Regulations impose that satellites in low Earth orbit must be deorbited after their mission lifetime to limit the proliferation of space debris, and that the probability of falling debris causing at least one ground casualty must be below 10^-4. Methods are thus needed to evaluate the area of debris fallout and compute the casualty risk, and to choose a reentry trajectory for which the risk is within the regulatory threshold. 

In the case of a fully uncontrolled natural reentry, the area of debris fallout cannot be chosen nor predicted because the uncertainty on the drag force, and the risk computation is thus straightforward as it only depends on the orbit inclination and the casualty area of surviving debris. In the case of a controlled reentry, a high delta-V maneuver is used to set the satellite on an elliptical orbit with a perigee low enough (< 80km) for a reentry within one orbit. The area of debris fallout is then small enough to fit in low-risk regions such as the South Pacific Ocean Uninhabited Area. 

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. A progressive controlled descent brings the satellite to an elliptical interface orbit with a very low perigee (~130 km), from which the satellite quickly reenters into the atmosphere after a few revolutions. While the short reentry time limits the accumulated uncertainty from drag, it is not as accurate as a controlled reentry and the resulting debris fallout area is a long and narrow band that can wrap a few times around the Earth, much like a satellite ground track. To find an interface orbit compliant with the casualty risk requirement, the casualty risk must be evaluated for many candidate orbits. The classical approach for computing the casualty risk involves computationally expensive Monte-Carlo simulations, and a more efficient approach is thus needed to efficiently explore interface orbit configurations. 

This paper presents a method for efficiently computing the casualty risk from a low altitude interface orbit and applies this method to find an ANR interface orbit compliant with the casualty risk requirements. Taking advantage of the fact that the fallout area is mostly spread along the satellite ground track, a coordinate system is proposed in which the fallout area can be accurately approximated with a gaussian distribution. The initial covariance at the interface orbit is then propagated in this coordinate system using unscented transform until the satellite reaches an altitude of 80 km, just before fragmentation occurs. Fragmentation and ablation are simulated once with a specialized tool to obtain the surviving debris spreading and casualty area, which are then assumed to be identical across all the fallout area. Finally, the casualty risk is integrated over the fallout area using population data. The casualty risk computed with this method is validated against Monte-Carlo simulations and the computation time between both methods is compared. The unscented transform approach limits the number of points required to compute the fallout area to 2N+1, where N is the number of uncertain parameters, and is thus much faster than the Monte-Carlo. The unscented transform is then used to efficiently explore and find elliptical interface orbits for the Assisted Natural Reentry compliant with casualty risk requirements.