Propagation and Reconstruction of Reentry Uncertainties Using Continuity Equation and Simplicial Interpolation

Abstract

This Paper proposes a continuum-based approach for the propagation of uncertainties in the initial conditions and parameters for the analysis and prediction of spacecraft reentries. Using the continuity equation together with the reentry dynamics, the joint probability distribution of the uncertainties is propagated in time for specific sampled points. At each time instant, the joint probability distribution function is then reconstructed from the scattered data using a gradient-enhanced linear interpolation based on a simplicial representation of the state space. Uncertainties in the initial conditions at reentry and in the ballistic coefficient for three representative test cases are considered: a three-state and a six-state steep Earth reentry and a six-state unguided lifting entry at Mars. The Paper shows the comparison of the proposed method with Monte Carlo–based techniques in terms of quality of the obtained marginal distributions and runtime as a function of the number of samples used.