In this chapter, on the basis of a rigorous mathematical formulation, a new algorithm for the identification of distributed systems by large scale collaborative sensor networks is suggested. The algorithm extends a KLT-based identification approach to a decentralized setting, using the distributed Karhunen-Loève transform (DKLT) recently proposed by Gastpar
. The proposed approach permits an arbitrarily accurate identification since it exploits both the asymptotic properties of convergence of DKLT and the universal approximation capabilities of radial basis functions neural networks. The effectiveness of the proposed approach is directly related to the reduction of total distortion in the compression performed by the single nodes of the sensor network, to the identification accuracy, as well as to the low computational complexity of the fusion algorithm performed by the fusion center to regulate the intelligent cooperation of the nodes. Some identification experiments, that have been carried out on systems whose behavior is described by partial differential equations in 2-D domains with random excitations, confirm the validity of this approach. It is worth noting the generality of the algorithm that can be applied in a wide range of applications without limitations on the type of physical phenomena, boundary conditions, sensor network used, and number of its nodes.