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Table 1 LTVFF-DRLS and LCTVFF-DRLS algorithms

From: Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

  LTVFF-DRLS Algorithm   LCTVFF-DRLS Algorithm
1 For each node k=1,2,…,N do 1 For each node k=1,2,…,N do
2 Initialize w k,−1=0, P k,−1=Π −1. 2 Initialize w k,−1=0, P k,−1=Π −1.
3 For time instant i=1,2,… do 3 For time instant i=1,2,… do
4 \(\lambda _{k}(i)=[1-\zeta _{k}(i)]_{\lambda _{-}}^{\lambda _{+}}\). 4 \(\lambda _{k}(i)=[1-\zeta _{k}(i)]_{\lambda _{-}}^{\lambda _{+}}\).
5 ζ k (i)=α ζ k (i−1)+β|e k (i)|2. 5 ζ k (i)=α ζ k (i−1)+β|ρ k (i)|2.
   6 ρ k (i)=γ ρ k (i−1)+(1−γ)|e k (i−1)||e k (i)|.
6 Set ψ k,i =w k,i−1, \(\mathbf {P}_{k,i}=\lambda ^{-1}_{k}(i)\mathbf {P}_{k,i-1}\). 7 Set ψ k,i =w k,i−1, \(\mathbf {P}_{k,i}=\lambda ^{-1}_{k}(i)\mathbf {P}_{k,i-1}\).
7 For \(l\in \mathcal {N}_{k}\) do 8 For \(l\in \mathcal {N}_{k}\) do
8 \(\boldsymbol {\psi }_{k,i}{\longleftarrow }\boldsymbol {\psi }_{k,i}+ \frac {C_{l,k}\mathbf {P}_{k,i}\mathbf {u}_{l,i}[d_{l,i}-\mathbf {u}_{l,i}^{*}\boldsymbol {\psi }_{k,i}]} {\sigma _{v,l}^{2}+C_{l,k}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}\mathbf {u}_{l,i}}\). 9 \(\boldsymbol {\psi }_{k,i}{\longleftarrow }\boldsymbol {\psi }_{k,i}+ \frac {C_{l,k}\mathbf {P}_{k,i}\mathbf {u}_{l,i}[d_{l,i}-\mathbf {u}_{l,i}^{*}\boldsymbol {\psi }_{k,i}]} {\sigma _{v,l}^{2}+C_{l,k}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}\mathbf {u}_{l,i}}\).
9 \(\mathbf {P}_{k,i}{\longleftarrow }\mathbf {P}_{k,i}- \frac {C_{l,k}\mathbf {P}_{k,i}\mathbf {u}_{l,i}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}}{\sigma _{v,l}^{2}+C_{l,k}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}\mathbf {u}_{l,i}}\). 10 \(\mathbf {P}_{k,i}{\longleftarrow }\mathbf {P}_{k,i}- \frac {C_{l,k}\mathbf {P}_{k,i}\mathbf {u}_{l,i}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}}{\sigma _{v,l}^{2}+C_{l,k}\mathbf {u}_{l,i}^{*}\mathbf {P}_{k,i}\mathbf {u}_{l,i}}\).
10 End 11 End
11 Generate the final estimate \(\mathbf {w}_{k,i}=\sum \limits _{l\in \mathcal {N}_{k}}A_{l,k}\boldsymbol {\psi }_{l,i}\). 12 Generate the final estimate \(\mathbf {w}_{k,i}=\sum \limits _{l\in \mathcal {N}_{k}}A_{l,k}\boldsymbol {\psi }_{l,i}\).
12 End 13 End
13 End 14 End