A Multiple Target Positioning and Tracking System Behind BrickConcrete Walls Using Multiple Monostatic IRUWB Radars
Abstract
:1. Introduction
2. ThroughWall Radar System
2.1. Hardware Design
2.2. ThroughWall Radar System Process
3. Positioning Algorithm
3.1. Trilateration Algorithm
3.2. DelayandSum Algorithm
3.3. Proposed Algorithm
Algorithm 1 Position Estimation with the Proposed Algorithm 
1. Initialization Generate grids ${{G}_{x,y}^{t}}_{t=0}$ for $x=1,\dots ,X$ and $y=1,\dots ,Y$, considering the coverage and performance of the radar system. For example, in our radar system, one grid is a square of 0.2${\mathrm{m}}^{2}$. 2. For $x=1,\dots ,X$ and $y=1,\dots ,Y$, calculate the cumulative likelihood as follows:
$${G}_{x,y}^{t}={G}_{x,y}^{t1}{\displaystyle \sum}_{i=1}^{N}{\displaystyle \sum}_{k=1}^{M}\mathcal{L}({p}_{x,y}{z}_{i,k}),$$
3. For $x=1,\dots ,X$ and $y=1,\dots ,Y$, normalize the cumulative likelihood for recursive operation as follows:
$${G}_{x,y}^{t}=\frac{{G}_{x,y}^{t}}{{{\displaystyle \sum}}_{x=1}^{X}{{\displaystyle \sum}}_{y=1}^{Y}{G}_{x,y}^{t}},$$
4. Find the coordinates over the threshold to estimate the location of multiple targets such that
$${G}_{x,y}^{t}>{G}_{thresh},$$
5. Calculate the effectivity of grids as follows:
$${N}_{eff}=\frac{1}{{{\displaystyle \sum}}_{x=1}^{X}{{\displaystyle \sum}}_{y=1}^{Y}{\left({G}_{x,y}^{t}\right)}^{2}},$$

3.4. Performance Comparison by Simulation
4. Experimental Results Based on the Designed Throughwall Radar Hardware
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Parameter  Value 

Central Frequency  1.8 GHz 
Bandwidth  2.8 GHz 
Average Transmission Power  −14 dBm 
Parameter  Value 

Position of Radar 1  (−0.49, −0.22) (m) 
Position of Radar 2  (−0.14, −0.22) (m) 
Position of Radar 3  (0.16, −0.22) (m) 
Position of Radar 4  (0.51, −0.22) (m) 
Detection rate of each radar  75% 
False alarm rate of each radar  10% 
Distance error of detected targets  Normal distribution with $\mathsf{\sigma}=0.03$ (m) 
Index  Number of Targets  Scenario 

Scenario 1  1  One target standing at the coordinates (0, 6) (m) 
Scenario 2  3  Three targets standing at the coordinates (1, 4.5), (−1.5, 2.5) and (0, 8) (m) 
Scenario 3  5  Five targets standing at the coordinates (−4, 2), (−2, 6), (0, 9), (3, 7) and (4, 3) (m) 
Scenario 4  2  Two targets standing very close each other 
Scenario 5  2  Two targets moving cross along parallel paths 
Scenario 6  3  Three targets moving along their respective paths 
Scenario 7  2  Two targets moving cross over 
Scenario 8  3  Two targets standing and one target moving 
Scenario 9  1  One target moving in a circle 
Scenario 10  2  One target moving in a circle and one target moving horizontally 
Scenario  Algorithm  Detection Rate (%)  False Alarm Rate (%)  $\mathbf{Position}\mathbf{Error}\left({\mathit{m}}^{2}\right)$ 

1  Trilateration  100  2.43  0.05 
Delay and Sum  99.86  33.95  1.22  
Proposed Algorithm  100  0.71  0.06  
2  Trilateration  99.76  3.99  0.20 
Delay and Sum  98.95  44.37  2.13  
Proposed Algorithm  100  0  0.06  
3  Trilateration  75.29  0.86  0.93 
Delay and Sum  94.41  57.49  7.02  
Proposed Algorithm  77.49  1.14  0.29  
4  Trilateration  98.93  21.26  0.86 
Delay and Sum  54.99  0.57  6.08  
Proposed Algorithm  99.50  0  0.08  
5  Trilateration  98.29  2.14  0.47 
Delay and Sum  93.15  25.11  1.24  
Proposed Algorithm  99.14  1.43  0.09  
6  Trilateration  90.35  7.56  0.59 
Delay and Sum  78.22  8.70  1.00  
Proposed Algorithm  95.91  1.43  0.24  
7  Trilateration  92.15  0.71  0.42 
Delay and Sum  80.39  8.27  1.05  
Proposed Algorithm  92.94  0.43  0.13  
8  Trilateration  99.52  12.27  0.68 
Delay and Sum  79.89  8.56  1.22  
Proposed Algorithm  98.48  1.71  0.13  
9  Trilateration  99.29  1.14  0.14 
Delay and Sum  98.43  12.13  0.59  
Proposed Algorithm  100  0.29  0.13  
10  Trilateration  96.36  1.43  0.29 
Delay and Sum  93.22  25.82  1.62  
Proposed Algorithm  96.93  1.14  0.11 
Index  Scenario 

Scenario 1  One person standing with a natural position at the coordinates (0, 6) (m) 
Scenario 2  Three persons standing with a natural position at (−1, 4), (2, 6) and (0, 9) (m) 
Scenario 3  One person walking back and forth in the radar coverage area 
Scenario  Algorithm  Detection Rate (%)  False Alarm Rate (%)  $\mathbf{Position}\mathbf{Error}\left({\mathbf{m}}^{2}\right)$ 

1  Trilateration  100  0  0.03 
Delay and Sum  100  2.18  0.57  
Proposed Algorithm  100  0  0.09  
2  Trilateration  84.53  1.63  1.35 
Delay and Sum  79.17  5.90  2.35  
Proposed Algorithm  86.65  0.64  0.89  
3  Trilateration  100  0  0.12 
Delay and Sum  97.59  14.82  0.49  
Proposed Algorithm  100  0  0.19 
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Yoo, S.; Wang, D.; Seol, D.M.; Lee, C.; Chung, S.; Cho, S.H. A Multiple Target Positioning and Tracking System Behind BrickConcrete Walls Using Multiple Monostatic IRUWB Radars. Sensors 2019, 19, 4033. https://doi.org/10.3390/s19184033
Yoo S, Wang D, Seol DM, Lee C, Chung S, Cho SH. A Multiple Target Positioning and Tracking System Behind BrickConcrete Walls Using Multiple Monostatic IRUWB Radars. Sensors. 2019; 19(18):4033. https://doi.org/10.3390/s19184033
Chicago/Turabian StyleYoo, Sungwon, Dingyang Wang, DongMin Seol, Chulsoo Lee, Sungmoon Chung, and Sung Ho Cho. 2019. "A Multiple Target Positioning and Tracking System Behind BrickConcrete Walls Using Multiple Monostatic IRUWB Radars" Sensors 19, no. 18: 4033. https://doi.org/10.3390/s19184033