Algorithm 2: A centralized Kalman filter based on the covariance intersection (CI) method.

For the node $i\in V$,   Initialize with:     ${\widehat{x}}_{i,0\mid 0}^{\mathrm{loc}}=\mathbb{E}{x}_0,$     $P_{i,0\mid 0}^{\mathrm{loc}}=\mathbb{E}\left[(x_0-\mathbb{E}{x}_0){(x_0-\mathbb{E}{x}_0)}^{\mathrm{T}}\right];$   Local update:     $P_{i,t\mid t-1}^{\mathrm{loc}}=A{P}_{i,t-1\mid t-1}^{\mathrm{loc}}{A}^{\mathrm{T}}+\mathsf{\Gamma }Q{\mathsf{\Gamma }}^{\mathrm{T}}$,     ${\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}}=A{\widehat{x}}_{i,t-1\mid t-1}^{\mathrm{loc}}$,     ${\widehat{x}}_{i,t\mid t}^{\mathrm{loc}}={\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}}+H_i^{\mathrm{T}}{R}_i^{-1}(y_{i,t-1}-H_i{\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}})$,     ${\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}={\left(P_{i,t\mid t-1}^{\mathrm{loc}}\right)}^{-1}+H_i^{\mathrm{T}}{R}_i^{-1}{H}_i;$   Fusion update:     $P_{t\mid t}^{-1}={\sum }_{i\in V}{w}_i{\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}$,     ${\widehat{x}}_{t\mid t}=P_{t\mid t}{\sum }_{i\in V}{w}_i{\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}{\widehat{x}}_{i,t\mid t}^{\mathrm{loc}}$,   where $w_j$ is calculated by Equation (5).