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Calibrating and verifying crystal plasticity material models is a significant challenge, particularly for materials with a number of potential slip and twin systems. Here we use digital image correlation on coarse-grained $��$-uranium during tensile testing in conjunction with crystal plasticity finite element simulations. This approach allows us to determine the critical resolved shear stress, and hardening rate of the different slip and twin systems. The constitutive model is based on dislocation densities as state variables and the simulated geometry is constructed from electron backscatter diffraction images that provide shape, size and orientation of the grains, allowing a direct comparison between virtual and real experiments. An optimisation algorithm is used to find the model parameters that reproduce the evolution of the average strain in each grain as the load is increased. A tensile bar, containing four grains aligned with the load direction, is used to calibrate the model with eight unknown parameters. The approach is then independently validated by simulating the strain distribution in a second tensile bar. Different mechanisms for the hardening of the twin systems are evaluated. The latent hardening of the most active twin system turns out to be determined by coplanar twins and slip. The hardening rate of the most active slip system is lower than in fine-grained $��$-uranium. The method developed in the present research can be applied to identify the critical resolved shear stress and hardening parameters of other coarse-grained materials.