Integrated INS/GPS Navigation System

Transcription

1 Intrnational Journal on Elctrical Enginring and Informatics - Volum 10, Numbr 3, Sptmbr 2018 Intgratd INS/GPS Navigation Systm Targ Mahmoud and Bambang Riyanto Trilaksono School of Elctrical Enginring and Informatics, Institut Tknologi Bandung, Bandung, Indonsia Targ_8@yahoo.com, Briyanto@lskk..itb.ac.id Abstract: Navigation quipmnt spcifications diffrs in th updat rat, accuracy, budgt, rliability, siz and mass. In som applications in ordr to mt navigation systm rquirmnt, a dad rckoning quipmnt i.. Inrtial Navigation Systm INS is could b intgratd with on or many position fixing quipmnt, i.. Global Navigation Satllit Systm GNSS. INS and GPS hav diffrnt bnfits and drawbacks, and thy complmnt ach othr whn intgrating thm to provid a navigation solution with highr bandwidth, and long-trm and short-trm accuracy. This rsarch invstigats th prformanc of an intgratd systm GPS/INS(MEMS) whn changing th algorithm updat rat, and compar btwn diffrnt intgration algorithm namly loosly and tightly intgration. Kywords: INS, GPS, Loosly coupl, tightly coupl 1. Introduction Concis Oxford Dictionary dfins navigation as any of svral mthods of dtrmining or planning a ship s or aircraft s position and cours by gomtry, astronomy, radio signals, tc. A navigation systm may b usd in diffrnt plant (aircraft, ship, car, tc.) and in diffrnt ways (automatically or manually); For xampl, dynamical motion of a car vhicl is rlativly lowr than a transport aircraft in trms of vlocity and angular motion. Th navigation systm in th car is usd by human drivr howvr in a transport aircraft an autopilot nd a navigational signal with a dtrmind spcification, and tchnical rquirmnt, including rliability and safty rquirmnt. A military application also has spcial rquirmnt such as immunity from jamming. Th navigation systm rquirmnts in trms updat rat, accuracy, budgt, rliability, scurity, siz and mass diffr basd on th plant and usag. Figur 1. Typical intgratd navigation architctur [1] Thr ar two catgoris of navigation systms basd on tchniqu it uss. Th first is basd on position fixing tchniqu to dtrmin position thn th othr navigational data could b obtaind. Position fixing tchniqus uss baring and/or distanc from known objcts to dtrmin location, trrstrial land marks, map and magntic compass, lasr, radio signal and radar ar usd to dtrmin rang and/or baring in position fixing navigation tchniqus. Th scond catgory of navigation systm is known as dad rckoning, in which a dvic is usd to acquir th chang in position and/or vlocity and intgrat it, givn that initial position is known. Rcivd: May 18 th, Accptd: Sptmbr 23 rd, 2018 DOI: /iji

2 Targ Mahmoud, t al. Dvic lik odomtr, undrwatr turbin, Dopplr radar, acclromtr and gyro ar usd as masurmnt dvic in dad rckoning navigation systm. For som application th two navigation tchniqus ar intgratd to giv on navigational solution, a typical intgration architctur is shown in figur 1, whr th output of position fixing dvic is corrctd to giv th intgratd navigation solution, a dad rckoning dvic is addd with Kalman filtr to provid th ncssary corrctions. A common xampl of intgrating two navigation systm is utilizing th Global Navigation Satllit Systm GNSS (position fixing navigation systm) to aid a dad rckoning systm i.. Inrtial Navigation Systm INS. Th INS hav advantags ovr GNSS lik rrors ovr shorttrm position ar rlativly small, updat rat highr, and not subjction to radio jamming. In othr hand GNSS hav an advantag ovr INS lik Long-trm position rrors do not dgrad with tim, lowr cost, and GNSS do not rquir anothr mans to initializ navigational solution as dad rckoning navigation systm. Morovr, th rror charactristics of position fixing and dad rckoning diffr which allow th us powrful rror stimation algorithms as th Kalman filtr. So th intgratd navigational systm will inhrnt th good fatur of GNSS and INS, and hav mor accurat navigational solation. For dcads, INS and GNSS intgration has bn invstigatd, loosly and tightly intgration mthodology which utiliz Kalman filtr ar succssfully implmntd for INS/GNSS intgration [3,4,5,6,7,8,9]. Kalman filtr ar considrd as powrful tool for stimation and data fusion, (optimum in statistical sns) givn that masurmnt modl and its stochastic ar known [10]. Howvr, in th rapid growth of mbddd systm tchnology, nw mbddd systm fatur has bn dvlopd to incras th computational spd of algorithm (rcntly, ARM dvlopd cortx-m4 procssor with floating point fatur); as th computational spd affct th Kalman filtr prformanc [1], only fw studis show th ffct of algorithm updat rat on th prformanc of INS/GPS intgration. Morovr, as th INS/GPS coupling algorithm complicity diffr [2], only fw studis compar th prformanc of diffrnt intgration algorithm which hlp in choosing appropriat algorithm for a crtain application. This rsarch invstigats th prformanc of an intgratd systm GPS/INS(MEMS) implmntd on mbddd microcontrollr whn changing th algorithm updat rat, and compar btwn diffrnt intgration algorithm namly loosly and tightly intgration. In this papr, thr diffrnt navigation mthod has bn simulatd and compard namly loosly coupld INS/GPS, tightly coupld INS/GPS, and INS. Morovr, th loosly coupld INS/GPS intgration algorithm has bn tstd using Cortx-M4 for diffrnt updat rat, rsults hav bn providd and discussd. Outlin of this papr is as follows. Inrtial masurmnt unit rror modl is prsntd in sction 2. Dscription of inrtial navigation unit is discussd in sction 3, followd by satllit navigation modl and solution in sction 4. In sction 5, INS/GPS intgration, loosly and tightly intgration architctur is discussd along with Kalman filtr algorithm. Simulation for navigation mthod is prsntd in sction 6, followd by loosly coupl intgration tsting in sction 7. Finally, conclusion is writtn in sction Inrtial Masurmnt Unit Error modl Inrtial snsors contain acclromtrs which masur th spcific forc f b ib, and gyroscops (gyros) which masurs th angular rat ω b ib. Th inrtial masurmnt in this rsarch considr MEMS tchnology. MEMS snsors ar mor light and small compard to th convntional mchanical gyro, in addition it xhibits gratr shock tolranc; Howvr, it givs poor prformanc. MEMS principally uss quartz and silicon snsor combind in a singl silicon wafr. As a masurmnt snsor an acclromtr and gyro ar subjctd bias rrors, scal factor rrors, and cross-coupling rrors, in addition to th random nois. Morovr, angular ratacclration cross-snsitivity and highr ordr rrors and may also occur. 492

3 Intgratd INS/GPS Navigation Systm Following snsor calibration and compnsation, th IMU acclromtr and gyro biass, could b dnotd by th vctors b a = (b a,x, b a,y, b a,z ) and b g = (b g,x, b g,y, b g,z ), rspctivly. Acclromtr and gyro scal factor rrors could b dnotd by th vctors s a = (s a,x, s a,y, s a,z ) and s g = (s g,x, s g,y, s g,z ), rspctivly. Anothr typ of rror found in acclromtr and gyro is th cross-coupling rrors, which ar rsultd from th misalignmnt btwn th orthogonal axis of th body fram and th snsor snsitiv axis. Th notation m a,αβ, dnot th cross-coupling cofficint of β-axis spcific forc snsd by th α-axis acclromtr, and m g,αβ, is usd dnots th cofficint of β-axis angular rat which ar snsd by th α-axis gyro. Th following matrix xprss th scal factor rror and cross-coupling rror, whn th acclromtr and gyro triad ar nominally orthogonal to ach othr: s a,x m a,xy m a,xz M a = ( m a,yx s a,y m a,yz ) (1) m a,zx m a,zy s a,z s g,x m g,xy m g,xz M g = ( m g,yx m g,zx s g,y m g,zy m g,yz ) s g,z (2) Th vctors w a = (w a,x, w a,y, w a,z ) dnot th random nois of IMU acclromtr, and w g = (w g,x, w g,y, w g,z ), dnot th random nois of IMU gyro. Th quation blow shows to what xtnd th rror contribut to th IMU output: f ib = b a + (I 3 + M a )f ib + w a (3) ω ib = b g + (I 3 + M g )ω ib + G g f ib + w g (4) b b b Whr f ib is IMU-output spcific forc, and ω ib ar th and angular rat vctors, f ib and b ar th tru quantity, and I 3 rprsnts th idntity matrix. ω ib 3. Inrtial Navigation Unit Figur 2. Schmatic of an inrtial navigation procssor [1] Th inrtial navigation systm (INS), somtims calld inrtial navigation unit (INU) catgorizd as a dad rckoning navigation systm. INS as shown in figur 2 compromisd from 493

4 Targ Mahmoud, t al. an inrtial masurmnt unit and a navigation procssor. Th navigation procssor basically intgrat th IMU output to produc a navigation solution. To comput a navigation solution four stps should b followd: attitud updat, thn transformation of th spcific-forc about th rsolving axs, followd by vlocity updat, and finally position updat. Morovr, th gravitational modl is includd for transforming th spcific forc to acclration Equation (5) to (8) shows how to us th masurmnt of th angular-rat and spcific-forc in th intrval from t to t+τi to updat th Earth-rfrncd attitud, vlocity, and position. Th abov four stps ar dscribd blow. Th suffixs ( ) dnot th valu at th bginning of procssing cycl at tim t, and th suffixs (+) dnot th valu at th nd of procssing cycl t+τi. For Attitud Updat th following quation apply [1] C b (+) C b ( )(I 3 + Ω b ib τ i ) Ω i C b ( )τ i (5) Whr, C b is th Earth-fram coordinat transformation matrix, and Ω i is th angular rat vctor skw-symmtric matrix. ` And for Spcific-Forc Fram Transformation th following quation ar usd f ib (t) = C b (t)f b ib (t) 1 (C 2 b ( ) + C b b (+))f ib (6) To giv Vlocity Updat th following quation is v b (+) v b ( ) + (f ib + g b (r b ( )) 2Ω i v b ( ))τ i (7) Whr, g b rprsnt th acclration du to gravity acting on th body rsolvd in ECEF fram. For Position Updat th following quation is r b (+) = r b ( ) + (v b ( ) + v b (+)) τ i (8) 2 Whr, v b and r b rprsnt th vlocity of th body in rlation to th ECEF fram, rspctivly, 4. Satllit Navigation Systms modl and solution Tabl 1. GPS Satllit Orbit Ephmris Paramtrs [2] 494

5 Intgratd INS/GPS Navigation Systm Global navigation satllit systms GNSS is a fixing point navigation systm, which provid th usr with a thr-dimnsional positioning solution by passiv ranging using radio signals transmittd by satllits orbiting around th arth. Thr ar many GNSS systm orbiting around th arth, on of thm is (NAVSTAR) Global Positioning Systm (GPS), which blong to th U.S. govrnmnt. In ordr to dtrmin satllit position and vlocity, GPS transmit phmris (satllit orbital data, 16 quasi-kplrian paramtrs which ar listd in Tabl 1, including th rsolution in trms of th last significant bit, this is applicabl to th lgacy GPS navigation data mssag). Th phmris paramtrs dscrib th orbit during th intrval of tim (at last 1 h) from which th paramtrs ar transmittd. Th cntr of th satllit s antnnas ECEF coordinats ar calculatd using a variation of th quations shown in Tabl 2. Th tru rang btwn satllit and usr antnna T could b obtaind by masuring th tim btwn th satllit signal transmission tst, and th usr s antnna tim signal arrival tsa and dividd by th spd of light. Th usr quipmnt obtains psudo-rang masurmnts bcaus of multipl inaccuracis and uncrtaintis, usr-quivalnt rang rror (UERE) rprsnt th uncrtainty of ach psudo-rang masurmnt. For satllit j th psudo-rang and psudo-rang rat which ar masurd by th usr quipmnt ar givn by [1]: T = Tj + δ ij + δ tj δ sj + δ rc (9) Rj = Tj + δ ij + δ tj δ sj + δ rc (10) Equation (9) and (10) ar usd to modl and simulat usr quipmnt masurmnt. Tabl 2. Algorithm for computing satllit position and vlocity [2] 495

6 Targ Mahmoud, t al. Whr δ ij and δ tj ar, th ionosphr and troposphr propagation rrors, rspctivly. δ sj is th rang rror du to th satllit clock, δ rc is th rang rror du to th rcivr clock, and δ ij, δ tj, δ sj and δ ar thir rang-rat countrparts. rc A st of th psudo-rang masurmnts cannot b usd to asily usd to driv th position solution in an analytical way. Thrfor, th quations ar linarizd by prforming a Taylor xpansion about a prdictd usr position, r P a, and clock offst δ P rc, th last-squars solution is usd. For th ECEF fram [1]: P ρ C1 ρ C1 P ( r b (t sa ) (t δ rc sa ) ) = ( r a T P ) + (G G ) 1 T G δ rc ( v b (t sa ) δ (t rc sa ) ) = ( v P a T P ) + (G δ G ) 1 T G rc Whr P rc P rc = [r sj (t st,j ) r a = u P as,j P ] T [r sj [v sj (t st,j ) v P a ] + δ rc P ρ C2 ρ C2 ( ρ Cn ρ Cn ( ρ P ) P ρ C1 ρ C1 ρ C2 ρ C2 P Cn ρ Cn P ) (11) (12) (t st,j ) r P a ] + δ P rc + δ i,j (13) P + δ i,j (14) And th gomtry matrix, G is obtaind as follow. Masurmnt matrix, H, is H = ρ 1 x a ρ 2 x a [ ρ n x a ρ 1 y a ρ 2 z a ρ n y a ρ 1 z a ρ 2 z a ρ n z a ρ 1 ρ rc ρ 2 ρ rc ρ n ρ rc ] i ip r ia=ria (15) Diffrntiating (15) with rspct to th usr position and clock offst rsult H = ( P u as,1,x P u as,2,x P u as,n,x P u as,1,y P u as,2,y P u as,n,y P u as,1,z P u as,2,z P u as,n,z ) = G (16) 5. INS/GPS intgration Hr, two typs of intgration architctur ar discussd loosly coupld, and tightly coupld. Th intgration algorithm compars th outputs of GPS usr quipmnt with th inrtial navigation solution, thn stimats corrctions to th inrtial position, vlocity, attitud solution, acclration bias and gyro bias. Kalman filtr is usd as an stimation algorithm. Th obtaind inrtial navigation solution aftr corrction rprsnt th intgratd navigation solution. In situation of GPS signal loss this architctur grant producing intgratd navigation solution. Th INS/GNSS intgratd navigation architctur could b classifid as an opn loop and closd loop. As shown in figur 3 th opn loop architctur intgration algorithm stimats th rror in th INS masurmnt and provid th solution. Whil in th closd loop architctur th INS driv th final solution and utilizing th algorithm output to driv th final navigation solution. 496

7 Intgratd INS/GPS Navigation Systm Figur 3. Opn- and closd-loop INS corrction architcturs A. Kalman Filtr Algorithm Th Kalman filtr can b dscribd as a st of mathmatical quations that implmnt a prdictor-corrctor typ stimator that is optimal in th sns that it minimizs th stimatd rror covarianc whn som prsumd conditions ar mt. Th Kalman Filtr basic tchniqu was invntd by R. E. Kalman in 1960 and sinc has bn dvlopd furthr by numrous authors. Th Kalman filtr mak an stimation to a procss by using a form of fdback control: th procss stat is stimatd at som tim and thn obtains fdback in th form of (noisy) masurmnts. As such, th quations for th Kalman filtr fall into two phas: tim updat phas and masurmnt updat phas. Th currnt stat and rror covarianc stimats fall in tim updat phas, which ar rsponsibl for projcting forward (in tim) to obtain th a priori stimats for th nxt tim stp. Whil, th masurmnt updat quations ar rsponsibl for th fdback i.. for incorporating a nw masurmnt into th a priori stimat to obtain an improvd a postriori stimat. Th tru stat vctor, x(t), at tim, t, of any Kalman filtr is dscribd by th following dynamic modl [1]: x (t) = F(t)x(t) + G(t)w s (t) (17) Whr w s (t) is th systm nois vctor, F(t) is th systm matrix and G(t) is th systm nois distribution matrix. Th xpctation valu of th tru stat vctor, x(t), is th stimatd stat vctor, x (t). Th xpctation valu of th systm nois vctor w s (t), is zro, as th nois is assumd to b of zro man. F(t) and G(t) ar assumd to b known functions. Th discrt and continuous forms of th Kalman filtr ar quivalnt, with x k = x (t) and x k 1 = x (t τ s ). Kalman filtr masurmnt vctor, z(t), is modld as a linar function of th tru stat vctor, x(t), and th whit nois sourcs, w m (t). Thus, z(t) = H (t)x(t) + w m (t) (18) Whr H(t) is th masurmnt matrix and is obtaind from th proprtis of th systm. Th Kalman filtr algorithm stps ar dscribd blow: 1. Transition matrix calculation k 1 : Transition matrix shows th stat vctor changs with tim as a function of th dynamics of th systm modld by th Kalman filtr. k 1 xp (F k 1 τ s ) (19) Th transition matrix is usually computd as a powr-sris xpansion of th systm matrix, F, and propagation intrval τ s. 497

8 Targ Mahmoud, t al. 2. Systm nois covarianc matrix calculation, Q k-1: Systm nois covarianc matrix shows how th uncrtaintis of th stat stimats incras with tim as a rsult of nois sourcs in th Kalman filtr systm modl (such as unmasurd dynamics and instrumnt nois). Usually th systm nois covarianc matrix form as diagonal and constant matrix. 3. Stat vctor stimat propagation from x k to x k 1 + : Th tim-propagatd stat stimats ar dnotd x k, its countrparts following th masurmnt updat is dnotd x k+, Th subscript k is usd to dnot th itration. Th stat vctor stimat is propagatd through tim using: x k + = k 1 x k 1 (20) + 4. Error covarianc matrix propagation from P k 1 to P k : Th tim-propagatd covarianc matrix is dnotd P k, its countrparts following th masurmnt updat is dnotd P k+, and th subscript k is usd to dnot th itration. Th covarianc matrix is propagatd through tim using: P k = k 1 P + T k 1 k 1 + Q k 1 (21) 5. Calculat th masurmnt matrix H k; Th masurmnt matrix dfins how th masurmnt vctor varis with th stat vctor. In navigation, H k is a function of th usr kinmatics and/or GPS satllit gomtry. 6. Calculat th masurmnt nois covarianc matrix, R k: Th masurmnt nois covarianc matrix, R k, could b assum constant or could b modld as a function of kinmatics or signal-to-nois masurmnts. 7. Kalman gain matrix calculation K k : Kalman gain dtrmin th wighting of th masurmnt information in updating th stat stimats. Th Kalman gain is a function of th ratio btwn uncrtainty of th tru masurmnt, z k, and th uncrtainty of th masurmnt prdictd from th stat stimats, H kx k. Th Kalman gain matrix is K k = P k H T k (H k P k H T k + R k ) 1 (22) 8. Formulat th masurmnt, z k: In som applications, th masurmnt vctor is prsntd in th systm modld by th Kalman filtr. In othr applications, z k should b calculatd as a function of othr systm paramtrs. 9. Stat vctor stimat Updat from x k to x k+ : Th stat vctor is updatd with th masurmnt vctor using x k+ = x k + K k (z k H k x k ) (23) 10. Error covarianc matrix updat from P k to P + k : Th rror covarianc matrix is updatd with P + k = (I K k H k ) P k (24) For INS/GPS thr ar intraction btwn th INS and GPS stat in th masurmnt modl, whil in systm modl thr is no intraction Thrfor, th systm, transition, and systm nois covarianc matrics could b xprssd as [1]: F = ( F INS 0 ), 0 F GPS = ( INS 0 ), Q = ( Q INS 0 ) (25) 0 GPS 0 Q GPS And x = ( x INS x ) (26) GPS Th stat vctor for INS rsolvd in th ECEF fram, Kalman filtr stimatd rror in th navigation solution: 498

9 Intgratd INS/GPS Navigation Systm x INS = δ b δv b δr b b a ( b g ) And, th systm matrix is F INS = Ω i F 21 2Ω i I 3 F 23 C b C b ) ( Whr; F 21 = [ (C b f b ib )^] (29) (27) (28) F 23 = 2g 0(L b) r S(L b) L b r b T 2 r b r b (30) Th INS systm nois covarianc matrix, Q INS, with assumption than th 15 stats ar stimatd as dfind by: n 2 rg I 3 n 2 ra I 3 Q INS = I 3 τ s (31) n bad I 3 2 ( n bgd I 3) Whr n rg, n ra, n bad, and n bgd ar th powr spctral dnsitis of, rspctivly, th gyro random nois, acclromtr random nois, acclromtr bias variation, and gyro bias variation, with th assumption that all gyros and acclromtrs possss nois with qual charactristics. Considr a masurmnt m G, acquird from GNSS usr quipmnt and a prdiction of that masurmnt m I, acquird from th raw inrtial navigation solution (and th GNSS navigation data mssag, whr appropriat). Using th Kalman filtr stat vctor an stimats of th rrors in ths masurmnts δm G and δm I, can thn b obtaind. Thr ar two mthods in which ths can lgitimatly b constructd into a Kalman filtr masurmnt, z, and stimat, in turn, ths ar z G = m G m I, z k = δm G δm I (32) And z G = m G, z G = m I + δm G δm I (33) Hr th closd-loop corrction of th INS is considrd, th prdictd masurmnt is drivd from th corrctd inrtial navigation solution and bcoms m I. B. Loosly coupld algorithm In loosly coupld INS/GPS intgration, for INS rrors stimation, th GPS usr quipmnt s position and vlocity solution ar usd, in which, th position and/or vlocity from th GPS navigation solution is considrd as a masurmnt in th Kalman filtr intgration. Th intgratd navigation solution is th takn from INS navigation solution (closd loop architctur), corrctd with th Kalman filtr stimats of its rrors. Figur 5.3 shows a loosly coupld INS/GPS intgration architctur. Th masurmnt innovation vctor could b dfind as th diffrnc btwn th GPS and corrctd inrtial position and vlocity solutions, in cas that INS and GPS antnna ar apart th lvr arm from th INS to th GPS antnna is to b dfind as I b ba,. Th coordinat frams for th masurmnt innovation should match thos for th stat vctor. Thus [1], r ag r b b C b I ba = ( δz G,k v ag v b C b (ω b ib ^ I b ba ) + Ω i b C b I ) ba k (34) 499

10 Targ Mahmoud, t al. Whr th subscript k rprsnts th masurmnt updat itration; dnots th ECEF fram implmntations; and th subscript G dnots GPS. Th loosly coupld masurmnt matrix for ECEF-fram is H G,k Whr H r1 H v1 H v5 = ( H r1 H v1 = [(C b I b ba = [{C b (ω ib = C b [I b ba ^] I 3 I 3 )^] b ^ I b ba ) H v5 k ) + Ω i C b I ba (35) (36) b }^] (37) (38) C. Tightly coupld algorithm Th GNSS ranging procssor s psudo-rang and psudo-rang-rat masurmnts ar usd in tightly coupld INS/GNSS intgration, which ar obtaind from cod and carrir tracking, rspctivly. Figur. 5.4 shows a tightly coupld INS/GPS intgration architctur. Th GPS Kalman filtr is subsumd into th INS/ GPS intgration filtr. Th Kalman filtr tak th psudo-rang and psudo-rang rats from th GPS ranging procssor as masurmnts input, and us thm latr to stimat th rrors in th INS and GPS systms. Th intgratd navigation solution forms th corrctd inrtial navigation solution (closd loop architctur). Th masurmnt innovation vctor is rsultd from th diffrncs btwn th GNSS masurd psudo-rang and psudo-rang rats, in addition to th valus prdictd from th corrctd inrtial navigation solution at th sam tim of validity, stimatd rcivr clock offst and drift, and navigation-data-indicatd satllit positions and vlocitis. Thus [1] δz ρ,k = (ρ C1 ρ C1, ρ C2 ρ C2, ρ Cn ρ Cn ) k δz G,k = ( δz ρ,k ), δz r,k δz r,k = (ρ C1 ρ, ρ C2 ρ, ρ Cn ρ (39) ) k C1 Th position and vlocity of th usr antnna could b drivd from th inrtial navigation solution, thus: r a = r b + c b b I ba (40) v a = v b + C b (ω b ib ^ I b ba ) + Ω b i C b I ba (41) Th stat vctor in tightly coupld intgration, ar compromisd from inrtial stats, rcivr clock offst, and drift. As follow: x = ( x INS δρ rc δρ rc C2 ) (42) Cn Th masurmnt matrix could b assmbld as follow: = ( H G,k z ρ δ b z r δ b 0 n,3 z r δv b z ρ δr b z r δr b 0 n,3 0 n,3 0 n,3 z ρ b g z ρ δρ rc 0 n,1 0 n,1 z r δρ rc ) x=x k (43) Th diffrntials may b calculatd analytically or numrically by prturbing th stat stimats and calculating th chang in stimat psudo-rang and psudo-rang rat. Th dpndnc of th masurmnt innovations on th attitud rror and of th psudo-rang-rat masurmnts on th position and gyro rrors is wak, so a common approximation to th analytical solution is 500

11 Intgratd INS/GPS Navigation Systm H G,k = 0 1,3 0 1,3 T u as,1 0 1,3 0 1, ,3 0 1,3 T u as,2 0 1,3 0 1, ,3 0 1,3 T u as,n 0 1,3 0 1,3 1 0 T 0 1,3 0 1,3 0 1, ,3 u as,1 T u as,2 0 1,3 0 1,3 0 1,3 0 1,3 1 0 T ( 0 1,3 u as,n 0 1,3 0 1,3 0 1,3 1 0 ) x=x k (44) 6. Simulation Thr Simulink fils wr dvlopd to compar diffrnt navigation mthod, INS, loosly coupld INS/GPS intgration, and tightly coupld INS/GPS intgration. In ach fil aircraft trajctory has bn usd to gnrat IMU and GPS masurmnt. Figur. 4 shows th input trajctory usd in th simulation. Figur 4. Aircraft 418 scond input profil Tactical grad IMU modl has bn built in Simulink for simulating spcific forc and angular rat masurmnt for th input trajctory, Figur 5 shows th tru spcific forc of body fram with rspct to ECEF fram, rsolvd along body-fram axs f b b. Figur 6 shows th tru angular rat of body fram with rspct to ECEF fram, rsolvd about body-fram axs ω b b. 501

12 Targ Mahmoud, t al. Figur 5. Simulation output of spcific forc masurmnt Figur 6. Simulation output of angular rat masurmnt In th INS simulation fil, no GPS aiding is usd to obtain th navigation solution. Figur 7 shows flow chart of th INS Simulink fil, Figur 8 shows th Simulink fil. Th GPS masurmnt is usd only to gt th initial position and vlocity. 502

13 Intgratd INS/GPS Navigation Systm Figur 7. INS Simulation flow chart Figur 8. INS Simulink fil Th loosly coupld INS/GPS intgration simulation fil algorithm is shown in figur 8, closd loop intgration architctur is usd, th INS masurmnt updat rat is 100Hz whil GPS masurmnt updat rat is 2Hz, discrt solvr wr applid. Simulink fil flow chart is shown in Figur 9, it s configurd to b applicabl for Matlab Codr c-cod gnration, and Figur 10 shows th Simulink fil. In th simulation fil closd loop intgration architctur is usd, th INS masurmnt updat rat is 100Hz whil GPS masurmnt updat rat is 2Hz, discrt solvr was applid. Simulink fil flow chart is shown in figur 11, it s configurd to b applicabl for Matlab Codr C-cod gnration, and figur 12 shows th Simulink fil. 503

14 Targ Mahmoud, t al. Start Dtrmin Tacticalgrad IMU spcification Tightly coupl Kalman filtr configuration Input profil (416sc Aircraft) NED_to_ECEF Kinmatics_ECEF IMU_modl tru_f_ib_b tru_omga_ib_b mas_f_ib_b mas_omga_ib_b GNSS_masurmnts GNSS Navigation procssor psudo-rang and psudo-rang rat masurmnts C-cod ECEF_to_NED Corrct IMU rrors Nav_quations_ECEF LC_KF Position and vlocity at low rat End Figur 9. INS/GPS loosly coupl intgration Simulink fil flow chart Figur 10. INS/GPS loosly coupl intgration Simulink fil 504

15 Intgratd INS/GPS Navigation Systm Start Dtrmin Tacticalgrad IMU spcification Tightly coupl Kalman filtr configuration Input profil (418sc Aircraft motion) NED_to_ECEF Kinmatics_ECEF IMU_modl tru_f_ib_b tru_omga_ib_b mas_f_ib_b mas_omga_ib_b GNSS_masurmnts psudo-rang and psudo-rang rat masurmnts + Satllit position and vlocity Corrct IMU rrors C-cod ECEF_to_NED Nav_quations_ECEF TC_KF End Figur 11. INS/GPS tightly coupl intgration Simulink flow chart Figur 12. INS/GPS tightly coupl intgration Simulink fil Simulation Rsult For th thr Simulink fil dscribd prviously (INS, INS/GPS loosly coupld intgration, INS/GPS tightly coupld intgration), 418 scond simulation is don for aircraft trajctory shown in Figur 6. Th absolut rror in navigation solution (position and vlocity in NED fram) in logarithmic to th bas of 10 is shown in Figurs 13, 14, 15, 16, 17 and

16 Targ Mahmoud, t al. Figur 13. Compar th thr navigation mthod - north position stimation Figur 14. Compar th thr navigation mthod - ast position stimation 506

17 Intgratd INS/GPS Navigation Systm Figur 15. Compar th thr navigation mthod - down position stimation Figur 16. Compar th thr navigation mthod - north vlocity stimation 507

18 Targ Mahmoud, t al. Figur 17. Compar th thr navigation mthod - ast vlocity stimation Figur 18. Compar th thr navigation mthod - down vlocity stimation Error root-man-squar valu (RMS) for NED fram position and vlocity navigation solution, has bn calculatd and shown in tabl

19 Intgratd INS/GPS Navigation Systm Tabl 3. Th RMS rror in position and vlocity for th NED fram 7. Tsting An xprimnt has bn don to tst INS/GPS loosly coupld algorithm with diffrnt updat rat, Figur 19 shows th xprimnt hardwar and connction, ublox-6 GPS rcivr has bn usd and configurd to output ECEF position and vlocity navigation solution in vry 0.5 scond. USB ( Powr + configur ) 5V UART (DB9) Widows 10 (CORE i5) + Kintis Dsign Studio (IDE) + LabVIEW (GUI) + MATLAB/SIMULINK + Tra Trm + u-cntr LOGIC LEVEL CONVERT USB (powr + Dbug + UART communcation) OpnSDA Micro USB EVK-6 Evaluation Kits contain-blox 6 GPS rcivr moduls 3.3V UART (Rx J2_8, Tx J2_10) UART (J5_P12 J1_2) Powr (J5_P10 J3_10) Ground (J5_P1 J3_14) VN 100 SMD Dvlopmnt Board contain 3-axis acclromtrs, gyros, FRDM-K64F Board (MK64FN1M0VLL12 MCU 120 MHz, 1MB flash mmory, 256 KB RAM, low-powr, crystal-lss USB, and 100 LQFP) Figur 19. xprimnt hardwar dscription diagram For spcific forc and angular rat masurmnt VN-100 IMU is usd and configurd to output masurmnt vry 0.02 sconds. FRDM-K64F (Cortx-M4 procssor) board wr programmd using C-ANSI cod and Kintis Dsign Studio Intgratd Dvlopmnt Environmnt IDE to acquir data from th VN-100 IMU and th ublox-6 GPS rcivr, thn th FRDM-K64F is programmd to procss th masurmnt and apply th loosly coupld intgration algorithm, in which it applis th INS navigation quation with diffrnt updat rat 5Hz, 25Hz, and 45Hz, and th Kalman filtr apply corrction at 2Hz updat rat. Thn th FRDM-K64F is programmd to output th navigation solution according to th INS navigation quation updat rat, th tst algorithm is shown in Figur20. A laptop was usd to acquir th navigation solution, display, and log th data. 509

20 Targ Mahmoud, t al. Tst Rsult Th INS/GPS loosly coupld intgration algorithm whr tstd thr tims ach tst with diffrnt INS quation updat rat (5Hz, 25Hz, and 45Hz) ach tst last for 300 scond, no movmnt wr applid (stationary tsting) so th ECEF vlocity is zro, that nabl to calculat th vlocity rror. Figur 21 shows th vlocity rror RMS valu for ach updat rat, and Figur 22 shows th stimatd vlocity of th body in ECEF coordinat fram whr Y-axs rprsnt vlocity (mtr/scond), x-axis rprsnt tim 300 scond. Figur 20. INS/GPS Loosly coupl softwar algorithm Figur 21. Error RMS valu of stimatd vlocity 510

21 Intgratd INS/GPS Navigation Systm a) 5Hz INS quation updat rat b) 25Hz quation updat rat c) 45Hz quation updat rat Figur 22. Estimatd vlocity of th body in ECEF coordinat fram 8. Conclusion From th simulation rsult it s shown that, Corrction of IMU masurmnt usd in updating th INS navigation quation using GPS and Kalman filtr, considrably incrass th navigation solution accuracy from rang of ( mtr) to rang of (1-10 mtr) in position, and from rang of ( mtr/scond) to rang of ( mtr/scond) in vlocity. Morovr, for navigational position, Tightly-coupld intgration givs bttr prformanc (RMS rror rang 0.25 to 2.3 mtr) than loosly-coupl mthod (RMS rror rang 1.9 to 3.4 mtr). For navigational vlocity, Tightly-coupld intgration givs bttr prformanc (RMS rror rang 0.06 to 0.8 mtr/scond) than loosly-coupl mthod (RMS rror rang 0.1 to 0.9 mtr/scond). From th tsting rsult it s shown that, highr navigation updat rat incrass th navigation solution accuracy, for loosly coupl intgration using 5Hz updat rat it givs (0.12 to 0.61) mtr/scond RMS valu rror in vlocity, whil for 45Hz updat rat it givs (0.03 to 0.19) mtr/scond RMS valu rror in vlocity. 9. Rcommndation For th navigation solution this rsarch analysis only th position and vlocity, to complt th navigation solution its rquird also to discuss th attitud and th inclination of th objct. In this rsarch only on loosly INS/GNSS intgration mthod it tstd, to validat th vlocity stationary tst wr applid, mthod for validating position and attitud is rquird. 511

22 Targ Mahmoud, t al. 10. Rfrncs [1]. Paul D. Grovs, Principls of GNSS, Inrtial, and Multisnsor Intgratd Navigation Systms, Artch hous, Boston London, [2]. S. Grwal, R. Will, P. Andrws, Global Positioning Systms, Inrtial Navigation, And Intgration-scond dition, John Wily & Sons, Inc.,2007. [3]. Wi M., K. P. Schwarz, Tsting a dcntralizd filtr for GPS/INS intgration, Procdings of IEEE PLANS 1990, March, Las Vgas, Nvada, USA, pp , [4]. Cannon, M. E., Airborn GPS/INS with an Application to Arotriangulation. PhD Thsis, UCGE Rport No , Th Dpartmnt of Gomatics Enginring, Univrsity of Calgary, Canada, [5]. Salychv, O, Inrtial Systms in Navigation and Gophysics. Bauman MSTU Prss, [6]. El-Shimy N., K. P. Schwarz, Navigating urban aras by VISAT - a mobil mapping systm intgrating GPS/INS/digital camras for GIS applications, Journal of Th Institut of Navigation, Vol. 45, No. 4, pp , [7]. Jkli, C., Inrtial Navigation Systms with Godtic Applications. Nw York, NY: Waltr d Gruytr, [8]. Schrzingr, B. M., Prcis robust positioning with inrtial/gps RTK, Procdings of ION GPS 2000, Sptmbr, Salt Lak City, UT, USA, pp , [9]. Ptovllo, M., O. Mzntsv, G. Lachapll and M.E. Cannon, High snsitivity GPS vlocity updats for prsonal indoor navigation using inrtial navigation systms, Procdings of ION GPS/GNSS 2003, 9-12 Sptmbr, Portland, OR, USA, pp , [10]. Glb, A., Applid Optimal Estimation. Cambridg, Massachustts: Th Massachustts Institut of Tchnology Prss, Targ Mahmoud was born in Yanbu, KSA in H obtaind his Bachlor Dgr in Aronautical Enginring (Avionics) in 2008, and his MSc in Elctrical Enginring, School of Elctrical Enginring & Informatics, ITB in Currntly, h srvs as Aronautical Enginr, Avionics Licnsd Aircraft Maintnanc Enginr, Elctrica.. Bambang Riyanto Trilaksono was born in Banyuwangi, Indonsia in H obtaind his undrgraduat dgr from Elctrical Enginring in Bandung Institut of Tchnology in H obtaind his mastr and PhD dgr from Elctrical Enginring, Wasda Univrsity, Japan, in 1991 and 1994, rspctivly. Currntly, h is a profssor in Control and Computr Systm Rsarch Group in Bandung Institut of Tchnology. His rsarch intrsts includ control, robotics and artificial intllignc. 512