Three-dimensional position-error modeling

Extend the planar position-uncertainty model for distributed satellite apertures to three-dimensional satellite position errors, accounting for the projection of the position error onto the propagation direction and its resulting phase perturbation.

Background

The adopted error model restricts satellite position uncertainties to the swarm plane, consistent with the planar aperture considered throughout the paper. The paper notes that a three-dimensional extension is conceptually straightforward because the resulting phase error depends on the projection of the position error onto the propagation direction, but this extension is not developed.

References

Extending the model to three-dimensional position errors is straightforward, as the resulting phase perturbation depends on the projection of the position error onto the propagation direction. Such an extension is left for future work.

— Satellite Swarms for Direct-to-Cell Networks: A Distribution-Performance Trade-off Analysis  (2609.01380 - Artiga et al., 1 Sep 2026) in Section VI, Positioning and synchronization errors