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Simulating Arctic sea ice conditions up to the present and predicting them several months in advance has high stakeholder value, yet remains challenging. Advanced data assimilation (DA) methods combine real observations with model forecasts to produce sea ice reanalyses and accurate initial conditions for sea ice prediction. This study introduces a sea ice DA framework for a sea ice model with a parameterization of the ice thickness distribution by resolving multiple thickness categories. Specifically, the Los Alamos Sea Ice Model, version 5 (CICE5), is integrated with the Data Assimilation Research Testbed (DART). A series of perfect model observing system simulation experiments (OSSEs) are designed to explore DA algorithms within the ensemble Kalman filter (EnKF) and the relative importance of different observation types. This study demonstrates that assimilating sea ice concentration (SIC) observations can effectively remove SIC errors, with the error of total Arctic sea ice area reduced by about 60% annually. When the impact of SIC observations is strongly localized in space, the error of total volume is also modestly improved. The largest simulation improvements are produced when sea ice thickness (SIT) and SIC are jointly assimilated, with the error of total volume decreased by more than 70% annually. Assimilating multiyear sea ice concentration (MYI) can reduce error in total volume by more than 50%. Assimilating MYI produces modest improvements in snow depth (errors are reduced by around 16%), while assimilating SIC and SIT has no obvious influence on snow depth. This study also suggests that different observation types may need different localization distances to optimize DA performance.