A matched filter approach for the calibration of GRACE and GRACE-FO accelerometers.

For the accurate determination of the gravity field of the Earth, the accelerometers on board GRACE and GRACE-FO missions need to be calibrated, which is a rather challenging task. In many gravitational field studies, the bias and scale factors are introduced, among others, as unknown parameters in the gravity field recovery process and are estimated concurrently with the gravity field parameters. In other studies, the calibration method makes use of modeled accelerometer data, and the parameters are estimated in a least squares adjustment.  Depending on the calibration process, the scale factors and biases may vary significantly. In this study, an alternative calibration method is followed using the matched filter method. This method is widely used in radar applications for scattered signal detection purposes since it maximizes the signal-to-noise ratio. The idea behind this method is that a known signal is transmitted out and the reflected signal is compared to the known transmitted signal. This allows the proposed method to be based only on the satellite measurements.  In this study, the total accelerations of the satellite derived from the GPS positions, play the role of the transmitted signal that contains both the gravitational and the non-gravitational accelerations. The penumbra transitions, which appear as jumps (offsets) of very short duration in the accelerometer measurements, are used as the known calibration pulses that need to be detected in the transmitted signal. The process of matching (focusing) the penumbra transition pulse on the GPS accelerations is presented step by step and as a result, 30 daily scale factors are calculated for both missions during different periods of solar activity. The biases of the instrument are calculated daily using a second order polynomial fit. The scale factor and the biases appear to be correlated with the β’ angle variations (the angle that indicates when the satellite is in a full sun orbit). The scale factors of the cross-track component in both missions show the largest variations, since the y-axis of the accelerometer is the least sensitive, while the scale factors in the x-axis show the largest sensitivity due to thermal variations in the atmosphere . The performance of the calibration parameters during high and low solar activity is examined and evaluated.