COMPUTATIONAL ERRORS AND THEIR CONTROL IN THE DETERMINATION OF SATELLITE ORBITS (NUMERICAL INTEGRATION, SOLAR, RADIATION PRESSURE)

One of the major sources of error in the precision orbit determination process is caused by the numerical integration process. Numerical integration errors are caused by a polynomial approximation of a nonlinear function (truncation error) and by the use of a finite computer word length (roundoff error). Numerical integration errors may be expected to grow in a nearly quadratic or exponential manner for the satellite problem, and they become severe for long orbital trajectories.;The application of these techniques indicate that the effect of numerical integration error on the batch estimation process can be reduced significantly, particularly for long orbital arcs, and provide for convergence in fewer iterations with a smaller contribuiton to the overall error. With these techniques, numerical integration errror may be significantly reduced with only a fraction of the cost compared to increasing the computer word size.;To reduce the problem of numerical integration error in the orbit determination process, certain techniques may be employed. One option to reduce integration error would be to use an increased computer word size in the computations; however, this option may be unacceptable due to increases in computer costs or limitations due to hardware or software considerations. Another course of action to reduce integration errors is to employ techniques which do not require a change in the computer word size. The techniques under investigation in this research were the use of the Encke method that reformulates the differential equations to reduce roundoff error, the use of empirical model parameters to compensate for some of the numerical integration error, and the modification of the integration process to reduce the errors caused by discontinuities (actual or perceived) in the force model with emphasis on the force due to solar radiation pressure.