location in the field is possibly a function of its own component and *neighboring* field components. As an example, in the smart grid context, a sensor at a node (location) may obtain a measurement of the power flowing into that node, which in turn is a function of the field components (e.g., voltages, angles) at that node and neighboring nodes. This coupling among parameter components in the measurements will be referred to as the *physical coupling* in the sequel. However, due to possible lack of identifiability, in order to come up with a provably consistent estimates of the parameter components of interest, each agent exchanges information with its neighborhood which conforms to a pre-assigned inter-agent communication graph. The inter-agent communication graph forms the cyber layer of the system and is different from that of the physical layer, i.e., the coupling structure among the parameter components induced by the distributed measurement model. Due to the high-dimensionality of the field, reconstructing the entire field at each agent may be too taxing, and hence, agents may only be interested in estimating certain components of the parameter field locally; furthermore, the components of interest at a given agent, referred to as the *interest set* 