On the error of a GPS baseline in a local Datum

The expression of the error committed when using GPS differential positioning directly within a local Datum (with no application of transformation formulas between the geodetic systems involved) is given. That error is considered both in cartesian and ellipsoidal coordinates and in the latter case it is shown, using covariant derivative, that it includes also a non-negligible term due to curvature induced in space by this kind of coordinates.