Algorithm 6: A distributed Kalman filter based on the non-repeated diffusion strategy.
For the node $i\in V$ and node $j\in N_i$.   Initialize with:     ${\widehat{x}}_{i,0\mid 0}^{\mathrm{loc}}=\mathbb{E}{x}_0,P_{i,0\mid 0}^{\mathrm{loc}}=\mathbb{E}\left[(x_0-\mathbb{E}{x}_0){(x_0-\mathbb{E}{x}_0)}^{\mathrm{T}}\right]$,     ${\widehat{x}}_{j\to i,0\mid 0}=0,P_{j\to i,0\mid 0}=\mathbb{E}\left[(x_0-\mathbb{E}{x}_0){(x_0-\mathbb{E}{x}_0)}^{\mathrm{T}}\right]$;   Local update:     ${\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}}=A{\widehat{x}}_{i,t-1\mid t-1}^{\mathrm{loc}}$,     $P_{i,t\mid t-1}^{\mathrm{loc}}=A{P}_{i,t-1\mid t-1}^{\mathrm{loc}}{A}^{\mathrm{T}}+\mathsf{\Gamma }Q{\mathsf{\Gamma }}^{\mathrm{T}}$,     ${\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}={\left(P_{i,t\mid t-1}^{\mathrm{loc}}\right)}^{-1}+H_i^{\mathrm{T}}{R}_i^{-1}{H}_i$,     ${\widehat{x}}_{i,t\mid t}^{\mathrm{loc}}={\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}}+P_{i,t\mid t}^{\mathrm{loc}}{H}_i^{\mathrm{T}}{R}_i^{-1}(y_{i,t}-H_i{\widehat{x}}_{i,t\mid t-1}^{\mathrm{loc}})$;   Diffusion incremental update:
$P_{i\to j,t}^{-1}={\sum }_{g\in N_i-j}{w}_{j,g\to i}{P}_{g\to i,t-1\mid t-1}^{-1}+w_{j,i\to i}{\left(P_{i,t-1\mid t-1}^{\mathrm{loc}}\right)}^{-1},$	(13)
${\widehat{x}}_{i\to j,t}=P_{i\to j,t}\left[{\sum }_{g\in N_i-j}{w}_{j,g\to i}{P}_{g\to i,t\mid t}^{-1}{\widehat{x}}_{g\to i,t-1\mid t-1}+w_{j,i\to i}{\left(P_{i,t-1\mid t-1}^{\mathrm{loc}}\right)}^{-1}{\widehat{x}}_{i,t-1\mid t-1}^{\mathrm{loc}}\right],$	(14)
${\widehat{x}}_{i\to j,t\mid t-1}=A{\widehat{x}}_{i\to j,t}$,     $P_{i\to j,t\mid t-1}=A{P}_{i\to j,t}{A}^{\mathrm{T}}+\mathsf{\Gamma }Q{\mathsf{\Gamma }}^{\mathrm{T}}$,     $P_{i\to j,t\mid t}^{-1}=P_{i\to j,t\mid t-1}^{-1}+H_i^{\mathrm{T}}{R}_i^{-1}{H}_i$,     ${\widehat{x}}_{i\to j,t\mid t}={\widehat{x}}_{i\to j,t\mid t-1}+P_{i\to j,t\mid t}{H}_i^{\mathrm{T}}{R}_i^{-1}(y_{i,t}-H_i{\widehat{x}}_{i\to j,t\mid t-1})$;   Communication and fusion update:     Send ${\widehat{x}}_{j\to i,t\mid t}$ and $P_{j\to i,t\mid t}$ to adjacent node i,     $P_{i,t\mid t}^{-1}={\sum }_{j\in N_i}{w}_{j\to i}{P}_{j\to i,t\mid t}^{-1}+w_{i\to i}{\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1},$     ${\widehat{x}}_{i,t\mid t}=P_{i,t\mid t}\left[{\sum }_{j\in N_i}{w}_{j\to i}{P}_{j\to i,t\mid t}^{-1}{\widehat{x}}_{j\to i,t\mid t}+w_{i\to i}{\left(P_{i,t\mid t}^{\mathrm{loc}}\right)}^{-1}{\widehat{x}}_{i,t\mid t}^{\mathrm{loc}}\right],$   where $w_j$ is calculated by Equation (19).