The X-ray Integral Field Unit (X-IFU) onboard the future European X-ray telescope Athena will be the first space instrument carrying an array of more than a thousand transition edge sensors. One of the key challenges of the X-IFU is the measurement of narrow X-ray atomic lines to determine velocity shifts at an unprecedented level of accuracy. For this reason, the energy scale of the instrument needs to be known with extreme accuracy, of 0.4 eV (1 \(\sigma\) ) up to 7 keV. The energy scale will be measured on the ground through a dedicated calibration campaign using fiducial X-ray sources. Though calibrated, the energy scale is extremely sensitive to the environmental conditions around the TES array, and drifts in the readout chain electronics. Uncorrected, the energy scale can naturally drift up to hundreds of eVs. Changes of the TES gain will be monitored via onboard X-ray calibration sources, and the energy scale will be corrected either per pixel, or within a small groups of pixels. Although simulations show that a 0.4 eV level can be achieved, the very high accuracy required by the X-IFU calls for experimental validation. A dedicated measurement campaign has been performed by NASA Goddard Space Flight Center to characterize the energy scale of a prototype kilo-pixel array of X-IFU-representative TESs. The analysis of the data demonstrated the ability to correct for various drifts using two fiducial lines to track the temporal gain variation. In this paper, we propose to extend this study on the same data set by investigating multi-parameter correction techniques based on both the pulse-height of the fiducial line and the prepulse baseline level, using the knowledge of the TES energy scale at reference temperature/magnetic field set points acquired on the ground. Investigations on the co-adding of pixels to perform a joint correction over pools of pixels is also explored.
