Description: Data assimilation is carried out for the Martian atmosphere with the Mars Climate Sounder (MCS) retrievals of temperature, dust and ice. It is performed for the period Ls=180°to Ls=320°of Mars Year 29 with the Local Ensemble Transform Kalman Filter scheme and the Laboratoire de Météorologie Dynamique (LMD) Mars Global Climate Model (GCM). In order to deal with the forcings of aerosols (dust and water ice) on atmospheric temperatures, a framework is given for multivariate analysis. It consists of assimilating a GCM variable with the help of another GCM variable that can be more easily related to an observation. Despite encouraging results with this method, data assimilation is found to be intrinsically different for Mars, and more challenging, due to the Martian atmosphere being less chaotic and exhibiting more global features than on Earth. This is reflected in the three main issues met when achieving various data assimilation experiments: 1) temperature assimilation strongly forces the GCM away from its free-running state, due to the difficulty of assimilating global atmospheric thermal tides; 2) because of model bias, assimilation of airborne dust is not able to reproduce the vertical diurnal variations of dust observed by MCS, and not present in the GCM; 3) water ice clouds are nearly impossible to assimilate due to the difficulty to assimilate temperature to a sufficient precision. Overall, further improvements of Martian data assimilation would require an assimilation that goes beyond the local scale, and more realism of the GCM, especially for aerosols and thermal tides.