Accuracy requirements in position and attitude for airborne vector gravimetry and gradiometry

Abstract

Airborne measurements of the gravitation vector and its gradients require auxiliary measurements of position and attitude, not just for registration (geolocation) purposes, but also to separate gravitational from kinematic accelerations (and gradients) according to the principle of equivalence. Very precise positioning is needed to compute accelerations by numerical differentiation, and very accurate angular rates are needed to compute orientation (by integration) and angular acceleration (by differentiation). GPS positioning and gyro data can be used for these purposes, but limits in accuracy of current technology thus also constrain the useful performance of the principal gravimetric sensors. This paper reviews the theory of airborne gravimetry and gradiometry, the sensitivities of various components of the gravitation vector, and the gradient tensor to position and attitude (rate) errors. Generally, one may conclude that scalar gravimetry and vector gravimetry are limited by orientation error coupled to the acceleration environment of the vehicle, as well as positioning (i.e., kinematic acceleration) uncertainty, while gradiometry depends, instead, on very precise angular rates of the measurement frame. The necessary error tradeoff between future developments in gradiometers and gyro technology is thereby also illustrated and shows that present gyro technology is sufficient to meet requirements for existing airborne gradiometers, but requires improvement for future gradient sensors.