Accurate Doppler Prediction Scheme for Satellite Orbits

Transcription

1 Accurat Dopplr Prdiction Schm for Satllit Orbits NASER AYAT, MOHAMAD MEHDIPOUR Computr nginring group Payam noor univrsity Lashgarak st., Nakhl st., Thran IRAN Abstract: - In satllit communications particular in low arth and lliptical orbits, Dopplr frquncy shift is on of th most important problms in communication channls. This papr scrutiny Dopplr frquncy shift in various satllit orbits. For this purpos an orbit gnrator is usd for accurat simulation of satllit orbits. Th nonsphrical mass distribution turbulnc considrd in th stimator. Simulation rsults of Dopplr frquncy shift for an lliptical LEO satllit in L-band also prsntd. Ky-Words: - Dopplr stimation, orbit gnrator, lliptical satllit orbit, LEO Introduction In communication systm that rcivr and transmittr ar not fixd and hav significant rlativ vlocity, Dopplr frquncy shift is high. For propr dsign of various parts of transcivrs lik input filtrs in rcivrs and PLL parts, nd to accuratly calculat carrir frquncy shift and compnsat. With th prsntd simulator, rcivrs can calculat Dopplr frquncy in ach tim and also tim intrval of viwing satllit. Accurat Dopplr information hav influnc in improvmnt of pashd lock loop prformanc, also ground sgmnt with notic of satllit viwing only in momnts that transmitting is possibl, turn on th powr and this rduc th powr consumption. Thr ar many rsarchs that focusd on mthodology to compnsat for Dopplr shifts but for accurat stimating of this paramtr in [] th author charactrizd Dopplr tim curvs in th simpl cas of circular in th quatorial plan and Dopplr obsrvd by points on th quator. In [] th author drivd analytical xprssion of Dopplr shift for circular LEO satllits, th prsntd schm includ any satllit orbit. Orbit dynamics Among many kinds of nongostationary orbits, thr ar two typical orbits for th communication satllits; highly lliptical and low-altitud orbits. Sinc th nongostationary satllits changs thir rlativ positions to arth stations, th signal suffr from Dopplr shift whos valu and drift rat ar vry larg compard with that in th systm with gostationary satllits or th trrstrial systms. On consqunc of th us of lliptical orbits is th xistnc of Dopplr shifts in all satllit/ ground link. To calculat th accurat Dopplr frquncy shift, w nd th rlativ vlocity btwn satllit and ground trminal. Th rlationship btwn th rlativ vlocity and Dopplr shift is givn by: f v t f = Whr f is th carrir frquncy and d c d( P P s ) v = in sphrical coordinats t dt Whr P and P s ar th position of satllit and arth transcivr rspctivly. For this purpos an orbit gnrator prsnt hr that calculats this rlativ vlocity. This stimator uss Kplr s quation to dtrmin position and vlocity of satllit in th orbit. To dtrmin an arth orbit w nd six paramtrs, th paramtrs ar dfind at som rfrnc tim or poch ( t ): smimajor axis ( a ) and ccntricity ( ) that dfin th siz and shap of th orbit, th inclination (i ) and right ascnsion of th ascnding nod (Ω ) that dfin th orbit plan, th rotation of th orbit within th plan that is dfind by th argumnt of prig (ω ), finally th man anomaly ( M ) spcifis th position of th satllit in its orbit at th poch tim. ) Low Earth Orbit

2 In figur if th plan of papr is th rfrnc plan and th dashd part of orbit is blow th papr, thn th nods ar as illustratd. dω dω = Rcosυ Ssinυ cos i () dt na cosυ dt i z dm = n+ R cosυ S sin υ (4) dt na cosυ + cosυ Ω ω P y Equations 9-4 show if th prturbing forc vctor is known thn th diffrntial changs of all six orbit paramtrs can b calculatd analytically. x Figur - Kplrian Orbital lmnts in ECI coordinat To dtrmin th rlativ vlocity w nd to calculat vlocity of satllit and ground station in a rfrnc coordinats. For this purpos th satllit vlocity calculats in ECI coordinats and thn convrts to ECF, also vlocity of ground station dtrmins in ECF coordinats. Diffrnt prturbing forcs lik Nonhomognity and oblatnss of th arth affct th orbit paramtrs as follow: Rat rang of orbit paramtrs influncd by prturbing forcs rprsnt by Gauss plantary quations along th axs of a moving Cartsian fram dfind in th following way: R along th radius vctor r; S in th local plan of osculating orbit, prpndicular to R, and in dirction of satllit motion; W prpndicular to both R and S, in th dirction of th momntum vctor R S. any prturbing forc can th b xprssd as: γ = RR + SS+ WW (4) p 4 K =.5* µ * J * RE / r (5) R = K sin ω + ν sin i (6) ( ( ) ( )) ( ( ω ν) ( )) ( ω ν) ( ) S = Ksin + sin i (7) W = Ksin + sin i (8) Th rsulting Gauss quations ar: da = R υ+ ( + υ) S ( ) dt sin cos (9) n d = ( Rsinυ + ( cos E+ cos υ) S) dt na () di r = cos ( υ + ω) W dt na a () ( υ + ω) dω r sin = dt na a sin i W () orbit gnrator satllit position and vlocity can b drivd from orbit paramtrs. Th man motion computs from smi major axis: µ n =, µ = (5) a Man anomaly in trm of man motion is: M = n( t T) (6) Eccntric anomaly can b computd from man anomaly and ccntricity. E = M + sin M + sin M + ( sin M sin M) +K (7) 8 With knowing th ccntric anomaly, tru anomaly calculats from th quation blow: / ( ) tan ν + E = tan (8) ( ) distanc of satllit from th cntr of arth is: r = a ( ) ( + cos( υ )) (9) With th drovd paramtrs, satllit position in ECI coordinats rprsnts as bllow: X cos( ω + υ) cos( Ω) sin ( ω + υ) sin ( Ω) cos( i) Y = r cos( ω + υ) sin ( Ω ) + sin ( ω + υ) cos( Ω ) cos ( i) () Z sin ( ω + υ) sin ( i) Satllit ECI vlocity drivs from diffrntiation of position rspct to tim. V bl cos E al sin E cos sin () X na VY = bm E am E r V Z bncos E ansin E Whr: ( ) / b= a () l = cos Ωcosω sin Ωsinωcos i () m = sin Ω cosω + cos Ωsinωcos i (4) n = sinω sin i (5) l = cosωsinω sin Ωcosωcos i (6) m = sinω sinω + cos Ωcosωcos i (7)

3 n = cosω sin i (8) r Vsat 4 Dopplr quations To calculat th rlativ vlocity w nd to hav vlocity vctor of satllit and ground station in th sam coordinat systm. position of ground station in ECF coordinats can b driv asily by knowing th longitud and latitud of station and hnc by transforming th satllit coordinat from ECI to ECF w rach th goal. Th transformation of an ECI position vctor r ECI to an ECF position vctor r ECF is givn by th r = T r. following vctor-matrix opration ECF [ ] ECI whr th lmnts of th transformation matrix [ T ] ar givn by cosθ sinθ T = sinθ cosθ (9) whr θ is th Grnwich sidral tim at th momnt of intrst. Grnwich sidral tim is givn by th following xprssion: θ = θ g + ω t () whr θ g is th Grnwich sidral tim at hours UT, ω is th inrtial rotation rat of th Earth, and t is th lapsd tim sinc hours UT. Th ECF vlocity vctor is dtrmind by diffrntiating this xprssion: VECF = T r& ECI + T& r ECI = TVECI + T& r ECI Th lmnts of th T& matrix ar as follows: () ωsinθ ωcosθ T& = ωcosθ ωsinθ () if latitud and longitud of ground sgmnt rprsnt as ϕ, λ thn th ground sgmnt position in ECF is as bllow : xg cos λcosϕ yg = RE sin λcos ϕ () z G sinϕ With knowing th position vctor of satllit and arth trminal in ECF coordinats, th position vctor of satllit with trminal rfrnc can drivd. With this vctor and th satllit vlocity vctor, rlativ vlocity of satllit rspct to arth trminal in lin of sight viw can driv. r r Figur - Position and vlocity vctors of satllit and arth trminal r is th arth trminal position vctor and r is th satllit position vctor. Hnc r dtrmin th rlativ position of satllit rspct to arth trminal in ECF coordinats. Rlativ vlocity btwn r r r satllit and ground trminal is: V ˆ rl = Vsat whr r rˆ = r and r = r r T R cos cos ˆ E λ φ x r ˆ = RE sin λcos φ y (4) R sin ˆ E φ z ( ω υ) ( θ) ( ω υ) ( θ) ( ω υ) ( θ) ( ω υ) ( θ) sin ( ω + υ) sin i cos + cos Ω+ sin + sin Ω+ cosi xˆ r ˆ = r cos + sin Ω+ + sin + cos Ω+ cos i y (5) zˆ In th abov quations V r sat is satllit vlocity in ECF coordinats. With knowing th accurat rlativ vlocity, Dopplr frquncy shift can b calculatd. An othr problm that sams in th abov quations is that th Dopplr drivs for th whol tims but w want to comput this paramtr in th visibl tim intrvals. For this purpos with using th minimum arth lvation angl, th satllit visibility intrvals can b dtrmind. 5 Simulation rsults Analytical rsults simulats in MATLAB simulink nvironmnt. Ground trminal has dgr north longitud and dgr ast latitud. Earth lvation angl is. Orbit paramtrs ar as blow: man anomaly = smi major axis = m inclination = 5 o ccntricity =. argumnt of prig = 7 o RAAN = 55 o T

4 Figur display th ground trminal and orbit in on cycl. 6 4 ECF Satllit Vlocity in X Axis STK MATLAB ECF Vlocity in X Axis Figur - Satllit in th orbit with th dtrmind paramtrs For vrify th simulation rsults, som MATLAB simulation rsults compard with STK rsults. Figur 4 shows th ECI satllit position for hours, th maximum diffrnc of two simulation rsults is lss than %. ECI position in X axis (m) ECI Satllit Position in X axis STK MATLAB Figur 4- ECI satllit position for hours Figur 5- ECF satllit vlocity Dopplr frquncy in satllit visibl durations is shown in figur 6. it shows that in a day in 9 duration intrvals satllit can communicat with th ground trminal..5 x Dopplr Frquncy Shift in 4 Hours x 4 Figur 6- Dopplr frquncy shift in 4 hours th forth pass of satllit zoomd in figur blow, as you can s bcaus of lliptical orbit, positiv and ngativ Dopplr shifts ar not sam..5 x 4 Dopplr Curv in on accss Priod ECF satllit vlocity in figur 4 shows that rror of transformation to ECF is blow % x 4 Figur 7- Dopplr curv in on path 4

5 Comparison of STK and MATLAB rsults is shown in th figur 8, as it shows accuracy is abov 99.5%..5 x Dopplr Curv for th forth pass of Satllit STK MATLAB Figur 8- comparison of STK & MATLAB rsults for th forth pass With changing th arth lvation angl, satllit viwing durations also changs, in th blow figurs Dopplr for 5 o and o prsnts. As it sms with incrasing th lvation angl visibility intrvals dcras..5 x Dopplr Curv in 4 Hours for 5 dg Earth Elvation x 4 Figur 9- Dopplr for 5 dgr arth lvation in a day.5 x Dopplr Curv for dg Earth Elvation Maximum valu of Dopplr shift in trm of ccntricity shows in figur, with dcrasing th ccntricity of this orbit, its circularity incras and satllit altitud in visibility durations dcras and hnc Dopplr frquncy shift incrass. Maximum of Ngativ Dopplr -.6 x 4 Maximum Ngativ Dopplr for Diffrnt Orbit Eccntricity Eccntricity Figur - maximum ngativ Dopplr in trm of ccntricity Maximum positiv of this paramtr also shown in figur Maximum of Positiv Dopplr.44 x 4 Maximum Positiv Dopplr for Diffrnt Orbit Eccntricity Eccntricity Figur - maximum positiv Dopplr frquncy in trm of ccntricity An othr important paramtrs is rat of Dopplr shift, figur shows th Dopplr rat in th forth pass, as it shows with. GHz carrir frquncy, Dopplr rat is blow Hz/sc x 4 Figur - Dopplr for dgr arth lvation in a day 5

6 Dopplr Rat (Hz/sc) Dopplr Rat for th 4th Pass x 4 Figur - Dopplr rat in forth passs An othr paramtr that considrd in th papr is th visibility durations. Th sum of visibility durations in a day in trm of various arth lvation angls prsnts in figur 4. Visiblity Duration (sc) Satllit Visibility from Ground Trminal Elvation Angl (dg) Figur 4- visibility durations in trm of arth lvation angl 6 Conclusion Rfrncs: [] M. Katayama, A. Ogawa, and N. Morinaga, Carrir synchronization undr Dopplr shift of th nongostationary satllit communication systm, in Proc. ICCS/ISITA 9, Singapor, 99, pp [] M. You, S. L, and Y. Han, Adaptiv Compnsation Mthod Using th Prdiction Algorithm for th Dopplr Frquncy Shift in th LEO Mobil Satllit Communication Systm, ETRI Journal, Volum, Numbr 4, Dcmbr. [] J. R. Wrtz, Spaccraft Attitud Dtrmination and Control, rd Edition, D. Ridl Publishing Company, 984. [4] M. J. Sidi, Spaccraft dynamics & Control, Cambridg Univrsity Prss, 997. [5] M. Richharia, satllit Communication Systm, nd Edition, MacMilian Prss, 999. [6] D. Roddy, Satllit Communication, McGraw- Hill, rd Edition,. [7] I. Ali, N. Al-Dahahir, J.E. Hrshly, Dopplr Charactrization for LEO Satllits, IEEE Transactions on Communication, Vol. 46, No., pp. 9-, March 998. [8] M.H. You, S.I. L, Dopplr Prdiction Schm for Usr Trminals in LEO Mobil Satllit Communication, Sixth Intrnational Mobil Satllit Confrnc, Ottawa, pp , Jun 999. [9] M. Katayama, N. Morinaga, A study of th communication systm using th low-altitud nongostationary satllits, IEEE intrnational Confrnc on Systm Enginring, pp , Sptmbr 99. In this papr, w hav proposd a Dopplr prdiction schm with information of satllit orbital paramtrs and ground trminal position. This schm can calculat Dopplr shift for various kind of satllit orbits. Bcaus th formr Dopplr prdiction schms considrd only circular orbits, w can t compar th simulation rsults with th prvious schms and STK softwar usd for vrifying th rsults. As it sms from compard rsults, th accuracy of this schm is abov 99%. Evn this simulator is asir to work than STK bcaus all th orbital and ground station paramtrs can input asily in simulink MATLAB nvironmnt. An othr rsult is that th maximum Dopplr rat is about Hz for. GHz carrir frquncy and rcivr phas lock loops can dsign proprly. 6