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\begin{document}
\title{The mechanisms of four consensus filtering approaches}
\begin{table}
\caption{The mechanisms of four consensus filtering approaches}
\centering
\begin{threeparttable}
\begin{tabular}{ccc}
%{m{15mm} m{70mm} m{18mm}}
Types & Structures of Consensus Filters \tnote{*} & References\\
\midrule\midrule
CE &
$\begin{aligned}
\hat{x}^i_k & = \hat{x}^i_{k\mid k-1} + K^i_k(z^i_k
- H^i_k \hat{x}^i_{k \mid k-1})+u^i_k \\
u^i_k & = C^i_k \sum_{j\in N_i}(\hat{x}^j_{k\mid k-1}-\hat{x}^i_{k\mid k-1})
\end{aligned}
$ & [58],[59] \\%new row
\cmidrule(l r ){1-3}
CM & $ \begin{aligned}
\Omega^{i}_{k\mid {k}} &= \Omega^{i}_{k\mid {k-1}}+ |\mathcal{N}|\sum_{j\in \mathcal{N}} \pi_{L,k}^{i,j} (H_k^j)^T (R_k^j)^{-1}H_k^j \notag\\
q_{k\mid {k}}^i &= q^{i}_{k\mid {k-1}}+ |\mathcal{N}|\sum_{j\in \mathcal{N}} \pi_{L,k}^{i,j} (H_k^j)^T (R_k^j)^{-1} z_k^j
\end{aligned} $ & \makecell{[16],[58]} \\
\cmidrule(l r ){1-3}
CI & $\begin{aligned}
\Omega^{i}_{k\mid {k}} &= \sum_{j\in \mathcal{N}} \pi_{L,k}^{i,j}\left[ \Omega^{j}_{k\mid {k-1}}+ (H_k^j)^T (R_k^j)^{-1}H_k^j\right] \notag\\
q_{k\mid {k}}^i &= \sum_{j\in \mathcal{N}} \pi_{L,k}^{i,j} \left[ q^{j}_{k\mid {k-1}}+ (H_k^j)^T (R_k^j)^{-1} z_k^j\right]
\end{aligned} $ & [19],[75] \\
\cmidrule(l r ){1-3}
\makecell{$H_\infty$\\
consensus }
& $\begin{aligned}
& \begin{cases}
\hat{x}^i_k = A_k \hat{x}^i_{k-1}
+ K^i_k(z^i_k- H^i_k\hat{x}^i_{k-1})
+ u^i_k \\
u^i_k = C^i_k \sum_{j\in N_i}(\hat{x}^j_{k-1}-\hat{x}^i_{k-1})
\end{cases}\\
& \frac{1}{n}\sum_{i\in \mathcal{N}} \|\tilde{z}^i\|^2
\leq \gamma^2 \{\|v\|_2^2
+ \frac{1}{n}\sum_{i\in\mathcal{N}} (e^i_0)^T S^i e^i_0\}
\end{aligned}
$ & [78],[80] \\% end of rows
\midrule\midrule
\end{tabular}
\begin{tablenotes}
\item[*] Throughout the table, $A_k$ is the systems matrix, $H_k^i$, $R_k^i$ and $z_k^i$ are respectively measurement matrix, covariance matrix of measurement noise and measurement output value of node $i$. Further, denote $\Omega_{k\mid k} \triangleq (P_{k\mid k})^{-1}$ and $q_{k\mid k}=(P_{k\mid k})^{-1}\hat{x}_{k\mid k}$ as information matrix and information vector.
\end{tablenotes}
\end{threeparttable}
\end{table}
\end{document}
