Frenet-Serret-Based Trajectory Prediction

Trajectory prediction is a critical component of guidance, navigation, and control (GNC) systems. This paper introduces a novel real-time trajectory-prediction method based on adaptive input and state estimation (AISE), Frenet-Serret (FS) frame, and real-time position measurements. The proposed method, termed AISE/FS, leverages the FS frame to model the target’s motion as a 3D curve, where the FS frame requires real-time estimates of the target’s velocity, acceleration, and jerk. To estimate velocity, acceleration, and jerk in real time, AISE computes first, second, and third derivatives of the position measurements. AISE does not rely on assumptions about the target maneuver, measurement noise, or disturbances. For trajectory prediction, both the baseline AISE/va method (which uses velocity and acceleration) and the proposed AISE/FS method extrapolate the trajectory from the current position using estimated derivatives. Numerical simulations demonstrate that AISE/FS significantly outperforms both AISE/va and the classical ��-��-�� filter, particularly in scenarios involving complex or aggressive target maneuvers.