Thermal Protection System (TPS) is required to shield an atmospheric entry vehicle against the high surface heating environment experienced during hypersonic flight. There are significant uncertainties in the tools and models currently used for the prediction of entry aeroheating and TPS material thermal response. These uncertainties can be reduced using experimental data. Analysis of TPS ground and flight data has been traditionally performed in a direct fashion. Direct analyses center upon comparison of the computational model predictions to data. Qualitative conclusions about model validity may be drawn based on this comparison and a limited number of model parameters may be iteratively adjusted to obtain a better match between predictions and data. The goal of this thesis is to develop a more rigorous methodology for the estimation of surface heating and TPS material response using inverse estimation theory. Built on theoretical developments made in related fields, this methodology enables the estimation of uncertainties in both the aeroheating environment and material properties from experimental temperature data. Unlike direct methods, the methodology developed here is capable of estimating a large number of independent parameters simultaneously and reconstructing the time-dependent surface heating profile in an automated fashion. This methodology is applied to flight data obtained from thermocouples embedded in the Mars Pathfinder and Mars Science Laboratory entry vehicle heatshields.