not only establish the consistency and asymptotic normality of the parameter estimate sequence but also, due to the employed mixed time-scale stochastic approximation obtain the asymptotic covariance of the estimate sequences to be independent of the particular communication network instance.\
**Paper Organization :** The rest of the paper is organized as follows. Spectral graph theory and notation are discussed next. The sensing model and the preliminaries are discussed in Section \[sec:sens\_prel\]. Section \[sec:cirfe\] presents the proposed distributed estimation algorithm, while Section \[sec:main\_res\] and Section \[sec:proof\_mainres\] concerns with the main results of the paper and the proof of the main results respectively. The simulation experiments for the proposed algorithm are presented in Section \[sec:sim\]. Finally, Section \[sec:conc\] concludes the paper.\
**Notation.** We denote by $\mathbb{R}$ the set of reals, and by $\mathbb{R}^{k}$ the $k$-dimensional Euclidean space. Vectors and matrices are in bold faces. We also denote by $\mathbf{A}_{ij}$ or $[\mathbf{A}]_{ij}$, the $(i,j)$-th entry of a matrix $\mathbf{A}$; $\mathbf{a}_{i}$ or $[\mathbf{a}]_{i}$ the $i$-th entry of a vector $\mathbf{a}$. The symbols $\mathbf{I}$ and $\mathbf{0}$ are the $k\times k$ identity matrix and the $k\times k$ zero matrix, respectively, the dimensions being clear from the context. The vector $\mathbf{e_{i}}$ is the $i$-th column of $\mathbf{I}$, 