Symbol

Description

N

Number of nodes in swarm

$n_{\text{CID}}$

Number of communication identifiers in use

$n_{\text{comm}}$

Number of nodes within communication radius

$r_{\text{comm}}$

Communication radius of nodes

$\mathcal{G}\left(\mathcal{V},\mathcal{E}\right)$

Graph with reconstructed nodes indicating positions as vertex $\mathcal{V}$ and distance between nodes as edges $\mathcal{E}$

$i\mathrm{,}j$

Unique (hardware) identification number (UID) of nodes i and j, other letters are also used to indicate other nodes. An additional bar in the indication stresses these are the true values (opposed to measured or hypothesised)

$\text{CID}\left(i\right)$

Communication identification number (CID) used by node i

$d_{i,j}$

Distance between node i and node j. Additional bars in the indication stress that these are true values (opposed to measured of hypothesised).

$s_i$

Position of node i

$\mathcal{C}$

Consistency function used for associating measured distances from two nodes into a mutual connection

${ϵ}_r$

Threshold value for maximum allowed distance deviation in consistency condition $\mathcal{C}$

$h_{i\mathrm{,}j}$

Set of hypothesised distances between node i and j

${\mathbb{A}}_I$

Number of additional identity ambiguities

${\mathbb{A}}_D$

Number of additional distance ambiguities

$a\in \mathcal{A},b\in \mathcal{B},c\in \mathcal{C}$

Individual nodes (small letter) in a set of nodes (capital) selected based on some criteria in reconstruction algorithm

$\mathcal{Q},\mathcal{Q}\left(b\right)$

Cliques in already reconstructed graph

$X\mathrm{,}Y\mathrm{,}Z$

Recall percentages of nodes that have been reconstructed; Y and Z have an additional condition on the accuracy of the reconstruction

${\mathbb{E}}_{\text{abs}},{\mathbb{E}}_{\text{glob}},{\mathbb{E}}_{\text{loc}}$

Error metrics of a reconstruction indicating the mean absolute squared error of the reconstructed positions

${\mathbb{E}}_{\text{rel}}$

Error metric of a reconstruction indicating the relative error of the reconstructed distances

$\nu$

Different noise parameters of distance measurements, expressed in percentages. Index indicates type of noise.