Computational errors and their control in the determination of satellite orbits

Numerical integration errors are caused by a polynomial approximation of a nonlinear function and by the use of finite computer word length. 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. To reduce the problem of numerical integration error in the orbit determination process, certain techniques may be employed. One option to reduce integration error is the use of an increased computer word size in the computations; another is to employ techniques which do not require a change in the computer word size. The techniques under investigation 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 numberical integration error, and the modification of the integration process to reduce the errors caused by discontinuities in the force model with emphasis on the force due to solar radiation pressure. It is indicated that the effect of numerical integration error on the batch estimation process can be reduced significantly, and provide for convergence in fewer iterations with a smaller contribution to the overall error. Numerical integration error may be reduced with only a fraction of the cost compared to increasing the computer word size.