This paper focuses on Distributed State Estimation over a peer-to-peer sensor network composed by possible lowcomputational sensors. We propose a new-step Neighbourhood Distributed Moving Horizon Estimation 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, convergence of the estimation error is improved by means of spreading the information amongst neighbourhoods, which comes natural in the sliding window data present in the Moving Horizon Estimation paradigm.