• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.487-504
• /
• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
• /
• 2022.06a
• /
• pp.150-154
• /
• 2022

The Automatic Ship Identification System(AIS) is importantly used to evaluate the trajectory of ships and the possibility of collision between ships. However, it is difficult to provide real-time information due to the limitation of the transmission intervals. Most of the studies to improve this are conducted based on ideal data, so there is a problem that it is hard to respond to the actual situation. Therefore, in this paper, we propose a discrete Kalman filter-based method that reflects the turning angle according to the type of trajectory, to provide real-time position information on real-time data. In addition, the accuracy evaluation of the proposed algorithm is conducted through experiments using actual data.