The aim of this work is to study the impact of the processing parameterization on the estimation of the zenith total delay (ZTD) from a shipborne GNSS antenna measurement. For this purpose, we used a simplified observation model, and simulated a realistic configuration of measurements (ephemerids, troposphere, motion of the shipborne antenna). Different sources of error that could affect the measurement were also simulated. The impact of these errors was then evaluated on the estimation by Kalman filtering, using different parameterizations (multi-constellation, solution sampling, random walk process noise for the ZTD estimates, observation weighting, cut-off angle). As it could have been expected, low cut-off angle (in the range of 3 to 7 degrees) and multi-constellation provide more accurate results. The choice of the data weighting is shown to significantly impact the difference on the estimates, and the use of a square-root of sine function, or uniform weighting of elevation gives the most conclusive results. High value of random walk process noise for ZTD estimates should also be avoided. Globally, the accuracy of the ZTD estimation can be improved up to more than 90% according to the configuration. The results of this work will be helpful to set up an optimal parameterization for the processing of massive dataset of GNSS measurements acquired from shipborne antennas.