Efficient Stochastic Orbit Modeling Techniques using Least Squares Estimators

Reduced-dynamic orbit determination for spaceborne GPS receivers of low Earth orbiting satellites is a successful method promising highest precision. We review the principles of (reduced) dynamic orbit determination and develop the mathematical background for different efficient stochastic orbit parametrizations (e.g., piecewise constant accelerations which provide not only continuous but also differentiable orbits) using least squares methods. Simulated as well as real data from the CHAMP GPS receiver show, to some extent, the equivalence of the different parametrizations and reveal the impressive performance of stochastic orbit modeling techniques. Independent comparisons with orbits determined by other groups and validations with SLR measurements show that our orbits are of high quality.