BAARTR: Boundary-Aware Adaptive Regression for Kinematically Consistent Vessel Trajectory Reconstruction from Sparse AIS

The Automatic Identification System (AIS) frequently suffers from data loss and irregular report intervals in real maritime environments, compromising the reliability of downstream navigation, monitoring, and trajectory reconstruction tasks. To address these challenges, we propose BAARTR (Boundary-Aware Adaptive Regression for Kinematically Consistent Vessel Trajectory Reconstruction), a novel kinematically consistent interpolation framework. Operating solely on time, latitude, and longitude inputs, BAARTR explicitly enforces boundary velocities derived from raw AIS data. The framework adaptively selects a velocity-estimation strategy based on the AIS reporting gap: central differencing is applied for short intervals, while a hierarchical cubic velocity regression with a quadratic acceleration constraint is employed for long or irregular gaps to iteratively refine endpoint slopes. These boundary slopes are subsequently incorporated into a clamped quartic interpolation at a 1 s resolution, effectively suppressing overshoots and ensuring velocity continuity across segments. We evaluated BAARTR against Linear, Spline, Hermite, Bezier, Piecewise cubic hermite interpolating polynomial (PCHIP) and Modified akima (Makima) methods using real-world AIS data collected from the Mokpo Port channel, Republic of Korea (2023–2024), across three representative vessels. The experimental results demonstrate that BAARTR achieves superior reconstruction accuracy while maintaining strictly linear time complexity (O(N)). BAARTR consistently achieved the lowest median Root Mean Square Error (RMSE) and the narrowest Interquartile Ranges (IQR), producing visibly smoother and more kinematically plausible paths-especially in high-curvature turns where standard geometric interpolations tend to oscillate. Furthermore, sensitivity analysis shows stable performance with a modest training window (n ≈ 16) and minimal regression iterations (m = 2–3). By reducing reliance on large training datasets, BAARTR offers a lightweight, extensible foundation for post-processing in Maritime Autonomous Surface Ship (MASS) and Vessel Traffic Service (VTS), as well as for accident reconstruction and multi-sensor fusion.