The Atomic Clocks Ensemble in Space (ACES/PHARAO mission, ESA & CNES) will be installed on board the International Space Station (ISS) next year. A crucial part of this experiment is its two-way microwave link (MWL), which will compare the timescale generated on board with those provided by several ground stations disseminated on the Earth. A dedicated data analysis center is being implemented at SYRTE—Observatoire de Paris, where our team currently develops theoretical modelling, numerical simulations and the data analysis software itself. In this paper, we present some key aspects of the MWL measurement method and the associated algorithms for simulations and data analysis. We show the results of tests using simulated data with fully realistic effects such as fundamental measurement noise, Doppler, atmospheric delays, or cycle ambiguities. We demonstrate satisfactory performance of the software with respect to the specifications of the ACES mission. The main scientific product of our analysis is the clock desynchronisation between ground and space clocks, i.e. the difference of proper times between the space clocks and ground clocks at participating institutes. While in flight, this measurement will allow for tests of general relativity and Lorentz invariance at unprecedented levels, e.g. measurement of the gravitational redshift at the level. As a specific example, we use real ISS orbit data with estimated errors at the 10 m level to study the effect of such errors on the clock desynchronisation obtained from MWL data. We demonstrate that the resulting effects are totally negligible.