1 Introduction
2 Related work
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Initiating nodes: Each node in the ad hoc network initiates its coordinate and the coordinate’s errors.
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Selecting origin-anchors: Three or more nodes are selected as origin-anchors, whose coordinate errors are considered as zero. Then, a relative coordinate system is built by using those nodes.
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Generating pseudo-anchors: An unknown node selects at least three located nodes from the neighbor nodes set to calculate its position. After the node is located, this node is updated as a pseudo-anchor.
3 Iterative localization based on least squares
4 Localization error upper boundary of anchors with errors
4.1 Orthogonally invariant norms
4.2 Upper boundary of localization error of LLS-RSS iterative algorithm
4.2.1 Upper boundary of localization of error LLS
4.2.2 Error upper boundary of LLS-RSS
4.3 Optimum algorithm of constructing LLS
5 Simulation and discussion
5.1 Evaluation indicator
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SMC: Let initial value of SMC be 0. SMC increases 1, if and only if, the minimum of rough upper bound and the minimum of localization absolute error are both obtained when ith anchor is selected as a BAN.
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LMC: It is similar to SMC. However, LMC increases 1 when localization absolute error is smallest or second smallest in the case of the upper bound is minimum with the same BAN.
5.2 Feasibility of the algorithm
5.3 Randomness of the algorithm
5.4 Effectiveness of the algorithm
5.5 Performance evaluation
5.6 Computational complex
Title | Add | MUL |
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‖Â
i
‖2(i = 1, ⋯, n) |
n(n − 1) |
n
2
|
\( {\left\Vert \varDelta {\boldsymbol{x}}_i\right\Vert}_2^2\left(i=1,\cdots, n\right) \)
| (n − 1) |
n
|
\( {\left\Vert {\boldsymbol{x}}_k-{\boldsymbol{x}}_i\right\Vert}_2^2\left(i,k=1,\cdots, n;k\ne i\right) \)
|
n(n − 1) | (n − 1)2(n − 2) |
\( {\widehat{d}}_i^2\left(i=1,\cdots, n\right) \)
|
n
|
n
|
\( {\left({\widehat{d}}_i^2-{\widehat{d}}_k^2\right)}^2\left(i,k=1,\cdots, n;k\ne i\right) \)
|
n − 1 | (n − 1)2(n − 2) |