the data samples obtained at each agent lacks information about all the features, the parameter estimates would be erroneous and sub-optimal. As in the case of the fusion center based approach outlined above, each agent maintains a $N$-dimensional estimate at all times and hence the messages exchanged in the neighborhood are $N$-dimensional and could be very large depending on the size of the network. Hence, as a surrogate to the global innovation in the centralized recursions, the local estimators compute a local innovation based on the locally sensed data as an agent has access to information only in its neighborhood. The information loss at a node is compensated by incorporating an agreement or consensus potential into their updates which is then incorporated (see, for example [@kar2011convergence; @kar2013distributed; @sahu2016distributedtsipn]) as follows: [$$\begin{aligned}
            \label{eq:benchmark_ci}
            &\mathbf{x}_{n}(t+1) = \mathbf{x}_{n}(t)-\underbrace{\frac{b}{(t+1)^{\delta_{1}}}\sum_{l\in\Omega_{n}(t)}\left(\mathbf{x}_{n}(t)-\mathbf{x}_{l}(t)\right)}_{\text{Neighborhood Consensus}}\nonumber\\&+\underbrace{\frac{a}{t+1}\mathbf{\Gamma}^{-1}\mathbf{H}_{n}^{\top}\mathbf{\Sigma}_{n}^{-1}\left(\mathbf{y}_{n}(t)-\mathbf{H}_{n}\mathbf{x}_{n}(t)\right)}_{\text{Local Innovation}},
            \end{aligned}$$]{} where $0 <\delta_{1}<1$, $\Omega_{n}(t)$ represents the neighborhood of agent $n$ at time $t$ and $a,b$ are appropriately chosen positive constants. In the above scheme, the information exchange among agent nodes is limited to the parameter estimates. It has been shown in previous work that under appropriate conditions (see, for example [@kar2011convergence]), the estimate sequence $\{\mathbf{x}_{n}(t)\}$ converges to $\btheta^{\ast}$ and is asymptotically normal, 