Energy-based approach for the discrete tracking problem of moving target groups

In this paper, we study a discrete dynamic system designed for asymptotic tracking of target groups under an uncertain environment. We analyze the tracking characteristics of this system in discrete settings by developing discretized energy functionals. Unlike the energy functional of a continuous system, the energy functional of a discrete system may not remain positive, and the estimation of the energy functional is more complicated. Therefore, we introduce cumulative residual energy, which ensures that the energy functional remains positive and non-increasing. Finally, we utilize the convergence of the discrete time step to overcome the velocity estimate difficulty brought by the random effects and infinite length of target particle trajectories, which enables us to establish target tracking for discrete systems. In particular, we also found that, under the controlled step size, the discretized solutions gradually converge to the tracking system of the continuous system. This continuous transition phenomenon has been verified through the simulation presented in this paper. By investigating the behavior of this discrete coupled system, we aim to facilitate practical applications of multi-particle tracking systems with information discontinuity and an uncertain environment.