In the past decade groundbreaking new satellite observations of the Arctic sea ice cover have been made, allowing researchers to understand the state of the Arctic sea ice system in greater detail than before. The derived estimates of sea ice thickness are useful but limited in time and space. In this study the first results of a new sea ice data assimilation system are presented. Observations assimilated (in various combinations) are monthly mean sea ice thickness and monthly mean sea ice thickness distribution from CryoSat-2 and NASA daily Bootstrap sea ice concentration. This system couples the Centre for Polar Observation and Modelling's (CPOM) version of the Los Alamos Sea Ice Model (CICE) to the localised ensemble transform Kalman filter (LETKF) from the Parallel Data Assimilation Framework (PDAF) library. The impact of assimilating a sub-grid-scale sea ice thickness distribution is of particular novelty. The sub-grid-scale sea ice thickness distribution is a fundamental component of sea ice models, playing a vital role in the dynamical and thermodynamical processes, yet very little is known of its true state in the Arctic. This study finds that assimilating CryoSat-2 products for the mean thickness and the sub-grid-scale thickness distribution can have significant consequences for the modelled distribution of the ice thickness across the Arctic and particularly in regions of thick multi-year ice. The assimilation of sea ice concentration, mean sea ice thickness and sub-grid-scale sea ice thickness distribution together performed best when compared to a subset of CryoSat-2 observations held back for validation. Regional model biases are reduced: the thickness of the thickest ice in the Canadian Arctic Archipelago (CAA) is decreased, but the thickness of the ice in the central Arctic is increased. When comparing the assimilation of mean thickness with the assimilation of sub-grid-scale thickness distribution, it is found that the latter leads to a significant change in the volume of ice in each category. Estimates of the thickest ice improve significantly with the assimilation of sub-grid-scale thickness distribution alongside mean thickness.