This paper presents a deep reinforcement learning (DRL) algorithm for orientation estimation using inertial sensors combined with a magnetometer. Lyapunov’s method in control theory is employed to prove the convergence of orientation estimation errors. The estimator gains and a Lyapunov function are parametrised by deep neural networks and learned from samples based on the theoretical results. The DRL estimator is compared with three well-known orientation estimation methods on both numerical simulations and real dataset collected from commercially available sensors. The results show that the proposed algorithm is superior for arbitrary estimation initialisation and can adapt to a drastic angular velocity profile for which other algorithms can be hardly applicable. To the best of our knowledge, this is the first DRL-based orientation estimation method with an estimation error boundedness guarantee.@en