Echo state network-based data recovery method for low-low satellite-to-satellite tracking missions in laser interferometry

As a follow-on mission to the GRACE low-low satellite-to-satellite tracking gravity mission, one of the twin satellites of laser ranging interferometer gravity mission GRACE Follow-On experienced an anomaly in its accelerometer payload after one month of operation. This anomaly resulted in the loss of scientific measurement data, a situation similar to the final phase of the GRACE. Therefore, research on accelerometer data recovery is important to achieve the detection objectives of both GRACE and GRACE Follow-On. This paper proposes a novel method for accelerometer data recovery and reconstruction based on the Echo State Network in machine learning. By constructing a mapping relationship of accelerometer data between the twin satellites using the Echo State Network and improving the network performance through Bayesian optimization, this method can achieve high-precision and high-efficiency reconstruction of missing accelerometer data. Through experimental comparison with measured data, in the frequency band of gravity field detection, the prediction results in the along-track and radial directions have been shown to reach the level of $ {10}^{-8} $ m∙s⁻²/$ \sqrt{H\textit{z}} $. In the cross-track direction, the results reach levels between $ {10}^{-8}$ m∙s⁻²/$ \sqrt{H\textit{z}} $~${10}^{-7} $ m∙s⁻²/$\sqrt{H\textit{z}} $. This reconstruction accuracy is comparable to, or even partially superior to, the official GRACE data transplant accuracy, making it preliminarily applicable to gravity field inversion. This research achieves high-precision accelerometer data recovery for low-low satellite-to-satellite tracking missions using machine learning methods.