Satellite Orbit and Ephemeris Determination using Inter Satellite Links

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