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Satellite observations of the magnetic field induced by the general ocean circulation could provide new constraints on global oceanic water and heat transports. This opportunity is investigated in a model-based twin experiment by assimilating synthetic satellite observations of the ocean-induced magnetic field into a global ocean model. The general circulation of the world ocean is simulated over the period of one month. Idealized daily observations are generated from this simulation by calculating the ocean-induced magnetic field at 450 km altitude and disturbing these global fields with error estimates. Utilizing an ensemble Kalman filter, the observations are assimilated into the same ocean model with a different initial state and different atmospheric forcing. Compared to a reference simulation without data assimilation, the corrected ocean-induced magnetic field is improved throughout the whole simulation period and over large regions. The global RMS differences of the ocean-induced magnetic field are reduced by up to 17%. Local improvements show values up to 54%. RMS differences of the depth-integrated zonal and meridional ocean velocities are improved by up to 7% globally, and up to 50% locally. False corrections of the ocean model state are identified in the South Pacific Ocean and are linked to a deficient estimation of the ocean model error covariance matrices. Most Kalman filter induced changes in the ocean velocities extend from the sea-surface down to the deep ocean. Allowing the Kalman filter to correct the wind stress forcing of the ocean model is essential for a successful assimilation.