As the connectivity of consumer devices is rapidly growing and cloud computing technologies are becoming more widespread, cloud-aided techniques for parameter estimation can be designed to exploit the theoretically unlimited storage memory and computational power of the cloud, while relying on information provided by multiple sources. With the ultimate goal of developing monitoring and diagnostic strategies, this report focuses on the design of a Recursive Least-Squares (RLS) based estimator for identification over a group of devices connected to the cloud. The proposed approach, that relies on Node-to-Cloud-to-Node (N2C2N) transmissions, is designed so that: (i) estimates of the unknown parameters are computed locally and (ii) the local estimates are refined on the cloud. The proposed approach requires minimal changes to local (pre-existing) RLS estimators.