPS (DGPS) correcton to rse the postonn ccurcy of the vehcle [-]. Secton 3. Fnlly, some conclusons re drwn n Secton 4.. Problem Formulton The mjor error sources of INS re rte yro nd ccelerometer. Let the sensn xes of the rte yro nd two other ccelerometers re respectvely lon the vehcle s z, x nd y xes, respectvely, nd ϕ s the hedn nle s shown n F.., whch s defned s the nle between the vehcle s x xs (center lne) nd the north drecton of the nvton system. In enerl, there re four types of rte yro errors [], such s rndom bs B, scle fctor SF, rndom drft rte ε nd rndom nose ω,.e., ϕ B + ε + ω + SF * ω where ω s the hedn nulr rte. The models of B nd SF cn be defned by the follown equtons: B SF The rndom drft ε s whte nose wth zero men nd stndrd devton Ε{ ε ( t ) ε ( τ )} ε δ ( t τ ) nd the rndom nose ω s modeled s ω ω + / τ ωn where τ s the correlton tme of the rndom nose ω, nd ω n s zero-men whte nose wth stndrd devton defned s : Ε { ω ( t) ω ( τ )} δ ( t τ ) n n n The power spectrum of the whte nose ω n s [3] The other prts of ths pper re ornzed s follows: The problem s formulted n Secton. The experment results wth GPS n norml opertn or lost trckn condtons re ven n Q n nτ Smlrly, the outputs of the ccelerometers ( x, y ) cn be expressed n terms of the error 4
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) prmeters such s rndom drft, rndom nose SF x, y,.e., Β, nd scle fctor ( ) where f s the ccelerton lon the vehc- le s xs ( x, y ), nd the errors SF of scle fctor nd rndom nose B cn be modeled s follows: F S ( x, y ) where B where B rndom nose / τ + ω ( x, y ) τ s the correlton tme of the, nd B ω s zero-men whte nose wth stndrd devton s: Ε { ω ( t) ω ( τ )} δ ( t τ ) ( x y) The power spectrum of the whte nose ω Q, τ ( x, y) The rndom drft s zero-men whte nose wth stndrd devton: { ( t) ( τ )} δ ( t τ ) Ε ( x, y ) It should be noted tht for the ske of speedn up the Klmn fltern processes, the rndom bses of the ccelerometers re nelected. Snce the postonn results should be expressed n the nvton coordntes, thus the ccelerton components of vehcle n the north f N nd the est f E re respectvely obtned s: s nd the nput nose vector f c s N x f s c E ϕ ϕ ω ( t ) n E.(9) s defned s: ϕ ϕ y c ϕ cosϕ sϕ snϕ ω( t) N E ε ωn ωx ωy In enerl, the postonn outputs of GPS receves re n terms of the lttude L nd the lontude λ, one cn trnsform them nto the coordntes lon the nvton xs,.e., the postons n the north P N, nd the est P E re obtned respectvely s follows: 5 N ( L L R e E ( λ λ ) R e CL P ) + B + SF f where R e s the rdus of the erth, L ( λ ) s the ntl lttude (lontude) of the vehcle. P By the bove dervton, one cn formulte the stte equton of the vehcle n the nvton system s [4]: x( t ) Ax( t) + ω ( t ) x( t) [ PN PE N E ϕω Bx B B SFn SFe SF ] nd the system mtrx A s [4] λ IsL Re A λ IsL Re λi sl λ IsL fe fn τ cϕ sϕ τx sϕ cϕ τy fn fe ω where λ I R cl E 9. 8 m sec e [ ] T 4 whch s zero men nd wth covrnce mtrx s Q d{ N E ε ω ωx ωy } 5
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) The mesurement equton s consderton, nd K k s the Klmn flter n mtrx. By the wy, the smpln perod of z( t) H ( t) x( t) + v( t) the INS s 4 ms n ths study. where H( t) nd v( t) s the mesurement nose of GPS recever wth zero men nd covrnce mtrx { } R( t) d P, P,,, ϕ N E N E where P ( P ), ( N E N ) nd E ϕ re respectvely the GPS stndrd devton errors of the north (est) poston, north (est) velocty nd hedn nle, nd The test ste for evlutn the performnce of the nterted system s n trpzodl reon ϕ tn ( E ) n Hsn-Chu, Twn s shown n F.4. The N sequence of the pth s lon the ponts The GPS/INS ntertn method uses the s, s, s3, s4 nd s 5, then bck to s fnlly. loosely-coupled closed-loop structure [5,6], s shown n F. by the trde-offs of mplemeentton, ccurcy performnce, nd system relblty. Let the dscrete stte nd mesurement equtons re s [6] x Φ x + Γ ω k k k k k nd z k H k x k + v k postonn result s reduced to 5 m. Althouh the results re not derded wth tme, but there s only one output per second. On the other hnd, the result obtned by the nterton method, k k k P ( ) Φ P ( t) Φ + Γ Q Γ k k k T k k k k T [ ] K P ( ) H H P ( ) H + R k k k T k k k T k 3. Experment Results The block drm of the vehcle nvton nd montorn system s shown n F 3(), n whch the GSM modems re dded to the vehcle s well s the bse stton, respectvely, such tht the postonn nformton of the vehcle, e.., the nvton results, obtned by usn GPS/INS s well s DGPS correcton, cn be receved by the bse stton v GSM communcton.the snl flow rph of the GPS/INS snl processn lorthm s shown n F.3(b). The vere speed of the vehcle s 4km/hr. The totl dstnce s bout 3.4 km, nd the testn perod s 3 sec. The prt numbers nd the error prmeters of the ccelerometers, rte yros s well s the GPS recever re lsted n Tble. F.5 shows the postonn result obtned by the system wth only INS, s t ws ntcpted tht the ccurcy of whch s derded wth tme. F.6 shows the postonn output of GPS recever n whch the dfferentl GPS correcton s ccomplshed by GSM lnkn from the bse stton, thus the stndrd devton of the wth GPS recever locked ll the wy, s shown n F.7. It cn be seen tht the chrcterstc performnces of both GPS lon-tme stblty nd INS hh speed dt rte re preserved. In x ( ) Φ ddton, the stndrd devtons of the poston, x ( t ) velocty nd hedn errors re convered s lon s the GPS locks whch re shown n Fs.8-. 4. Conclusons x k ( t ) x ( k ) + K k z k H k x k ( ) By the results of experments one cn drw some conclusons: Pk ( t ) [ I K k H k ] Pk ( ). It s ood del to nterte INS wth GPS recever. Ths method s not only relble but where x k ( )( P k ( )) nd x k ( + )( P k ( + )) lso cost-effectve. re the estmted stte (covrnce mtrx). The nterted system cn preserve the before nd fter tkn the mesurements nto dvntes nd vod the dsdvntes 6
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) of both INS nd GPS recever,,e., the hh postonn rte of INS nd the lon tme stblty of GPS recever re preserved, whle the derded performnce s tmes o by of INS, nd the lower postonn rte of GPS recever re voded. 3. The loner the GPS recever locks, the better the errors of INS re clbrted, thus the nvton system of INS ded wth GPS recever s better then those systems wth only GPS recever or INS. Ths performnce nlyss s screcely dscussed n the other ppers. 4. The other dvnte of the proposed system s tht t s modulrzed e.., the GPS/INS nvton module, nd GSM communcton module, whch cn be esly ppled for the vehcle nvton nd montorn system. In ddton, t s nether senstve to the mnetc dsturbnce of the erth or the envronments, nor the wern nd/or slppn effects of the tre, whch s the dsdvnte of the vehcle nvton system developed by usn the yrocompss nd odometer. ACKNOWLEDGEMENT Ths work ws supported by the Ntonl Scence Councl of the Republc of Chn (rnt No. NSC-89--E-6-), Chun-Shn Insttute of Scence nd technoloy (rnt No. BB9L36P-P), nd the Mnstry of Educton under the rnt of Avoncs Educton Improvement Prorm. References [] Slter, J.M., et.l., Inertl Nvton Anlyss nd Desn, McGrw-Hll Book Co., (964). [] Cunnnhm, J. R. Performnce of GPS-Aded INS Durn Hh-Dynmcs Mneuvers, Mster Thess, Dept. of the Ar Force Insttute of Technoloy Ar Unversty, AFIT/ GE/ENG/87D- (987). [3] Bncroft, S. An Alebrc Soluton of the GPS Equtons, IEEE Trns. on Aerospce nd Electronc Systems, ol. AES-, No.7, pp.56-59 (985). [4] Kruse, L.O., A Drect Soluton to GPS-Type Nvton Equtons, IEEE Trns. on Aerospce nd Electronc Systems, ol. AES-3, No., pp.5-3 (987). Ln, H.C., An Interted Study of INS wth GPS Adn, Mster Thess, School of 7 Aeronutcl nd Astronutcl Enneern, Chun-Hu Unversty (995). Ln.J.M, Ln.H.C, nd P.K.chn, A Study of INS Aded by GPS, Trns. of Aeronutcl nd Astronutcl Socety of the Republc of Chn, ol. 6, No, 3,pp.3- (995). Ln.J.M. nd Ln.H.C, GPS Nvton Dt Snl Processn, Trns. of Aeronutcl nd Astronutcl Socety of the Republc of Chn, ol. 8, No., pp. 53-6 (996). Ln.J.M. nd Ln.H.C, Performnce Anlyses On Some of GPS Nvton Equton nd Dt Smoothn Mtthod, J. Control, Systems nd Technoloy, ol. 5, No,,pp. 35-44 (998), [9] Splker, Jr, J.J., GPS Snl Structure nd Performnce Chrcterstcs, Nv- ton, J. of the Insttute of Nvton, ol. 5, No.,pp. -46 (978). [] Wn, K.B., Computer Archtecture Study of Interted GPS/INS, Mster Thess, School of Aeronutcl nd Astronutcl Enneern, Chun-Hu Unversty (995). [] Blckwell.E.G., Overvew of Dfferentl GPS, Nvton, Journl of the Insttute of Nvton, ol.35, pp. 89- (988). [] Hunter,J,,W.Kosmlsk, nd P.Truon, ehcle Nvton Usn Dfferentl GPS, IEEE Conference of Poston Locton nd Nvton System, pp. 39-398 (99). [3] Stllrd, D.., Clsscl nd Modern Gudnce of Homn Interceptor Mssles, Semnr of Deprtment of Aeronutcs nd Astronutcs, Msschusetts Insttute Technoloy, Cmbrde, MA, pp. 6-6 (968). [4] Br-Itzhck, I.Y., nd N.Bermn,, Control Theoretc Approch to Inertl Nvton Systems, J. of Gudnce, Control, nd Dynmcs, ol., pp.37-45 (988).
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) Tble. The prt numbers nd the error prmeters of the ccelerometers, rte yros s well s the GPS recever. Accelerometer (Lucs Rte Gyro (Murt GPS Recevers LSBC-) EN-.5A) (Astech G) B.4 /sec B. de/sec P N m x ϕ.4 /sec ε. de/sec P E m ϕ( ) y.8 τ. sec n.44de/sec τ N.5 m/sec E F. The reltonshp between the coordntes of vehcle nd the nvton system.. sec.5 m/sec INERTIAL MEASUREMENT UNIT NAIGATION EQUATION CORRECTED POSITION,ELOCITY, AND ATTITUDE INSTRUMENT ERRORS AND POSITION, ELOCITY,AND ATTITUDE CORRECTIONS INERTIAL KALMAN FILTER GPS RECEIER GPS KALMAN FILTER GPS POSITION AND ELOCITY F. The Loosely-coupled closed-loop structure of GPS/INS. F.3() The block drm of the vehcle nvton nd montorn system. 8
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) F.5 The postonn result obtned by the system wth only INS. F.3(b) The snl flow rph of the GPS/INS snl processn lorthm. F.6 The postonn result of GPS recever. F. 4 The test ste for evlutn the performnce of the nterted system. F.7 The result obtned by the nterted system wth GPS recever locked ll the wy. 9
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) F.8 The stndrd devtons of the poston errors wth the nterted system. F. The postonn result of GPS recever for lost trckn durn 6~4 sec nd ~8 sec. F.9 The stndrd devtons of the velocty errors wth the nterted system. F. The postonn result obtned by the nterted system wth GPS recever lost trckn for two perods of tme. F. The stndrd devtons of the hedn nle nd turnn rte errors wth the nterted system. F.3 The stndrd devtons of the poston errors for the nterted system wth GPS
Chun Hu Journl of Scence nd Enneern, ol.,no., pp.3-(3) recever lost trckn for two perods of tme. F.4 The stndrd devtons of the velocty errors for the nterted system wth GPS recever lost trckn for two perods of tme.