Probabilistic orbit solutions in GNSS

We discuss a concept of probabilistic orbit. If correctly constructed, an ensemble of equally plausible orbits is a proper representation of the underlying true and unknown probability distribution of orbits. Hence, the probabilistic orbit is determined by the entire sample and its statistical properties rather than any individual ensemble member. We explore the concept by starting from an ensemble of atmospheric state estimates generated at ECMWF (N=51). The ensemble mean closely corresponds to the most likely atmospheric state estimate, and the ensemble spread to its inherent uncertainty. We compute separately a GNSS orbit solution for each unique atmospheric state (N=51). Thus, we essentially sample one uncertain information source the GNSS orbits are known to be sensitive for. Thereby, uncertainty in the atmospheric state estimate is explicitly propagated to the ensemble of orbit solutions. The concept leads to interesting corollaries. Precise point positioning using the probabilistic orbit, for instance, becomes probabilistic, too.