This letter studies the problem of $H_{\infty }$ filtering for attitude estimation using rotation matrices and vector measurements. Starting from a storage function on the Special Orthogonal Group $SO\text {(3)}$ , a dissipation inequality is considered such that the energy gain from exogenous disturbances and initial estimation errors to a generalized estimation error respects a given upper bound, $\gamma$ . Thereafter, an approximate deterministic nonlinear $H_{\infty }$ filter is derived which satisfies the dissipation inequality at least locally. The approach followed builds on earlier results on attitude estimation, in particular on nonlinear $H_{\infty }$ filtering using quaternions, and develops a robust filter directly on $SO\text {(3)}$ . The filter employs the same innovation term as the Multiplicative Extended Kalman Filter (MEKF), as well as a matrix gain updated in accordance with a Riccati-type gain update equation. However, in contrast to the MEKF, the filter has an additional tuning gain, $\gamma$ , which enables it to be more aggressive during transients. Thus, the proposed $H_{\infty }$ filter can be seen as a robust counterpart of the MEKF.