Table 2 Complexity of proposed method
Computational unit | Complexity for each unit | Total computational complexity |
|---|---|---|
A 1 | M − N + Ml | \( {\displaystyle \begin{array}{l}O\left({\left(M-N\right)}^3\right)+O\left({\left(N+l+1\right)}^3\right)+O\left({l}^3\right)+\left({N}^2+2N+1\right)\\ {}\cdot \left[3\left(M-1\right){\left(M-N\right)}^2+{\left(M-1\right)}^2\left(M-N\right)+{\left(M-1\right)}^3\right]\\ {}+2{\left(M-N\right)}^2\left(M-1\right)+\left(M-N\right){\left(M-1\right)}^2+2\left(M-N\right){M}^2{l}^2\\ {}+{\left(M-N\right)}^2 Ml+{\left(M-N\right)}^3+{M}^3{l}^3+\left(M-N\right) Ml+{Ml}^2\\ {}+2 Ml+\left(N+l+1\right){\left(M-N\right)}^2+{\left(N+l+1\right)}^2\left(M-N\right)\\ {}+2{\left(N+l\right)}^3+{\left(N+l\right)}^2\left(M-N\right)+\left(N+l\right){\left(M-N\right)}^2\\ {}+2{l}^2\left(N+l\right)+2l{\left(N+l\right)}^2+l\left(N+l\right)+M+N+2l\end{array}} \) (where M denotes the number of receivers, N is the grouping number and l represents the l dimensional localization scenario) |
W 1 | \( {\displaystyle \begin{array}{l}O\left({\left(M-N\right)}^3\right)+\left(M-N\right){M}^2{l}^2\\ {}+{\left(M-N\right)}^2 Ml+2{\left(M-N\right)}^2\left(M-1\right)\\ {}+\left(M-N\right){\left(M-1\right)}^2+{\left(M-N\right)}^3\end{array}} \) | |
Ω | \( {\displaystyle \begin{array}{l}\left({N}^2+2N+1\right)\cdot \Big[3\left(M-1\right){\left(M-N\right)}^2\\ {}+{\left(M-1\right)}^2\left(M-N\right)+{\left(M-1\right)}^3\Big]\\ {}+{M}^3{l}^3+{M}^2{l}^2\left(M-N\right)+ Ml\left(M-N\right)\\ {}+{Ml}^2+ Ml\end{array}} \) | |
φ 1 | \( {\displaystyle \begin{array}{l}O\left({\left(N+l+1\right)}^3\right)+\left(N+l+1\right){\left(M-N\right)}^2\\ {}+{\left(N+l+1\right)}^2\left(M-N\right)+N+l\end{array}} \) | |
\( {\tilde{\mathbf{B}}}_2^{-1} \) | N + l | |
\( {\tilde{\mathbf{W}}}_2 \) | 2(N + l)3 + (N + l)2(M − N) + (N + l)(M − N)2 | |
\( {\tilde{\boldsymbol{\upvarphi}}}_2 \) | O(l3) + 2l2(N + l) + 2l(N + l)2 + l(N + l) |