Towards Efficient Data Collection in Space-Based Internet of Things

. 2019 Dec 13;19(24):5523. doi: 10.3390/s19245523

Algorithm 2 Sampling Node Selection

Input:

N

M

T_{i}

(

i = 1, \dots, N

D_{i}

(

i = 1, \dots, N

t_{0}

L

T

K

{k_{1}, \dots, k_{N_{k}}} (k = 1, \dots, K)

r_{i}

(

i = 1, \dots, N

w_{1}

w_{2}

Output:

s_{1}, \dots, s_{M}

/* Calculating time dimension curvature ${\bar{c}}_{i}$ */
for each $i \in {1, \dots, N}$ do
$s (t) = C u b i c S p l i n e (T_{i}, D_{i})$ ( $t \in [t_{0} - (L - 1) T, t_{0} - T]$ )
for each $l \in {L - 2, \dots, 2}$ do
$M_{l} = s^{″} (t_{0} - l T)$
$c_{i} (t_{0} - l T) = | M_{l} | / {(1 + {(s^{'} (t_{0} - l T))}^{2})}^{3 / 2}$
end for
${\bar{c}}_{i} = (\sum_{l = 2}^{L - 2} c_{i} (t_{0} - l T)) / (L - 3)$
end for
/* Calculatingspatialdimensioncurvature $k_{G} (p_{i})$ */
for each $k \in {1, \dots, K}$ do
for each $i \in {k_{1}, \dots, k_{N_{k}}}$ do
/* Estimating the normal vector $v_{\min}$ */
${\tilde{N}}_{i} = {p_{i_{1}}, \dots, p_{i_{m}}, p_{i}} = {p_{j} | ‖ p_{i} - p_{j} ‖ < r_{i}}$
${\bar{p}}_{i} = (p_{i_{1}} + \dots + p_{i_{m}}) / m$
$C = {(p_{i_{1}} - {\bar{p}}_{i})}^{2} + \dots + {(p_{i_{m}} - {\bar{p}}_{i})}^{2}$
$v_{\min} = M i n E i g e n v e c t o r (C)$
/* Determining the set of neighbors $N_{i}$ */
$P (p_{i}) = P r o j e c t ({\tilde{N}}_{i}, p_{i})$
$T_{i} = D e l a u n a y (P (p_{i}))$
$N_{i} = {p_{j} | p_{j} is the neighbor of p_{i} in T_{i}}$
/* Calculating Gaussian curvature */
$T_{i}^{'} = T r i G r i d (p_{i}, N_{i})$
$θ = S u m A n g l e ({T^{'}}_{i})$
$A_{mixed} = A r e a M i x e d (p_{i})$
$k_{G} (p_{i}) = (2 π - θ) / A_{mixed}$
end for
end for
for each $i \in {1, \dots, N}$ do
$k_{C_{i}} = w_{1} {\bar{c}}_{i} + w_{2} k_{G} (p_{i})$
end for
${s_{1}, \dots, s_{M}} = S e l e c t M a x (k_{C_{1}}, \dots, k_{C_{N}}, M)$
return $s_{1}, \dots, s_{M}$