Linear covariance analysis of atmospheric entry for sample return mission

Linear covariance analysis is an uncertainty analysis tool comparable to Monte Carlo analysis; both provide similar statistical information about the performance and uncertainties of a dynamic system. Linear covariance analysis linearizes the models of a dynamic system and propagates the state uncertainties alongside a reference trajectory. These uncertainties are similar to those computed from post processing a Monte Carlo analysis and require potentially significantly fewer computational resources. A comparison of the two analyses is performed on an example sample return atmospheric entry mission. The example mission is an unguided entry vehicle similar to the Stardust Sample Return Mission. Flight dynamics for entry are modeled with the three-degree-of-freedom translational equations of motion. Uncertainty in vehicle, environmental, and mission design parameters are included to determine expected flight performance. In the analysis, linear covariance results match Monte Carlo within 4% in determining the state uncertainties over the trajectory,while requiring only 0.48% the computational effort relative to Monte Carlo analysis. Further analysis using linear covariance shows that uncertainty in position is the largest contributor to state dispersions. The final state dispersion is highly sensitive to uncertainty in initial position. Comparatively uncertainty in initial velocity contributes much less to the final state dispersion and is insensitive. Varying the initial position dispersion by ±50% results in the largest changes in the 3−σ uncertainty in the altitude at parachute deploy which ranges from 995 m to 2076 m compared to the nominal 1495 m uncertainty