A Trajectory Simulator Using Frenet–Serret Formulas Applied to Punctual Objects

In target tracking problems, it is important to know the dynamics of moving objects in the plane or space. These can be defined using differential geometry theory. One of the most important techniques to describe trajectories using differential geometry is the Frenet-Serret formulas, that give information about the kinematic properties of moving objects. However, in practice, the position measurements captured by sensors are commonly noisy. Thus, the objective of this paper is to present a trajectory simulator of a punctual object that generates noisy position measurements based on Frenet-Serret formulas and stochastic models. Some scenarios are presented at the end showing some results provided by the proposed trajectory simulator.