Assisted Natural Reentry (ANR) is a semi-controlled deorbiting strategy that allows satellites with limited thrust capabilities to perform a targeted reentry to reduce the risk of casualty on ground. This strategy starts with a progressively controlled descent to bring the satellite to an elliptical interface orbit with a very low perigee (~130km) using both its propulsion system at apogee and drag force at perigee. This descent phase is followed by a short uncontrolled reentry within only a few revolutions thanks to the very low perigee. This limits the uncertainty on the debris fallback area and allows to target unpopulated regions, reducing the risk of casualties on ground. This strategy is, thus, an alternative to controlled reentry, more accurate but requiring high thrust capabilities, for satellites that would not meet the casualty risk requirements with a fully uncontrolled reentry. 

For satellites with low thrust propulsion, the controlled descent of the ANR can last several months, most of which are spent in an elliptical Very Low Earth Orbit. At each passage at perigee the satellite is subjected to a very high drag force. Thus,  the variations of the drag acceleration due to modeling errors and atmosphere variations will deviate the satellites from its nominal descent trajectory. However, to satisfy the casualty risk requirement, the target interface orbit must be reached with a specified error covariance. Thus, a robust guidance is needed to compensate for trajectory deviations and ensure that the satellite reaches the target interface orbit with sufficient accuracy. In addition, due to the long duration of the low-thrust ANR, the satellite should be able to correct its trajectory autonomously to reduce the burden on the ground segment. 

This paper presents a robust guidance scheme for the controlled descent of the ANR, with on-board estimation and prediction of atmosphere density variations. Density variations are modeled as a time-correlated stochastic process, and this model is tuned and validated with atmosphere simulations. The guidance estimates both the satellite state error and density variations using the output of an on-board navigation system and is thus independent from external inputs. The robust guidance control that achieves the specified error covariance is obtained by solving a covariance control problem where predicted density mean value and covariance are derived from the modeled stochastic process. This guidance scheme allows the satellite to autonomously detect atmosphere variations relative to the nominal model and adapt its trajectory in consequence. Finally, an analysis of the navigation and control capabilities required to achieve the specified accuracy with this guidance scheme is proposed.