of the agent nodes at each time. Assumption \[as:2\] ensures that if a hypothetical fusion center could stack all the data samples together at any time $t$, it would have sufficient information so as to be able to unambiguously estimate the parameter of interest. Hence, the requirement for this assumption naturally extends to our distributed setup. As far as reconstructing the parameter $\btheta$ is concerned, there is an inherent scalability issue as the dimension of the parameter scales with the size of the network. Owing to the ad-hoc nature of setups as described above and observations being made at different agents in a sequential manner, one has to resort to recursive message-passing schemes while conforming to a communication protocol specified by a inter-agent communication graph. Given the possibly high-dimensional state of the field, it is not desirable and communication-wise feasible to exchange the high-dimensional data in the form of parameter estimates and for each agent to estimate the entire vector. Before, going over specifics of our algorithm, we next review recursive estimation both in the centralized and distributed setups.

Preliminaries {#subsec:prel}
-------------

In this section, we go over the preliminaries of classical distributed estimation.\
**Distributed Estimation:**\
In the setup described 