Satellite Orbit and Ephemeris Determination using Inter Satellite Links

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Orbit ComputationInter Satellite LinksThe so called broadcast ephemeris message contain the actual parameters of an orbit model,which is accurate enough over a short period of validity. The parameter model is designed in away that it represents only the desired orbit class with a sufficient accuracy over the period ofvalidity, using only modest computation power. There are various possible models suited forthe broadcast ephemeris message, but they all share some common characteristics:• The state prediction requires no other information than included in the navigationmessage, or constants which are permanently stored in the receiver and need not to beupdated.• The user-receiver has to compute the positions of maybe up to 12 satellites. It is obviousthat this should require only modest computational effort. That means, the statecalculation has to be done using a geometric model(like the GPS broadcast ephemeris) orthe numerical integration of a state vector (like the GLONASS broadcast ephemeris) usinga simple force model.• The ephemeris are given in Earth centred Earth fixed co-ordinates. Otherwise the userwould have to compute all the earth rotation parameters (precession, nutation, polarmotion, sidereal time).The broadcast ephemeris are not derived directly from measurements. From the orbitdetermination process, the satellites state as well as some physical parameters have beendetermined to a certain accuracy. This information is used to extrapolate the satellites statevector. The computed satellite positions have to be converted into the earth centred earth fixedcoordinate frame. The parameters of that simple, earth fixed broadcast ephemeris model areadjusted using a least squares estimator so that the position difference between the preciseephemeris and the broadcast ephemeris becomes minimal over that fit interval. It is obviousthat the derived broadcast ephemeris is only optimal and therefore valid for that specified fitinterval.Both navigation satellite systems (GPS and GLONASS) provide an additional format of orbitrepresentation, the almanac. This is an even more simple orbit description, fit over a longerinterval, typically a week. This orbit propagator is only for visibility evaluations, thereforeaccuracy lies in the range of several kilometers. Both almanac types consist of a Keplerianorbit including the secular perturbation due to earth's oblateness.In the following section, an overview over a few broadcast models is given, to show thevariety of orbit representation possibilities.Page 62R. Wolf
Inter Satellite LinksOrbit Computation4.4.1 GLONASS Broadcast EphemerisThe GLONASS navigation message consists, besides some other information, of 9 ephemerisstates:x Position in Cartesian ECEF coordinates0, y0, z0x Velocity in Cartesian ECEF coordinates0, y0, z0D xRe s, DD yRe s, DzRe sResidual acceleration over the fit interval, mainly due to lunisolarattraction, in Cartesian ECEF coordinatest 0Reference time of ephemerisA broadcast message as described above, requires a very simple force model, referenced inthe earth fixed frame, which accounts for the following components:• central force of earth's gravity• dynamic oblateness represented by the C 20 coefficient• centripetal acceleration introduced by the rotating reference frame• Coriolis acceleration introduced by the rotating reference frameThe simplified equations of motion expressed bydxdtdydtdzdtdxDdtdyDdtdzDdt= xD= yD= zD=µ223e z−2x3 + C20x 1 5 ωex 2ω2ey5r 2 r⎜r⎟ + + D +⎝ ⎠22µ 3 GMae⎛ z ⎞= −2y C3 +20y 1 5 ω52 ey 2ωexDr 2 r⎜ −r⎟ + − +⎝ ⎠22µ 3 GMae⎛ z ⎞= − z C3 +20z⎜35 ⎟+5 −2r2GMar⎛ −⎜⎝r⎞⎟⎠DD xDD yDD zResResResEq. 4.4-1with− −ω e = 7. 292115⋅10 5 s 1 Angular velocity of Earth's rotationR. Wolf Page 63
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Satellite Orbit and EphemerisDeterm
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Inter Satellite LinksAbstractGlobal
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Inter Satellite LinksTable of Conte
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Inter Satellite Links6.2.2 IGSO WAL
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Inter Satellite LinksIntroduction1
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Inter Satellite LinksState Estimati
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State EstimationInter Satellite Lin
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Simulations and ResultsInter Satell
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Satellite Orbit and Ephemeris Determination using Inter Satellite Links

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