Quantitative estimates for time-discrete tracking models on Riemannian manifolds

In this paper, we provide quantitative estimates for two time-discrete target tracking models on Riemannian manifolds. The proposed time-discrete models correspond to the time-discretization of the continuous tracking models in [1] via the first-order forward Euler discretization. For each time-discrete model, we introduce a sufficient framework for quantitative target tracking, and we show how the speed of target tracking depends on the relaxation speeds of moving target configurations, relaxation strength, and relaxation kernel. The proposed sufficient frameworks are formulated in terms of target configuration, system parameters, kernels in forcing terms, initial data, and time-step.