An Error-State Kalman Filter with Multibody Integrator for State Estimation of Flexible Cable-Net Systems

The advancement of arresting cable-net recovery technology is expected to promote the application of heavy-lift reusable launch vehicles in low-cost and high-frequency space exploration. However, this process faces challenges such as insufficient or indirect measurement in complex noisy environments, as well as high complexity of the system model itself. These issues make it difficult to accurately obtain the state information of flexible arresting cables for precise control and capture of landing reusable rockets. Although the Kalman filter combined with multibody dynamics models can address state estimation in complex systems, conventional numerical integration methods often suffer from slow convergence or fail to handle the stiffness caused by strong nonlinearities and flexible effects. This study develops an error-state extended Kalman filter based on multibody integrators. The method utilizes the generalized-α method and backward differentiation formula for one-step state prediction, without model transformation or linearization of the complex nonlinear multibody system. Then, scaling and index reduction by an augmented Lagrangian formulation are carried out to improve the conditioning of the Jacobian matrix. The state prediction via the multibody integrator and an additional constraint violation correction are implemented to ensure that the estimated state remains on the constraint manifold. Simulations of state estimation performed on a flexible cable-net system model verify the effectiveness of the proposed approach. This study will provide technical support for future cable-net recovery of heavy-lift reusable launch vehicles.