This paper addresses the problem of decentralized state estimation of distributed physical phenomena observed by a sensor network. The centralized approaches are not scalable for large sensor networks, because all information has to be transmitted to a powerful central processing node requiring an extensive amount of communication bandwidth and a lot of processing power. Thus, for a decentralized reconstruction of distributed phenomena, we propose a novel methodology consisting of three steps: (a) conversion of the distributed phenomenon into a lumped-parameter system description, (b) decomposition of the resulting system in order to map the description to the actual sensor network, and (c) decomposition of the density representation leading to a decentralized estimation approach. The main problem of a decentralized approach is that due to the propagation of local information through the network, unknown correlations are caused. This fact needs to be considered during the reconstruction process in order to get correct and consistent estimation results. For that reason, we employ a robust estimator (based on Covariance Bounds) for the local reconstruction update on each sensor node. ... mehrBy this means, the individual sensor nodes are able to estimate the local state of the distributed phenomenon using local estimates obtained and communicated by adjacent nodes only. The information about their correlations is not stored in the sensor network.