Satellite Orbit and Ephemeris Determination using Inter Satellite Links

Orbit ComputationInter Satellite Linksthe satellite, as can be seen from the figure. Although the along track error seems to have asecular trend, the approximately quadratic trend is only the ascending branch of a sine wave,with the major semi axis being the amplitude. This isn't very surprising due to the fact that theequations of motion are described by a second order differential equation.400300RadialAlong TrackCross TrackOrbit Error [m]200100020:52:30.000 05:12:30.000 13:32:30.000UTC [hours:minutes:seconds]Figure 4-1 Prediction Error of LEO 1250 km with 15 x 15 GeopotentialThe following tables show the evaluations of the orbit errors induced by successivelyneglecting more higher order harmonics down to a pure spherical gravity field, as well as acomparison to other gravity models. The gravity model "deviated JGM-3" has been obtainedby adding to a coefficient the one sigma value of that coefficients uncertainty times a normaldistributed random number with zero mean and variance one.Table 4-5 shows the orbit error after one day for the LEO satellite. The neglecting ofharmonics above 30 causes an error of the same order of magnitude as the uncertainties of thegravity model, represented by "deviated JGM-3". The differences to other gravity models(besides GEM-T3) are higher, but JGM-3 can be regarded as the state of the art gravitymodel. Comparison to the Kepler orbit shows a large error. For precise orbit determination,even for short time prediction with frequent measurement updates, a model considering lessthan degree and order 30 x 30 is not acceptable.Table 4-6 shows the orbit error after shorter prediction period of 6 hours. Here, neglectingharmonics above 50's degree and order causes only small but noticeable orbit errors. But theyare far below the model uncertainties.Page 40R. Wolf