Orbit error estimation in the presence of force model errors
Abstract
The analysis and control of a loworbit Earthsatellite mission needs reliable and reasonably good data of satellite ephemerides. But various types of force model errors affect the lowaltitude artificial satellite ephemerides generated by longterm orbit propagation procedures. Predominant among them are the errors in modeling the terrestrial gravitational force. Treating the geopotential model error, one of the aims of this work is to extend the equations of motion and the orbit error covariance function, derived for circular orbits previously, to elliptical orbits, and to propose a methodology to be adopted for estimating orbit errors in the case of elliptical orbit propagations. The whole theory and mathematical development for elliptical orbits is explained here in detail. Considering the model errors caused by incorrect truncation of gravity field, the other aim of this work is to extend the stochastic procedure, developed previously to evaluate the order of magnitude of the accumulated global error in shortterm circular orbit propagations, to longterm circular orbit propagations. Here, the statistical estimates of uncertainties in orbital elements are obtained in terms of their covariances. After testing the theory developed with some simple examples, it is applied to a satellite with the orbital configuration similar to that of the first Brazilian satellite, launched on 9th February 1993. The results obtained here have been analyzed in detail in order to check the validity of the theory developed.
 Publication:

NASA STI/Recon Technical Report A
 Pub Date:
 1993
 Bibcode:
 1993STIA...9585721R
 Keywords:

 Covariance;
 Earth Gravitation;
 Ephemerides;
 Equations Of Motion;
 Error Analysis;
 Low Earth Orbits;
 Mathematical Models;
 Orbital Position Estimation;
 Brazilian Space Program;
 Loads (Forces);
 Mission Planning;
 Space Communications, Spacecraft Communications, Command and Tracking