Relative Positioning Method of Using Single-frequency Model for Formation Flying Missions

Size: px

Start display at page:

Download "Relative Positioning Method of Using Single-frequency Model for Formation Flying Missions"

Felicity Todd
5 years ago
Views:

1 Inenaional Induial Infomaic and Compue Engineeing Confeence (IIICEC 205) Relaive Poiioning Mehod of Uing Single-fequency Model fo Fomaion Flying Miion Hanyi Shi, Qizi Huangpeng2,a, Yuanyuan Qiao3,4, Yong Li3, Wenwei Huang4 College of Aeopace Science and Engineeing, Naional Univeiy of Defene echnology 2 College of Five, Naional Univeiy of Defene echnology, Changha, China 3 School of Suveying & Spaial Infomaion Syem, he Univeiy of New Souh Wale, Aualia 4 College of Nine, Naional Univeiy of Defene echnology, Changha, China a hpqz9925@63com Keywod: Saellie in fomaion flying, Ionophee-fee model, Relaive poiioning, EKF Abac Ue of Global Poiioning Syem (GPS) fo pace applicaion, epecially in low-eah obi (LEO) fomaion flying miion, ha ecenly aaced moe and moe aenion hi pape popoe an Exended Kalman File (EKF) o inceae he accuacy of elaive poiion of LEO fomaion flying miion he EKF ue aellie obial dynamic model, wih combinaion of GPS and caie phae meauemen upon he ionophee-fee model he caie phae fuzzine and he poiion of pacecaf fom he ae veco, which ae pediced in he EKF Meanwhile, influence of unceainy of yemaic eo i aken ino accoun he opimal eimaion and i modified covaiance maix ae deived upon he pinciple of minimum eo covaiance he popoed EKF mehod i compaed wih he adiional double diffeence mehod in he imulaed expeimen he eul demonae he validiy and impovemen of he popoed mehod epecially in he long baeline cenaio Inoducion GPS ha been widely ued in he field of mapping and pace applicaion, ec, and i wa iniially applied in land-baed poiioning Howeve, in ecen yea, pace applicaion baed on GPS, epecially in low-eah obi (LEO) fomaion flying miion, ha ecenly aaced moe and moe aenion [] he dipeed ucue of he fomaion flying miion offe bee flexibiliy and edundancy compaed o a epaae lage pacecaf And i i conducive o a moe efficien ue of eouce and complee he ak in le ime A baic poblem in fomaion flying miion i o deemine he elaive ae beween he aellie he double diffeence mehod [2] i a commonly ued in elaive poiioning, which can eliminae a eie of yem eo Howeve, he ignal anmiion may delay due o ionophee diubance ha can educe he eimaion peciion A lo of eeache ae woking on i [3][4][5][6] o educe he diubance of he ionophee, bu he eul i fa fom aifacion hi pape popoe an Exended Kalman File (EKF) o inceae he accuacy of elaive poiion of LEO fomaion flying miion he EKF ue aellie obial dynamic model, wih combinaion of GPS and caie phae meauemen upon he ionophee-fee model he caie phae fuzzine and he poiion of pacecaf fom he ae veco, which ae pediced in he EKF Meanwhile, influence of unceainy of yemaic eo i aken ino accoun he opimal eimaion and i modified covaiance maix ae deived upon he pinciple of minimum eo covaiance Modelling of Space Syem Meauemen of GPS Fo ingle-fequency eceive which inalled in he low obi aellie, he meauemen model fo he peudo ange and caie phae in band L i [2]: () ( ) = ( ) + c(δ ( ) δ ( ( ))) + I ( ) + S ( ) + ε P ( ) 205 he auho - Publihed by Alani Pe 546

2 φ () = () + c( δ() δ ( ())) I() + S () + λϕ + εϕ () (2) Whee i meauemen of he peudo ange, i meauemen ime in GPS, i he geomeic diance beween GPS aellie and eceive a ime ( ), τ i ime of ignal anmiion, I i eo in ionophee, δ i clock coecion of eceive, δ i clock coecion of GPS aellie, S i ohe yem eo, ε P i noie in he peudo ange, φ i diance of he Caie phae, λ i ignal wavelengh, ϕ i he cycle of caie ambiguou, ε ϕ i noie in he Caie phae Uually, he noie in meauemen of peudo ange and in he caie phae ae aume a: 2 E( ε ( )) = 0, D( ε ( )) = P P P Ionophee-fee Model of Single-fequency Receive Alhough in equaion () and (2), he ionophee eo only eflec he fi-ode effec of he ionophee, i epeen he main effec of he ionophee he highe-ode of ionophee effec will caue he effec below millimee level which can be ofen ignoed hu, he Ionophee-fee model of ingle-fequency Receive can be obained accoding o addiive of equaion () and (2), which emove of he effec ionophee: () = 05( () + φ ()) = + c( δ () δ ( ())) + S + 05 λϕ + e () (3) Whee new noie mee: _ new, P _ new E( e P _ new ) = 0, D( e P _ new ) = (/ 4)( P + ϕ ) = new In equaion (3), he aellie clock coecion, eceive clock coecion and main yem eo can be eliminaed by double diffeence mehod he unknown paamee ha need o be eimaed include LEO poiion and fuzzine of caie phae he meauemen model afe double diffeence poceing i: _ ( ) 05 new = + λ ϕ + e P _ new ( ) (4) Hee, i double diffeence opeao,, i he geomeic diance beween aellie in double diffeence, λ i wavelengh of L band, ϕ i he fuzzy degee of double diffeence, e P _ new i noie afe double diffeence poceing Exended Kalman File Model A fo wo LEO aellie including a age a and an objecive a ha inalled he ingle-fequency eceive, aume ha he locaion of main a obained uing he ingle-poin poiioning when he locaion of age a elaive i an eimaed vaiable Suppoe he numbe of ohe aellie ha wo aellie can obeve a a momen i n, he ae vaiable i defined a a 6+n- degee vaiable: n X = x v y v z v 05 ϕ 05 ϕ which compoed of he locaion of objecive a and x y y fuzzy degee hu, he meauemen equaion hough EKF lineaizaion accoding o (4) i: _ new() ( _ new() M _ new()) ( _ new() M _ new()) = n n n _ new() ( _ new() M _ new()) ( _ new() M _ new()) x x x x y y y y z z z z + λ ϕ ,,,,,, = + ( X X ) + e P _ new() n n x x x xn y y y yn y y y yn + λ ϕ , n,, n,, n, = hx ( ) + H X+ e k Whee, _ new, _, k= new,, nk, i he ionophee-fee obevaion of objecive a, navigaion efeence a and ohe viible navigaion a k epecively Hee epeeen momen, epeen he obained value of momen baed on momen -, i he geomeic diance beween he objecive a and navigaion efeence a,,,,, k, k= nk i he geomeic diance beween he objecive a and ohe viible navigaion a he dicee fom of ae equaion i below X =Φ(, ) X + w (6) (5) 547

3 Relaive Poiioning Mehod Baed on EKF famewok, we can eimae he ae vaiable by uing pedic infomaion a peudo obevaion Define ˆ X a he Opimal eimaion baed on obevaion _ new,, _ new, When conideing dynamic model pedicion eo and yem meauing eo ogehe, he yem equaion i (7) Hee, χ i dynamic model pedicion eo and κ i yem meauing eo { κ},{ χ} and { w, ε, X 0 } i muually excluive, X 0, { w } and { ε } i unelaed Aume ha Z = poj{ Z / Z } X =Φ(, ) X + χ + w (7) Z = hx ( ) + H X + κ + ε Hee, Z = col{ Z0, Z,, Z } In fac, Z and ε 0, ε ε, 2 κ, k i elaed o: Z = poj{ Z / Z } = poj{ h( X ) + H X + κ + ε / Z } = h( X ) + H X + M (8) X = poj{ X / z } = poj{ Φ(, ) X + χ + w / z } =Φ(, ) X + N (9) One ep of ae pedicion value i: = =Φ(, ) + χ + ( Φ(, ) + ) =Φ(, ) X X X w X N X + w + χ N (0) One ep of ae pedicion vaiance i: P = E{ X } =Φ(, ) P Φ (, ) + Q + CN( ) () he new infomaion obained: = = ( ) + + κ + ε ( ( ) + + ) = Z Z h X H X h X H X M H X + ε + κ M (2) Accoding o he pojecion heoem: X = poj( X / Z ) = X + cov{ X, Z }va { Z } Z (3) New vaiance i: RL( ) = va{ } (4) Gain maix i: K = E{ }va { } = E{ X } RL( ) (5) heefoe, he file value i: X = X + K = X + P H RL () (6) = X + P H ( H P H + R + CM( )) Eimaed eo i: = X X =Φ(, ) X + χ + w ( X + P H ( H P H + R + CM( )) ) =Φ(, ) X + χ + w ( Φ(, ) X + N + P H ( H P H + R + CM( )) ) =Φ(, ) + χ( ) N + w P H R( ) Pedicion vaiance ae a follow: L P = E{ X } =Φ(, ) P Φ(, ) + Q+ C ( ) P H R( ) H P N L P P H RL() H P X = We can ee ha he yem eo in ae eqauion how in pedicion ae and pedicion vaiance P he yem eo of meauemen equaion i in new infomaion and covaiance R L Simulaion Expeimen Fi, we deemine he equied imulaion paamee: he ode of eah' gaviy field model i 30 he viible hielding angle of navigaion a i 5 degee he andad deviaion of fuzzy degee i week he aliude of wo aellie obi i 300 km and he baeline beween hem i 00 km he imulaion condiion i: he aellie obi i in elaively low aliude, and influenced by 548 (7) (8)

4 ionophee a lo Compae popoed mehod wih RKLIB in calculaing wo aellie baeline RKLIB ue he claical double diffeence mehod o obain he elaive poiion in he moving bae aion mode Uing peudo ange and double diffeence caie phae obevaion value o ge he elaive poiion of he age a by lea quae mehod, and hen ue LAMBDA algoihm o ge he fuzzy degee and coec he calculaion eul he elaive poiion eimaion eo of objecive a calculaed by RKLIB i hown in able I decibe he eo in mode A Fix and Hold can ge he eul by fix he value and ge fuzzy degee he eul in mode B Inananeou I ge evey momen fuzzy degee hough coecion Uually, if he obevaion eul obained by double diffeence poceing i no affeced by yem eo, he mode A i no affeced by he qualiy of he daa wih ime meauing I can defined a a common model which wok well In hi imulaion expeimen, meaue he accuacy by he hee axi eimaion mean quae oo, he accuacy of he eul in he eleive poiioning mehod i inceaed by 949% compaed o RKLIB in mode A he accuacy of he eul i inceaed by 7808% compaed o RKLIB in mode B I een ha popoed mehod enchance he accuacy compaed o claical mehod a lo able Compaion of diffeen mehod Mehod Peciion in x axi Peciion in y Peciion in z axi axi Mode A Mode B Releive Poiioning Concluion Aimed a he ingle-fequency GPS eceive which ha he advanage of low co and ligh in weigh, hi pape pu fowad a mehod of uing ingle-fequency ionophee-fee model fo fomaion flying miion of low eah obi aellie elaive poiion calculaion he mehod in he famewok of he EKF, combined he eimae of fuzzy degee and caie phae oghe Meanwhile, popoed mehod aking he effec of ohe yem eo ino accoun, coeec he noie covaiance maix and ge opimal eimaion of he minimum vaiance In he imulaion expeimen, he elaive poiioning mehod i compaed wih he eul obained in RKLIB in diffeen poceing claical mode I how ha he popoed mehod could gealy impove he peciion of elaive poiioning of he age ahe fuue wok i mainly o udy he highe peciion elaive poiioning mehod in UKF heoy and he eeach of how o impove he abolue poiioning baed on ingle fequency GPS eceive Acknowledgemen hi wok i uppoed by he Chinee Naional Science Foundaion gan and Refeence [] Simone D Amico (200), Auonomou fomaion flying in Low Eah Obi, Publihed by Riddepin BV, Delf [2] Gleaon Sco (2009), GNSS Applicaion and Mehod, Aech Houe pe, Nowood, MA [3] B Hofmann-Wellenhof, H Lichenegge, E Wale (2007), GNSS-global navigaion aellie yem, Spinge-Velag pe, New Yok, [4] Chang-Moon Lee, Kwan-Dong Pak (20), Geneaion of Klobucha ionophee eo model coefficien uing fouie eie and accuacy analyi, Jounal of Aonomy and pace cience, 28():

5 [5] HAMaque, JFGMonico, MAquino (20), RINEX_HO: econd- and hid-ode ionopheic coecion fo RINEX obevaion file, GPS oluion, 5(3): [6] P Yunck, Coping wih he amophee and ionophee in pecie aellie and gound poiioning, in: A Valance-Jone (Ed), Envionmenal Effec on Spacecaf ajecoie and Poiioning, AGU Monogaph,

Wide Area Based Precise Point Positioning

Wide Area Based Precise Point Positioning Wide Aea Baed Pecie Poin Poiioning Rodigo F. Leando and Macelo C. Sano Geodeic Reeach Laboaoy, Depamen of Geodey and Geomaic Engineeing Univeiy of ew Bunwick, Fedeicon, Canada BIOGRAPHIES Rodigo Leando