This paper focuses on the estimation of the aircraft mass in ground-based applications. Mass is a key parameter for climb prediction. It is currently not available to groundbased trajectory predictors because it is considered a competitive parameter by many airlines. There is hope that the aircraft mass might become widely available someday, but in the meantime it is possible to estimate an equivalent mass from the data already available, assuming the thrust to be known (maximum or reduced climb thrust for example). In this paper, we compare the performances of two mass estimation methods proposed in recent publications. Both methods estimate the aircraft mass by fitting the modeled energy rate (i.e. the power of the forces acting on the aircraft) with the energy rate observed at several points of the past trajectory. The first method, proposed by Schultz et al. ([1]), dynamically adjusts the weight parameter so as to fit the energy rate, using an adaptive sensitivity parameter to weight each observation. The second method, introduced in one of our previous publications ([2]), estimates the mass by minimizing the quadratic error on the observed energy rate, taking advantage of the polynomial expression of the modeled power when using the BADA model. The robustness of both methods to the observation errors is assessed, using simulated data with various distributions of the noise added to the observed state variables. The results show that both methods are able to find mass estimates that are very close to the "actual" mass, with slightly better performances for the least squares method.