Satellite Orbit and Ephemeris Determination using Inter Satellite Links

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Orbit ComputationInter Satellite LinksNumber of Function Evaluations [-]180001600014000120001000080006000400020000RK4_NfABM4_NfABM8_Nf0 10000 20000 30000 40000 50000Orbit Altitude [km]Figure 4-14 Number of Function Evaluations vs. Orbit AltitudeThe "sawtooth" figure results from the fact that the number of function evaluations is halvedwhen the step width is doubled. It can be seen that the 4 th order Runge-Kutta method requiresabout double the number function evaluations than the 4 th order Adams-Bashford-Moultonmethod. This is also not surprising, due to the fact that The Runge-Kutta requires for eachstep 4 function evaluations, and the Adams-Bashford-Moulton only two, regardless of theorder.Page 60R. Wolf
Inter Satellite LinksOrbit Computation0.050.04RK4_dxABM4_dxABM8_dxAbsolut Error [m]0.030.020.010.000 10000 20000 30000 40000 50000Orbit Altitude [km]Figure 4-15 Absolute Error vs. Orbit AltitudeFigure 4-15 Absolute Error vs. Orbit Altitude shows the absolute position error after onerevolution. A surprising result is that the position error is nearly independent from the methodused but depends linear on orbit altitude. However, this is only true if the optimum step widthhas been applied.Another intresting fact is that the absolute error is not bounded by the local error, which iskept constant at 1 cm. Thus, it can be said that the numerical accuracy is not the primarydriver for the choice of the integration method. If long arcs have to be integrated without adiscontinuing change in acceleration (e.g. thruster firing), one would choose a high ordermultistep method to save computation time. If only short arcs are processed, e.g. because theephemeris data is needed every 10, 30 or 60 seconds, lower order algorithms are sufficient.Furthermore one has to keep in mind that mulistep methods need a starter calculation from aone-step method. When the orbit integration has to be reinitiated frequently, e.g. because oforbit manoeuvres (discontinuity in acceleration) or trajectory corrections from the stateestimation process, the Runge-Kutta method will be in operation most of the time.4.4 Precise Short Term Orbit RepresentationIn satellite navigation, the position of a satellite is required with a certain accuracy rangingfrom a few meters down to decimeter level. To achieve such an accuracy over a long time, asophisticated orbit model is required, as has been shown in the preceding sections.Unfortunately, a user receiver is not equipped with a super computing facility, thus a simplerorbit representation is required.R. Wolf Page 61
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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 LinksList of Figure
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Inter Satellite LinksFigure 6-38 Tr
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Inter Satellite LinksList of Tables
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Inter Satellite LinksJ2Earths Oblat
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Inter Satellite LinksIntroduction1
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Inter Satellite LinksIntroductionGE
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Inter Satellite LinksISL Observatio
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Inter Satellite LinksState Estimati
Page 26 and 27: State EstimationInter Satellite Lin
Page 36 and 37: Orbit ComputationInter Satellite Li
Page 86 and 87: Software DescriptionInter Satellite
Page 108 and 109: Simulations and ResultsInter Satell
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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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