In many applications, attitude estimation algorithms rely mainly on magnetic and inertial measurements from MARG sensors (consisting of a magnetometer, a gyroscope, and an accelerometer). One of the main challenges facing these algorithms is that the accelerometer measures both gravity and an unknown external acceleration, while these algorithms assume that the accelerometer measures only the gravity. In this paper, an attitude estimation algorithm on the special orthogonal group SO(3) is designed, considering the external acceleration as an unknown input with direct feedthrough to the output, with a local approximation approach. The proposed algorithm is validated through Monte Carlo simulations and real datasets, demonstrating better accuracy and enhanced performance than existing solutions.