This paper addresses the problem of model-based reconstruction and parameter identification of distributed phenomena characterized by partial differential equations. The novelty of the proposed method is the systematic approach and the integrated treatment of uncertainties, which naturally occur in the physical system and arise from noisy measurements. The main challenge of accurate reconstruction is that model parameters, i.e., diffusion coefficients, of the physical model are not known in advance and usually need to be identified. Generally, the problem of parameter identification leads to a nonlinear estimation problem. Hence, a novel efficient recursive procedure is employed. Unlike other estimators, the so-called Hybrid Density Filter not only assures accurate estimation results for nonlinear systems, but also offers an efficient processing. By this means it is possible to reconstruct and identify distributed phenomena monitored by autonomous wireless sensor networks. The performance of the proposed estimation method is demonstrated by means of simulations.