of the graph is represented by the symmetric $N\times N$ adjacency matrix $\mathbf{A}=[A_{ij}]$, where $A_{ij}=1$ if $(i,j) \in E$, and $0$ otherwise. The degree matrix is given by the diagonal matrix $\mathbf{D}=diag(d_{1}\cdots d_{N})$. The graph Laplacian matrix is defined as $\mathbf{L}=\mathbf{D}-\mathbf{A}$. The Laplacian is a positive semidefinite matrix, hence its eigenvalues can be ordered and represented as $0=\lambda_{1}(\mathbf{L})\le\lambda_{2}(\mathbf{L})\le \cdots \lambda_{N}(\mathbf{L})$. Furthermore, a graph is connected if and only if $\lambda_{2}(\mathbf{L})>0$ (see [@chung1997spectral] for instance).\

SENSING MODEL AND PRELIMINARIES {#sec:sens_prel}
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Consider $N$ physical agents monitoring a field over a large physical area. Each agent $n$ is associated with a scalar state $\theta_{n}^{\ast}$, which represents the field intensity parameter at its location. The agents are equipped with sensing capabilities. We assume each agent observes a time-series of measurements, given by noisy linear functions of its state and the states of *neighboring* agents. Due to this coupling in the observations, an agent should cooperate with neighbors to reconstruct its own state. For simplicity, we assume that the individual agent states are scalars. Our results can be generalized to vector valued states, though at the cost of extra notation. The observation at each agent is of the form: [$$\begin{aligned}
            \label{RLU-prob1}
            \mathbf{y}_{n}(t)=\mathbf{H}_{n}\mathbf{\btheta}^{\ast}+\mathbf{\gamma}_{n}(t),
            \end{aligned}$$]{} where 