Prescribed-time distributed direct estimation under relative state measurements

The distributed estimation technology is prevalently utilized to solve the leader-following multi-agent tracking problem. This technology poses a challenge in practice, since it generally relies on the available absolute state measurements. For this reason, a novel distributed estimation approach based on relative state measurements is developed in this article. The proposed method directly estimates the tracking error between the leader and each follower, rather than using an existing indirect way of estimating and making subtraction under absolute state measurements. Specifically, a distributed directed estimation is first studied to complete estimation tasks within prescribed time under the known directed networks. Then, a fully distributed directed estimation problem is considered under the unknown directed networks. Both distributed and fully distributed results are extended to the robustness cases to resist external disturbances. Simulation examples, including numerical examples and a multiship coordination example, are provided to demonstrate the effectiveness and advantages of the proposed distributed estimation method.