A Support Vector Learning-Based Particle Filter Scheme for Target Localization in Communication-Constrained Underwater Acoustic Sensor Networks

. 2017 Dec 21;18(1):8. doi: 10.3390/s18010008

Algorithm 2 Support vector learning-based particle filter algorithm

1:
Initialization: generate $N_{p}$ initial particles ${x_{0}^{i}, i = 1, \dots N_{p}}$ and give them uniform weights ${w_{0}^{i} = 1 / N_{p}, i = 1, \dots, N_{p}}$
2:
for all $k = 1, 2 \dots$ do
3:
for all $i = 1, 2 \dots N_{p}$ do
4:
- Draw particles according to state transition model (4)
5:
$x_{k}^{i} \sim p (x_{k} | x_{k - 1}^{i})$
6:
- Compute the observation according to the Algorithm 1
7:
$Z_{k} = Z_{k}^{(ν + 1)}$
8:
- Compute the likelihood function based on (30): $p (Z_{k} | x_{k}^{i}) = N (Z_{k}; x_{k}^{i}, σ)$
9:
- Update the weights based on (31): $w_{k}^{i} = w_{k - 1}^{i} \frac{1}{\sqrt{2 π} σ} e x p (- \frac{∥ Z_{k} - x_{k}^{i} ∥^{2}}{2 σ^{2}})$
10:
end for
11:
- Obtain total particle weights $w_{k}^{i} (i = 1, 2 \dots N_{p})$
12:
- Normalize the weight: $w_{k}^{i} = w_{k}^{i} / \sum_{i = 1}^{N_{p}} w_{k}^{i}$
13:
- Resample the particles according to the weights $w_{k}^{i}$ :weed out low-weight particles
14:
- Estimate the target state ${\hat{X}}_{k} = \sum_{i = 1}^{N_{p}} w_{k}^{i} x_{k}^{i}$
15:
end for