This technical note considers the problem of obtaining minimum-energy state estimates for a system defined on the rotation group, SO(3). The signals of the system are modeled as purely deterministic signals. We derive a nonlinear observer ("filter") posed directly on SO(3) that respects the geometry of the group and achieves a performance that is close to optimal in the sense of minimizing an integral cost that is measuring the state energy. The performance of the proposed filter is demonstrated in simulations involving large initialization, process and measurement errors where the results are compared against a quaternion implementation of an Extended Kalman Filter. Our results indicate that the proposed filter achieves better robustness against a range of noise levels and initialization errors.