OPTILOD: Optimal Beacon Placement for High-Accuracy Indoor Localization of Drones

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. 2024 Mar 14;24(6):1865. doi: 10.3390/s24061865

Algorithm 2 GDOP Optimal Beacon Placement

Input:
Drone domain (D), Beacon domain (B), Beacon Range (R), K-connectivity (K), $G D O P_{a v g}$ threshold (g), The number of required beacons (N) obtained from the other Algorithm, The final set ${P_{1}, \dots, P_{C}}$ obtained from the other Algorithm.
Output:
Optimal Placement for N beacons that provides four-connectivity and keeps the $G D O P_{a v g}$ below the threshold g over the entire domain D.
Initialization:
Individuals in this algorithm are sets of N beacons. The initial individuals are ${P_{1}, \dots, P_{C}}$ from the last algorithm.
Optimization Framework:
1:
while $f o u r - c o n n e c t i v i t y = = 0$ do
2:
while $G D O P_{a v g} > g$ do
3:
for $i = 1$ to $i = C$ do
4:
for all the points $(x, y, z) \in D$ do
5:
Calculate the $G D O P$ at point $(x, y, z)$ from ${(C^{T} C)}^{- 1}$ ;
6:
end for
7:
Calculate the $G D O P_{a v g}$ over all the points in D.
8:
end for
9:
Sort individuals based on the calculated $G D O P_{a v g}$ (fitness) from the lowest to highest (lower is better);
10:
Select the individuals with better fitness as Parents;
11:
Crossover each two adjacent parents and make a new offspring individual;
12:
Kill the worst ones to keep having C individuals;
13:
Update $P_{1}, \dots, P_{C}$ with these new survivor individuals.
14:
end while
15:
if at least one of the ${P_{1}, \dots, P_{C}}$ has the full four-connectivity coverage over entire set D then
16:
$f o u r - c o n n e c t i v i t y = 1$
17:
end if
18:
end while