A Local Least-Squares Modification of Stokes’ Formula

The combination of Stokes’ formula and an Earth Gravity Model (EGM) for geoid determination has become a standard procedure. However, the way of modifying Stokes’ formula vary from author to author, and numerous methods of modification exist. Most methods are deterministic, with the primary goal of reducing the truncation bias committed by limiting the area of Stokes’ integration around the computation point, but there are also some stochastic methods with the explicit goal to reduce the global mean square error of the geoid height estimator stemming from the truncation bias as well as the random errors of the EGM and the gravity data. The latter estimators are thus, at least from a theoretical point of view, optimal in a global mean sense, but in a local sense they may be far from optimality.