Frenet-Serret-Based Trajectory Prediction

Abstract: Trajectory prediction is a crucial element of guidance, navigation, and control systems. This paper presents two novel trajectory-prediction methods based on real-time position measurements and adaptive input and state estimation (AISE). The first method, called AISE/va, uses position measurements to estimate the target velocity and acceleration. The second method, called AISE/FS, models the target trajectory as a 3D curve using the Frenet-Serret formulas, which require estimates of 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 methods use measurements of the target position and estimates of its derivatives to extrapolate from the current position. The performance of AISE/va and AISE/FS is compared numerically with the $\alpha$-$\beta$-$\gamma$ filter, which shows that AISE/FS provides more accurate trajectory prediction than AISE/va and traditional methods, especially for complex target maneuvers.