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The Basic Principles of the GOCE Gradiometer In-Flight Calibration

Daniel Lamarre(1)

(1) ESA, Keplerlaan 1, 2201 AZ Noordwijk, Netherlands


The GOCE gradiometer is comprised of six accelerometers arranged in 3 pairs, mounted in the so-called ‘diamond’ configuration. To achieve the required accuracy in the retrieval of the diagonal terms of the gravity gradient, a nominally performing gradiometer requires two characterization operations to be done in flight:

1) Measurement of the quadratic factor of the response of each accelerometer, & 2) Measurement of relative misalignments and scale factors between accelerometers

1) The working principle of the GOCE accelerometers is based on a levitating proof mass maintained at a constant position in the accelerometer reference frame, by application of forces through electrostatic actuators. The voltages applied by the control loops then constitute the outputs and are related to the accelerations experienced by the proof mass in a nearly linear manner. However, second order terms due to manufacturing dissimilarities are not negligible and need to be measured (and then adjusted physically to be minimized). The innovation in the measurement of the quadratic factor consists in the introduction of a train of pulses inside the control loop of each accelerometer. These pulses can be seen as a modulated carrier. The frequency of modulation rests within the control bandwidth of the accelerometer, while the carrier frequency lies outside. The result is a beat appearing at the accelerometer output, which frequency follows the pulse rate, and which amplitude is proportional to the quadratic factor. 2) The main objective of the gradiometer calibration is to reject common mode accelerations. This translates into the need to determine with high accuracy the relative responses and misalignments of accelerometers between themselves, rather than their common characteristics. To achieve this, it is not necessary to apply known accelerations to the gradiometer, since the main goal is to null the common signal contributions in the gravity gradient measurements. This principle is the basis of this innovative calibration where pseudo-random linear and angular accelerations are applied to the spacecraft through simple on/off cold gas thrusters. Through an empirical iterative algorithm, only the signals from the gradiometer itself and the star tracker are used to retrieve the gradiometer parameters.


Workshop presentation

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry