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.