Precise estimation of the load swing angle is a prerequisite for high-performance control of quadrotor-suspended-payload systems. Existing model-based filters often suffer from reduced precision due to model simplifications and external disturbances. Pure data-driven methods face generalization challenges and lack physical guarantees. This paper proposes a physics-informed hybrid estimation framework that combines an extended Kalman filter (EKF) and a residual learning long short-term memory (LSTM) network. In this framework, the EKF provides a robust nominal estimate, while the LSTM compensates for model mismatches induced by aerodynamic disturbances and dynamic coupling. Experimental validation reveals that the proposed method effectively mitigates model mismatches, significantly reducing estimation errors. Furthermore, a comparative analysis against deep learning baselines demonstrates that the proposed hybrid approach achieves comparable accuracy while demanding significantly fewer computational resources. The results establish the efficacy of the proposed framework as a lightweight and high-frequency solution for real-time onboard implementation.
Zhang et al. (Mon,) studied this question.