Through photosynthesis plants remove atmospheric carbon dioxide (CO2), storing the carbon as biomass. The fate of this stored carbon partly determines the amount of CO2 in the atmosphere, now and into the future. Current estimates of global terrestrial photosynthesis vary by about a factor of two therefore limiting our understanding of the carbon cycle as a whole. Recent satellite measurements of a phenomenon termed chlorophyll fluorescence now provide us with an unprecedented window into this carbon flux. This thesis examines how these measurements can be combined with a process-based land surface model using a data assimilation system to estimate global terrestrial photosynthesis. This includes uncertainty analysis, comparison with other estimates and insights into improving the model.