A derivative-free robust Kalman filter algorithm is proposed for nonlinear uncertain systems. The unscented transform (UT) is adopted instead of the linearization technique to obtain the solution of the H ∞ filter Riccati equation. A robust unscented Kalman filter (RUKF) is derived to guarantee an optimized upper bound on the estimation error covariance despite the model uncertainties and the approximation error of the UT. The proposed algorithm is applied to a satellite attitude determination system. Simulation results show that the RUKF is more effective than the unscented Kalman filter (UKF) in cases where alignment errors are present.