The effect of stochastic gravity models in airborne vector gravimetry

Abstract

Measurements of specific force using inertial measurement units (IMU) combined with Global Positioning System (GPS) accelerometry can be used on an airborne platform to determine the total gravitational vector. Traditional methods, originating with inertial surveying systems and based on Kalman filtering, rely on choosing an appropriate stochastic model for the gravity disturbance components included in the set of system error states. An alternative procedure that uses no a priori stochastic model has proven to be as effective, or moreso, in extracting the gravity vector from airborne IMU/GPS data. This method is based on inspecting acceleration residuals from a Kalman filter that estimates only sensor biases. Using actual data collected over the Canadian Rocky Mountains, this method was compared to the traditional approach adapted for different types of stochastic models for the gravity disturbance vector. In all test cases, the estimation filter without a gravitational model yielded better results—up to 50%. This implies that accurate gravity vector determination from airborne IMU/GPS need not rely on an a priori stochastic model of the field, even though the theory of optimal estimation requests it. However, no filter was able to remove all systematic errors from the data; these remaining errors could only be reduced by elementary methods such as endpoint matching and correlative processing of adjacent passes of the system over the gravity field. The final, best gravity estimates had standard deviations with respect to control data of 6 mGal in the horizontal components and 3–4 mGal in the vertical component.