Multi-Target Localization and Tracking Using TDOA and AOA Measurements Based on Gibbs-GLMB Filtering

. 2019 Dec 10;19(24):5437. doi: 10.3390/s19245437

Algorithm 1 Particle Filter

1:
for $k = 1, \dots, T$ do
2:
for $i = 1, \dots, N$ do
3:
Sample ${\tilde{X}}_{k}^{(i)} \sim p (\cdot |X_{k - 1}^{(i)}, Z_{k})$ ;
4:
Set ${\tilde{ω}}_{k}^{(i)} = ω_{k - 1}^{(i)} \frac{g_{k} (Z_{k} |{\tilde{X}}_{k}^{(i)}) f_{k |k - 1} ({\tilde{X}}_{k}^{(i)} |X_{k - 1}^{(i)})}{p_{k |k - 1} ({\tilde{X}}_{k}^{(i)} |X_{1 : k - 1}^{(i)}, Z_{1 : k})}$ ;
5:
Normalise weights $ω_{k}^{(i)} = \frac{{\tilde{ω}}_{k}^{(i)}}{\sum_{j = 1}^{N} {\tilde{ω}}_{k}^{(j)}}$ , here $\sum_{i = 1}^{N} ω_{k}^{(i)} = 1$ ;
6:
end for
7:
end for
8:
Resample ${\{ω_{k}^{(i)}, X_{k}^{(i)}\}}_{i = 1}^{N}$ and get ${\{{\tilde{ω}}_{k}^{(i)}, {\tilde{X}}_{k}^{(i)}\}}_{i = 1}^{N}$ ;
9:
Set ${\hat{π}}_{k} = \sum_{i = 1}^{N} ω_{k}^{(i)} δ_{X_{k}^{(i)}}$ as the estimated posterior probability density;