  In this paper, we consider the problem of precise attitude control for
geodetic missions, such as the GRACE Follow-on (GRACE-FO) mission. Traditional
and well-established control methods, such as Proportional-Integral-Derivative
(PID) controllers, have been the standard in attitude control for most space
missions, including the GRACE-FO mission. Instead of significantly modifying
(or replacing) the original PID controllers that are being used for these
missions, we introduce an iterative modification to the PID controller that
ensures improved attitude control precision (i.e., reduction in attitude
error). The proposed modification leverages Gated Recurrent Units (GRU) to
learn and predict external disturbance trends derived from incoming attitude
measurements from the GRACE satellites. Our analysis has revealed a distinct
trend in the external disturbance time-series data, suggesting the potential
utility of GRU's to predict future disturbances acting on the system. The
learned GRU model compensates for these disturbances within the standard PID
control loop in real time via an additive correction term which is updated at
regular time intervals. The simulation results verify the significant reduction
in attitude error, verifying the efficacy of our proposed approach.
