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This video is the presentation of the following paper presented at the 60th Conference on Decision and Control (CDC 2021): DOI: https://doi.org/10.1109/CDC45484.2021... Abstract: This paper focuses on Distributed State Estimation over a peer-to-peer sensor network composed by possible low-computational sensors. In this context, we propose a new L-step Neighbourhood Distributed Moving Horizon Estimation (DMHE) technique with fused arrival cost and pre-estimation, improving the accuracy of the estimation, while reducing the computation time compared to other approaches from the literature. Simultaneously, the proposed technique enhances the convergence of the estimation error by mean of spreading the information from neighbourhood to neighbourhood, which comes natural in the sliding window data present in the Moving Horizon Estimation paradigm. Illustrative numerical simulations are provided to analyse the performance of the proposed approach, with respect to existing algorithms, considering as metrics accuracy of the estimates and computation time. 0:00 Intro 0:23 Distributed State Estimation 1:48 Objectives 2:19 System Setup 3:33 Diffusion Information Mechanism 4:38 Proposed algorithm 5:49 Numerical examples 8:11 Conclusions