above in , if a hypothetical fusion center having access to the data samples at all nodes at all times were to conduct the parameter estimation in a recursive manner, a (centralized) recursive least-squares type approach could be employed as follows: [$$\begin{aligned}
            &\mathbf{x}_{c}(t+1)=\mathbf{x}_{c}(t)\nonumber\\&+\underbrace{\frac{a}{t+1}\sum_{n=1}^{N}\mathbf{H}_{n}^{\top}\mathbf{\Sigma}_{n}^{-1}\left(\mathbf{y}_{n}(t)-\mathbf{H}_{n}\mathbf{x}_{c}(t)\right)}_{\text{Global Innovation}},
            \end{aligned}$$]{} where $a$ is a positive constant such that $a> N/\left(\lambda_{min}\left(\sum_{n=1}^{N}\mathbf{H}_{n}^{\top}\mathbf{R}_{n}^{-1}\mathbf{H}_{n}\right)\right)$. However, such a fusion center based scheme may not be implementable in our distributed multi-agent setting with time-varying sparse inter-agent interaction primarily due to the fact that the desired global innovation computation requires instantaneous access to the entire set of network sensed data at all times at the fusion center. Moreover, the fusion center intends to reconstruct the entire high-dimensional state and thus, maintains a $N$-dimensional estimate at all times. If in the case of a distributed setup, an agent $n$ in the network were to replicate the centralized update by replacing the global innovation in accordance with its local innovation, the update for the parameter estimate becomes [$$\begin{aligned}
            &\widehat{\mathbf{x}}_{n}(t+1)=\widehat{\mathbf{x}}_{n}(t)\nonumber\\&+\underbrace{\frac{a}{t+1}\mathbf{H}_{n}^{\top}\mathbf{\Sigma}_{n}^{-1}\left(\mathbf{y}_{n}(t)-\mathbf{H}_{n}\widehat{\mathbf{x}}_{n}(t)\right)}_{\text{Local Innovation}},
            \end{aligned}$$]{} where $\left\{\widehat{\mathbf{x}}_{n}(t)\right\}$ represents the estimate sequence at agent $n$. The above update involves purely decentralized and independent local processing with no collaboration among the agents whatsoever. However, note that in the case when 