LAUSR

State estimation in the presence of unknown input presents a significant challenge in many domains. Few works in the literature have addressed this problem when the state belongs to the special orthogonal group SO(3), which is not a vector space. This paper proposes a state estimation algorithm designed for SO(3) with unknown input, specifically for cases where the unknown input affects the state dynamics without direct feedthrough to the output, with a proof of local optimality and local stability, which has not been explored yet. Finally, this paper demonstrates an application in gyro‐free attitude estimation, using only measurements from a 3‐axis accelerometer and a 3‐axis magnetometer, by considering the angular velocity from a 3‐axis gyroscope as an unknown input. Monte Carlo simulations show better accuracy and performance over existing attitude estimation methods using only accelerometer and magnetometer sensors.