Bandwidth-Aware Traffic Sensing in Vehicular Networks with Mobile Edge Computing

. 2019 Aug 14;19(16):3547. doi: 10.3390/s19163547

Algorithm 2 The Convex-based Data Recovery (CDR) Algorithm

Input: Collected traffic state matrix

X_{m}^{c}

, indication matrix

B_{m}

, regularization coefficient

λ

, rank factor r, and learning rating

l r

Output: Estimation matrix

\hat{X}_{m}

1:
$\hat{P} \leftarrow$ a $m \times r$ matrix generated by standard normal distribution
2:
$\hat{Q} \leftarrow$ a $m \times r$ matrix generated by standard normal distribution
3:
Compute $Ω_{m}$ based on Equation (15)
4:
Compute $C_{m}$ based on Equation (16)
5:
Initialize $e_d i f f = 2$
6:
$p r e_e = 0$
7:
while $e_d i f f > ρ_{3}$ do
8:
for i from 1 to $R_{m}$ do
9:
for j from 1 to T do
10:
${\hat{q}}_{i} = {\hat{q}}_{i} + l r \cdot (e \cdot {\hat{p}}_{j} - λ {\hat{q}}_{i})$
11:
${\hat{p}}_{j} = {\hat{p}}_{j} + l r \cdot (e \cdot {\hat{q}}_{i} - λ {\hat{p}}_{j})$
12:
end for
13:
end for
14:
$e = λ (‖ \hat{P} ‖^{2} + ‖ \hat{Q} ‖^{2}) + ‖ B_{m} . \times (\hat{P} \hat{Q^{T}}) - X_{m}^{c} ‖^{2}$
15:
if $p r e_e > e$ and $i n d e x > 0$ then
16:
$e_d i f f = p r e_e - e$
17:
$\hat{P} \leftarrow \hat{P}$
18:
$\hat{Q} \leftarrow \hat{Q}$
19:
$p r e_e \leftarrow e$
20:
end if
21:
end while
22:
${\hat{X}}_{m} \leftarrow \hat{P} {\hat{Q}}^{T}$
23:
fori from 1 to $R_{m}$ do
24:
for j from 1 to T do
25:
$\hat{x}_{i, j} = \hat{x}_{i, j} + Ω_{m} \cdot C_{m}$
26:
end for
27:
end for
28:
Output ${\hat{X}}_{m}$