The analysis of ship voyages using Automatic Identification System (AIS) data plays a crucial role in enhancing our understanding of maritime behavior and improving navigational safety. In this study, we focused on elucidating ship voyages by applying the elastic trend filter to AIS data and analyzing turns using circle-fitting techniques. Our primary objective was to gain insight into a ship's navigational characteristics and decision-making processes during turning maneuvers. To achieve this, we identified turns in the ship's trajectory, approximated their radii by fitting circles to the data points, and extracted the underlying route using the elastic trend filter. The consistent turn radii observed in the results indicated the presence of a common navigational strategy. However, variations in turn radii were also observed, suggesting instances of sharper turns made to avoid obstacles or navigate through constrained spaces. To assess the accuracy of our circle fitting method, we compared its precision to manual measurements and previous investigations, demonstrating its reliability. These findings have important implications for autonomous ship control systems, navigational regulations, and marine safety. Recognizing ship maneuvers and their associated radii can contribute to enhancing navigation procedures and optimizing route planning. By leveraging the analysis of AIS data, our study contributes to advancing transparency and providing novel insights into the navigational behavior of ships. The acquired knowledge holds significance in understanding and explaining ship voyages, making a valuable contribution to this field of study.