Rotational motion (or attitude) estimation algorithms in navigation rely mainly on measurements from a set of sensors, including a magnetometer, gyroscope and accelerometer, also known as magnetic, angular rate, and gravity (MARG) sensor array. However, the significant power consumption of the gyroscope and its intrinsic bias motivate the need for more suitable solutions. In this paper, a robust two-stage Kalman filter is designed for attitude estimation in the special orthogonal group SO(3), by considering the angular velocity as unknown input. The performance of the proposed algorithm was evaluated through Monte Carlo simulations compared to the known TRIAD algorithm, which utilizes measurements from only accelerometer and magnetometer sensors, and to the Invariant Extended Kalman Filter (IEKF), which is applied for SO(3) estimation using MARG sensor array.