A framework for modelling kinematic measurements in gravity field applications

The determination of the local gravity field from sensors mounted in a fixed wing aircraft has long been a dream of geodesists and geophysicists. The progress in sensor technology during the last decade has brought its realization within reach and recent tests indicate that results at the level of a fewmGal are possible. To assess different sensor configurations and their effect on the resolution of the gravity field spectrum, a state model for motion in the gravity field of the earth is formulated. The resulting set of differential equations can accommodate first and second order gravity gradients, specific force, kinematic acceleration, vehicle velocity and position as input. It offers therefore a rather general framework for gravity field determination from a variety of kinematic sensors, such as gravity meters, gravity gradiometers, inertial systems, differentialGPS, laser altimeters and others. The derivation of the basic kinematic model and its linearization are given in detail, while sensor error models are discussed in a generic way. A few remarks on the modelling of gravity gradiometer measurements conclude the paper.