Efficient semi-analytic integration of GNSS orbits under tesseral effects

• Reformulation of the relegation algorithm for the case of the Geopotential.
• Allows for partial simplification in the case of tesseral resonances.
• Efficient simplification in the case of classical GNSS satellites.

The algebra underlying the elimination of the parallax transformation is known to be useful in relegating short-period effects due to tesseral harmonics of the Geopotential. In the case of low-eccentricity orbits, a judicious selection of the generating function of the relegation algorithm allows for a straightforward simplification. Application to low-eccentricity orbits in the medium Earth orbits region illustrates the benefits of the relegation approach.