distributed estimation algorithm of the $\emph{consensus}+\emph{innovations}$ form ([@kar2011convergence; @kar2013consensus+]), namely $\mathcal{CIRFE}$, *consensus+innovations* Random Fields Estimator, where each agent reconstructs only a subset of the field by simultaneously processing information obtained from its neighbors (*consensus*) and the latest sensed information (*innovation*). It is of particular interest, that the information about the state vector is constrained to neighborhoods; in that, an agent has only information about the components of the state vector which potentially affect its own measurements, alleviating storage and model knowledge requirements.\
Our main contributions are as follows:\
**Main Contribution 1:** We propose a scheme, namely $\mathcal{CIRFE}$, where each entity reconstructs only a subset of the components of the state modeled by a vector parameter, and thereby also reducing the dimension of messages being communicated among the agents. Under mild conditions of the connectivity of the network, we establish consistency of the estimate sequence at each agent with respect to the components of the parameters in its interest set. The proposed scheme allows heterogeneity in terms of agents’ objectives, while still allowing for inter-agent collaboration.

**Main Contribution 2:** Technically, the consensus+innovations type approach that we employ for state reconstruction in the current setting constitutes a mixed time-scale stochastic approximation procedure 