Exploring the behavior feature of complex trajectories of ships with Fourier transform processing: a case from fishing vessels

Abstract

The significant uncertainty and complexity of vessels at sea poses challenges for regulatory bodies in the fishing industry. This paper presents a method for identifying fishing vessel trajectory characteristics involving the Fourier series transform. The model utilizes the Fourier series and Gaussian mixture clustering to address the complexity and uncertainty issues in fishing vessel trajectories. First, the vessel trajectories undergo a process of dimensionality expansion and projection along the temporal axis. The relationship between trajectories and complex plane projection was elucidated in this process. Second, a vessel trajectory identification model involving Fourier transformation was constructed. Subsequently, the phase spectrum was assigned binary values using differentiation, and the phase spectrum characteristics of the transformed trajectories through Fourier transformation were analyzed. Finally, six encoding formats for fishing vessel motion trajectories in phase spectrum encoding are introduced, along with the determination of uncertain vessel motion range through mixed Gaussian clustering. This method has been validated using a dataset comprising 7,000 fishing vessel trajectories collected from the Beidou satellite positioning system. The results demonstrate that the range of uncertain vessel motion was able to be obtained with the assistance of Gaussian mixture clustering, with an 80% probability position of approximately 1,000 m and a 50% probability position of around 2,000 m. Effective identification of fishing vessel operating and navigational states was achieved, leading to the determination of a safety distance for fishing vessels in the range of 1,000m–2,000 m. This research holds important reference value for fishery regulatory agencies in terms of supervising fishing vessels and maintaining a safe navigational distance.