Algorithm 3: A diffusion distributed Kalman filter with the CI method.
For the node $i\in V$ and node $j\in N_i$,   Initialize with:     ${\widehat{x}}_{i,0\mid 0}=\mathbb{E}{x}_0$,     $P_{i,0\mid 0}=\mathbb{E}\left[(x_0-\mathbb{E}{x}_0){(x_0-\mathbb{E}{x}_0)}^{\mathrm{T}}\right];$   Local update:     ${\widehat{x}}_{i,t\mid t-1}=A{\widehat{x}}_{i,t-1\mid t-1}$,     $P_{i,t\mid t-1}=A{P}_{i,t-1\mid t-1}{A}^{\mathrm{T}}+\mathsf{\Gamma }Q{\mathsf{\Gamma }}^{\mathrm{T}}$,     ${\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}={\left(P_{i,t\mid t-1}\right)}^{-1}+H_i^{\mathrm{T}}{R}_i^{-1}{H}_i$,     ${\widehat{x}}_{i,t\mid t}^{\mathrm{loc}}={\widehat{x}}_{i,t\mid t-1}+P_{i,t\mid t}{H}_i^{\mathrm{T}}{R}_i^{-1}(y_{i,t}-H_i{\widehat{x}}_{i,t\mid t-1})$;   Communication and fusion update:     Send ${\widehat{x}}_{j,t\mid t}^{\mathrm{loc}}$ and $P_{j,t\mid t}^{\mathrm{loc}}$ to adjacent node i,     $P_{i,t\mid t}^{-1}={\sum }_{k\in N_i+i}{w}_k{\left(P_{k,t\mid t}^{\mathrm{loc}}\right)}^{-1}$,
${\widehat{x}}_{i,t\mid t}=P_{i,t\mid t}\left[{\sum }_{k\in N_i+i}{w}_k{\left(P_{k,t\mid t}^{\mathrm{loc}}\right)}^{-1}{\widehat{x}}_{k,t\mid t}^{\mathrm{loc}}\right],$	(7)
where $w_k$ is calculated by Equation (5).