Gradient-accelerated nutation-based fast alignment for transmitter-receiver misalignment in inter-satellite free-space optical communication systems.

Free-space optical (FSO) communication has been widely adopted for inter-satellite links. To address the challenge of transmitter-receiver misalignment in FSO systems, this study proposes a gradient-accelerated nutation algorithm. The proposed method retains the inherent advantages of conventional nutation approaches while leveraging the optical field distribution of the FSO link to significantly enhance convergence speed. Specifically, an analytical relationship between the step size and the optical power gradient is derived, enabling the algorithm to automatically switch between rapid convergence and high-precision alignment based on the derived optical power gradient model. Moreover, the hyperparameters are determined by the optical link characteristics and remain independent of the instantaneous coaxial error. Additionally, the impact of signal-to-noise ratio and the step-size scaling factor on convergence performance are analyzed, with simulation results providing practical guidance for engineering implementation. Both numerical simulations and a 10.4 km field experiment validate that the proposed method substantially accelerates misalignment calibration, reducing the required calibration iterations by approximately 65%.