ANALYSIS ON THE COVERAGE CHARACTERISTICS OF GLONASS CONSTELLATION

ANALYSIS ON THE COVERAGE CHARACTERISTICS OF GLONASS CONSTELLATION Itm Typ txt; rocdings Authors Hui, Liu; Qishan, Zhang ublishr Intrnational Foundation for Tlmtring Journal Intrnational Tlmtring Confrnc rocdings Rights Copyright Intrnational Foundation for Tlmtring Download dat 02/05/2018 21:38:10 Link to Itm http://hdl.handl.nt/10150/606822

ANALYSIS ON THE COVERAGE CHARACTERISTICS OF GLONASS CONSTELLATION Liu Hui Zhang Qishan Bijing Univrsity of Aronautics and Astronautics ABSTRACT Th covrag charactristics of th GLONASS constllation is analyzd. Th almanac data of GLONASS navigation mssag ar usd in th computation according to th opration of th satllits. Th ground tracs of th GLONASS satllits ar plottd. And th probability of visibl satllit numbr is calculatd undr diffrnt latitud conditions. Th rsults ar analyzd to giv dscriptions of th GLONASS constllation. And thy ar compard with thos of GS's. Th conclusion is vrifid that GLONASS constllation provids bttr covrag at high latitud. KEY WORDS Covrag, ground trac, visibility, satllit navigation, and GLONASS INTRODUCTION Russian GLONASS navigation satllit systm is vry similar to GS. Th GLONASS systm can provid th sam positioning capability as GS. But bcaus GLONASS dosn t adopt Slctiv Availability th civil prcision of GLONASS is much bttr. Combind GLONASS and GS us has th advantags of bttr accuracy, availability, and intgrity and attracts much attntion of th Intrnational Civil Aviation Organization. Th GLONASS constllation also consists of 24 satllits that provid continuous covrag on th surfac of th arth. Th satllits ar placd in thr nar-circular orbits at a hight of 19,100km, with 8 satllits qually spacd in ach orbit. Th opration of a satllit in its orbit can b dscribd by its basic orbit lmnts such as major smi-axis, ccntricity, tru anomaly, right ascnsion, orbit inclination and tc. In GLONASS navigation mssag immdiat and non-immdiat componnts ar usd to dscrib th moving of th GLONASS satllits. Thy ar both in th form of orbit lmnts of th GLONASS satllits. Th diffrnc is that th immdiat mssag (or phmris) is rlativly prcis and is usd in rcivr positioning, whil th non-

immdiat mssag (or almanac) is coars dscription of GLONASS satllits and is usually usd in th prdiction of th satllits' opration. In this papr, th almanac data of GLONASS satllits ar utilizd to analyz th covrag charactristics of th GLONASS constllation. And th rsults ar compard with thos of GS's to giv an valuation of th covrag faturs of th two systms. DETERMINATION OF THE SATELLITE OSITION Th almanac data chosn ar from th nt (providd by 3S Navigation Corporation). Th data on March 4, 1996 ar slctd bcaus all th GLONASS satllits wr oprating wll at that tim. Th contnt of th almanac data is shown in tabl 1. Th maning of th paramtrs is: - alm: th ordinal numbr of th GLONASS satllit; - p: th orbit numbr of th satllit; - day: th calndar day numbr sinc last lap yar; - st: th halth status of th satllit; - ET(s): th first ascnding tim during th day; Th following paramtrs ar rfrncd to ET: - EL( ): th longitud of th first ascnsion; - T(s): th priod of th satllits in its orbit; - incl( ): th orbital inclination; - prig( ): th prig of th satllit orbit; - cc: th ccntricity of th satllit orbit. With abov almanac paramtrs, th satllits' positions can b dtrmind rfrncd to th momnt ET. Th man motion of th satllit (n) is calculatd from T and major smi-axis a is from n. Th man anomaly of th ascnding nod is dtrmind from prig and is usd to calculat th man anomaly of th satllit. Th ccntric anomaly E and tru anomaly θ of th satllit ar dtrmind accordingly. With θ, a and cc spcifid, th satllit's radius vctor r is obtaind. Thn th satllit's thr dimnsional coordinats undr orbital axis systm S o (r,0,0) ar dtrmind. In th calculation th orbit drift causd by th ccntricity of th arth and th attractions of th moon and th sun ar takn into account for bttr prdiction. THE GROUND TRACES OF THE GLONASS SATELLITES Th ground trac is th collction of th satllit's substllar points. Th substllar point can b dscribd by its gographic longitud and latitud. Whn th arth is

approximatd as a standard sphoid, gographic longitud and latitud ar th sam as th gocntric longitud ϕ and latitud λ, which ar dtrmind by th satllit coordinats undr th gocntric quatorial rotating axis systm S (x, y, z ): sin ϕ = z / r ; tgλ = y / x ; r = x + y + z (1) 2 2 2 Th S can b transformd from th S o by th rlation L o = L ω +θ ) L ( i) L ( λ ) (2) z ( x z B whr ω is th corrctd prig of th orbit, i is th inclination, and λ B is th ascnding longitud of th satllit at th computation momnt. λ B is calculatd from EL and th rotation rat of th arth. With th abov mthod w obtain th ground tracs of th GLONASS satllits. Th computation is rfrncd to th ascnding tim of th numbr 1 satllit (whos alm is qual to 1). Th rsults ar shown in Figur 1(a). THE VISIBILITY OF THE GLONASS SATELLILTES Th visibility of a satllit rlativ to th ground obsrvr point is judgd by its lvation angl θ E, which is spcifid by th satllit's coordinats undr obsrvr axis systm S p according to th rlation: tgθ = ρ + (3) E 2 2 2 z / ρ x + ρ y ρ z whr ρ ( ρ x, ρ y, ρ z )is th vctor from to th satllit. Th coordinats of point in S can b xprssd by[1]: x y z = ( R = R = ( R cosϕ cosϕ sin ϕ + H + H + H cosϕ cosϕ sin ϕ d d d )cosλ )sin λ (4) whr R is th arth radius at point, H, ϕ, λ and ϕ d ar rspctivly th gographic hight, latitud, longitud and gocntric latitud of point. ϕ d and R can b approximatd by[1]: R ϕ = 2 (5) d ϕ + f sin ϕ p = R ( 1 f ) / 1 f (2 f )cosϕ (6) E whr f is th ccntricity and R E th major smi-axis of th arth. With th gographic coordinats of th point known, (x, y, z ) can b calculatd.

Suppos r is th gocntric vctor of, ρ is th vctor from to th satllit, w hav ρ = r r (7) If th componnts of th thr vctors in quation (7) ar xprssd in S, quation (7) can b writtn as: ρ ρ ρ x y z x = y z x y z (8) Th transformation rlation of S and S is[1]: L = L ϕ π / 2) L ( λ ) (9) y ( d z So th componnt array of ρ in S is: T [ ρ ρ ] [ ρ ρ ] T ρ = (10) x y z L x y ρ z Thn th θ E of th satllit can b dtrmind according to quation (3). If θ M is th masking angl, thn th visibility of a satllit rfrncd to ground obsrvr can b spcifid as: visibl if θ M <θ E <90 invisibl if -90 <θ E <θ M And th largr th θ E, th bttr th visibility. Tabl 2 givs th rsults of th visibility statistics according to th almanac at 100 qually spacd points during 24 hours. Th masking angl is takn as 10. Four latituds of 0, 35, 55 and 90 ar considrd. DISCUSSION Ground tracs: th computation shows that th latituds of th substllar points of GLONASS satllits vary from -65.08 to 65.08. Th two tracs in Figur 1 ar for th numbr 1 and numbr 4 satllits in orbit 1. Thy xhibit long standing tim in high latitud ara and rlativly short standing tim in low latitud ara, which mans GLONASS satllits giv bttr covrag at high latitud than mdium and low latitud. Comparing th rsults with thos of GS satllits' shown in Figur 1(b)[2], w can s GS ground tracs stay longr at low and mdium latitud whil shortr at high latitud. Bsids, th GS tracs ar constraind within (-60, 60 ). Obviously GS has bttr covrag in low latitud ara.

Visibility: Th statistical rsults in tabl 2 ar xprssd in th form of histogram as shown in Figur 2. Tabl 2 and Figur 2 show that at 10 masking angl - Th ground obsrvrs can s at last 4 GLONASS satllits at all tim. - Most of th tim th obsrvrs can s at last 5 satllits. Only at 35 latitud, at a small quantity of tim with th probability of 0.15% th usrs s mor than 4 satllits. - Th visibl numbr of th GLONASS satllits incrass with th rising of th latitud. For xampl, th obsrvrs can s mor than 7 satllits 60.29% of th tim at 35 latitud, 98.08% of th tim at 55, and 100% of th tim at 90 latitud. Figur 3 shows th GS visibility statistical rsults at 10 masking angl givn by J.J.Spilkr[2]. Th computational condition is th sam as that of GLONASS. Comparing th two rsults, w can s that: - At 0 latitud, obsrvrs can s at last 7 satllits 90-95% of th tim in GS cas and 75% of th tim in GLONASS cas. And 40% of th tim th obsrvr can s 9 GS satllits and 35% of th tim can s 9 GS satllits, which is much bttr than GLONASS cas. GS visibility is bttr than GLONASS at this latitud. - At 35 latitud, th visibility of GS and GLONASS cas is similar. - At 55 latitud, obsrvrs can s at last 7 satllits 95% of th tim in GLONASS cas, whil 55-60% in GLONASS cas. And mor than half tim obsrvr can s 8 GLONASS satllits. So th visibility of GLONASS is obviously bttr than GLONASS. - At 90 latitud, obsrvrs can s mor than 9 GLONASS satllits with about 50% of th tim. But thy s mor than 9 satllits with 15-20% of th tim. Most of th tim th obsrvr can s at last 8 or 9 GLONASS satllits. GLONASS visibility at this latitud is much bttr than GS. CONCLUSION From th ground tracs and visibility analysis of th abov sction it can b sn that GLONASS constllation has good covrag on th arth. And it has bttr covrag at high latitud. So from th covrag point of viw GLONASS is mor suitabl to b usd by high-latitud nations (such as Russia, Canada, and Australia) and polar aras. This is mainly du to orbit inclination of th two systms (GLONASS has an inclination of 64.8 and GS satllits inclination is 55 ). Combind us of GS and GLONASS will bnfit th usr of dual covrag.

REFERENCES 1. Xiao Ylun, rincipals of spaccraft flight dynamics, Bijing: Astronautic ublishing Hous,1995. 2. J.J. Spilkr Jr., Satllit Constllation and Gomtric Dilution of rcision, in B.W.arkinson, J.J.Spilkr,.Axlrad,.Eng, Global ositioning Systm:Thory and Applications, vol.i, Amrican Institut of Aronautics and Astronautics, Washington, DC, 1996:177-207. Tabl 1 GLONASS almanc data on March 4 1996 alm prig EL cc incl ET day chn T p st 1-155.97-75.26 0.00063 65.08 11076.47 64 23 40543.93 1 OK 2-166.26-95.50 0.00058 65.09 15888.06 64 5 40543.86 1 OK 3-169.76-116.84 0.00286 65.02 21009.62 64 21 40543.86 1 OK 4-52.70-138.32 0.00030 65.00 26148.03 64 12 40543.96 1 OK 5-81.79-167.59 0.00090 65.13 33256.06 64 23 40544.56 1 OK 6-34.96 179.71 0.00131 65.01 36196.16 64 13 40543.92 1 OK 7-174.40-32.08 0.00094 65.11 708.94 64 21 40543.91 1 OK 8 17.87-51.37 0.00171 65.08 5356.44 64 2 40543.54 1 OK 9 167.50 52.22 0.00064 64.82 9166.44 64 6 40544.12 2 OK 10 165.70 31.04 0.00177 64.84 14251.72 64 9 40544.10 2 OK 11 158.91 9.95 0.00374 64.84 19298.97 64 4 40544.04 2 OK 12 123.98-11.45 0.00093 64.78 24454.41 64 22 40544.11 2 OK 13-25.18-32.53 0.00175 64.84 29447.53 64 6 40544.12 2 OK 14 54.40-53.50 0.00030 64.77 34522.81 64 9 40544.05 2 OK 15 155.43-74.51 0.00190 64.83 39512.69 64 4 40543.98 2 OK 16 2.03 73.58 0.00153 64.77 4113.50 64 22 40544.06 2 OK 17 153.78 179.58 0.00039 64.71 7440.72 64 24 40544.02 3 OK 18 38.72 158.15 0.00136 64.69 12570.62 64 10 40544.11 3 OK 19-167.67 137.32 0.00102 64.72 17623.75 64 3 40544.02 3 OK 20-160.96 116.24 0.00031 64.72 22664.12 64 1 40543.99 3 OK 21-14.05 93.75 0.00083 64.83 27900.00 64 24 40544.09 3 OK 22-9.03 73.59 0.00067 64.71 32872.94 64 10 40544.18 3 OK 23-159.65 52.57 0.00267 64.70 37836.34 64 3 40543.99 3 OK 24-40.94-159.41 0.00033 64.82 2323.06 64 1 40543.97 3 OK Tabl 2 Visibility statistical data of GLONASS satllits numbr 4 5 6 7 8 9 10 11 Man robability (%), M=10 numbr 0 0 1.4235 23.5283 62.6136 11.6815 0.6612 0.0918 0 6.8690 35.1469 7.3435 32.2196 19.5337 35.6159 4.9569 0.1836 0 6.9870 55 0 0 1.9160 24.8124 55.8199 16.8130 0.6387 0 7.8945 90 0 0 0 1.6509 48.1132 46.6981 3.5377 0 8.5212 latitud

50 0-50 -150-100 -50 0 50 100 150 Figur 1(a) Ground tracs of Numbr 1 and 4 GLONASS satllits in orbit 1 90 60 30 0-30 -60-90 Figur1 (b) Ground tracs of two GS satllits a) 0 b) 35 c) 55 d) 90 Figur 2. Visibility statistics of GLONASS constllation

Figur 3 Visibility statistics of GS constllation