Objective Due to mixed-frequency multi-source disturbances, unmanned surface vehicles (USVs) encounter challenges in accurately capturing state information and ensuring path-tracking precision. To address this issue, a composite anti-disturbance control method based on an extended state observer combined with Kalman filter (KFESO) is proposed for distributed cooperative path following of multiple USVs.

Methods Firstly, an extended state observer combined with Kalman filter is constructed to estimate the state variables and lumped disturbances of USVs. Secondly, a distributed state observer is designed to obtain the speed information of the virtual leader. Based on the consistency theory and the line-of-sight guidance law, a kinematic cooperative controller is designed by combining the output of the KFESO and the estimated reference speed. Furthermore, a kinetic anti-disturbance controller is designed using the backstepping method and the dynamic surface control technique. The Lyapunov stability theory is employed to prove that all error signals in the control system are uniformly ultimately bounded.

Results Simulation experiments show that the proposed method can accurately obtain the states of USVs. Under mixed-frequency multi-source disturbances, compared with the standard ESO-based control method, it has higher tracking precision and stronger anti-disturbance ability. Regarding path tracking trajectories, the proposed method achieves reduced lateral deviations and more stable trajectories. For position errors, the convergence times are comparable, but the proposed method effectively eliminates oscillations. In terms of path parameter coordination error, the proposed method can stabilize the formation, whereas the comparison method suffers from high-frequency oscillations. In terms of state estimation accuracy, the proposed method significantly improves the estimation accuracy of various state variables, enables the distributed state observer to effectively estimate the speed of the virtual leader, and achieves smaller errors in speed and control force (moment), effectively mitigating the frequent actuator response to noise.

Conclusion This method can resolve the trade-off between estimation speed and accuracy in ESO, and improve the precision of multi-USV cooperative path following.