Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (4): 1030-1039.doi: 10.13229/j.cnki.jdxbgxb.20210776

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Variational Bayesian cooperative target tracking with unknown localization noise statistics

Xiao-bo CHEN(),Ling CHEN   

  1. Automotive Engineering Research Institute,Jiangsu University,Zhenjiang 212013,China
  • Received:2021-08-12 Online:2023-04-01 Published:2023-04-20

Abstract:

In order to enhance the reliability of cooperative target tracking under unknown localization noise statistics, a Bayesian model is proposed for joint estimation of the states of target vehicle and cooperative vehicle and localization noise statistics parameters. An online variational Bayesian inference algorithm is further developed to realize recursive estimation. The simulation results show that the algorithm can effectively improve the accuracy of target tracking when the statistical characteristics of localization noise is uncertain and changes dynamically. Comparing with non-cooperative algorithm, the tracking error can be reduced by 18.7%~23.6%. In comparison with other cooperative algorithms, the tracking error can be reduced by 4.8%~9.7%.

Key words: vehicle engineering, multi-vehicle cooperative, target tracking, variational Bayesian inference, joint state estimation

CLC Number: 

  • TP301.6

Fig.1

Scenario diagram of cooperative target tracking"

Fig.2

Schematic diagram of model Bayesian structure"

Fig.3

Position of TV and CV in the HV coordinate system"

Fig.4

Dynamic variation of heading angle of CV in HV coordinate system"

Fig.5

Observation position of TV in CV coordinate system"

Table 1

Comparison of tracking performance of different algorithms with σ2=0.1"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.36040.36040.3618
[100~200]0.22900.19050.19350.1805
[200~300]0.19050.16320.16460.1467
[300~400]0.17110.14710.14270.1310
1~400]0.26790.21490.21490.2046

Table 2

Comparison of tracking performance of different algorithms with σ2=0.2"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.37560.37560.3635
[100~200]0.22900.20220.20030.1883
[200~300]0.19050.17070.16950.1550
[300~400]0.17110.15500.14590.1335
1~400]0.26790.22550.22240.2097

Table 3

Comparison of tracking performance of different algorithms with σ2=0.3"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.38650.38650.3657
[100~200]0.22900.20960.20440.1925
[200~300]0.19050.17490.17210.1598
[300~400]0.17110.15990.14780.1356
1~400]0.26790.23230.22730.2130

Table 4

Comparison of tracking performance of different algorithms with σ2=0.4"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.39480.39480.3683
[100~200]0.22900.21500.20730.1952
[200~300]0.19050.17780.17380.1630
[300~400]0.17110.16340.14920.1374
1~400]0.26790.23740.23090.2156

Table 5

Comparison of tracking performance of different algorithms with σ2=0.5"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.40120.40120.3713
[100~200]0.22900.21910.20940.1972
[200~300]0.19050.18010.17520.1652
[300~400]0.17110.16620.15040.1389
1~400]0.26790.24120.23360.2177

Fig.6

Variation curve of tracking errors of TV by different algorithms"

Fig.7

Comparison of tracking performance of three methods"

Fig.8

Trajectory of CV under different motion models"

Table 6

Comparison of tracking performance of different algorithms with σ2=0.3 under scene 1"

时 段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.38700.38700.3747
[100~200]0.22900.20880.20450.1946
[200~300]0.19050.17240.16940.1594
[300~400]0.17110.16170.14830.1394
1~400]0.26790.23210.22690.2166

Table 7

Comparison of tracking performance of different algorithms with σ2=0.3 under scene 2"

时段KFEKF?C/SEKF?C/DVBIW?C
1~100]0.48310.38700.38700.3747
[100~200]0.22900.20900.20460.1949
[200~300]0.19050.17550.17280.1638
[300~400]0.17110.15840.14980.1398
1~400]0.26790.23210.22810.2179

Table 8

Execution time of different algorithms"

σ2KFEKF?C/SEKF?C/DVBIW?C
0.10.01500.02900.02980.1197
0.20.01530.02910.02930.1203
0.30.01500.02880.02940.1190
0.40.01580.02900.02920.1184
0.50.01590.02950.02900.1180

Fig.9

Graph of tracking error as forgetting factor changes"

Fig.10

Illustration of tracking error as number of iteration changes"

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