﻿ 多模型GGIW-GLMB算法跟踪机动群目标<sup>*</sup>
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Maneuvering group target tracking with multi-model GGIW-GLMB algorithm
GAN Linhai, LIU Jinmang, WANG Gang, LI Song
Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China
Received: 2018-01-22; Accepted: 2018-04-20; Published online: 2018-05-21 10:42
Foundation item: National Natural Science Foundation of China (61703412, 61503407)
Corresponding author. LIU Jinmang, E-mail:liujinmang1@163.com
Abstract: An multi-model Gamma Gaussian inverse Wishart-generalized labeled multi-Bernoulli (MM-GGIW-GLMB) algorithm is proposed for multiple maneuvering group target tracking. A multi-model approach is introduced for kinematic modeling, and best fitting Gauss (BFG) approximation is used to fuse the multiple models in the prediction stage, which subsequently ease the computational burden of multi-model approach. For a further performance improvement for target maneuvering, strong tracking filter (STF) is introduced to correct the predicted covariance calculated by BFG. The optimal sub-pattern assignment (OSPA) metric and its one standard deviation and labeling correctness are used to measure the maneuvering group target tracking performance of the algorithm. The simulation results indicate that the proposed algorithm can improve the performance of maneuvering group target tracking in accuracy and stability.
Keywords: generalized labeled multi-Bernoulli (GLMB)     Gamma Gaussian inverse Wishart (GGIW)     best fitting Gauss (BFG) approximation     strong tracking filter (STF)     group target tracking

1 背景知识

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GLMB随机有限集的概率密度分布可表示为

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2 GGIW分量的预测与更新 2.1 群目标状态的概率密度分布

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2.2 多模型GGIW分量的预测与更新

2.2.1 基于STF-BFG的GGIW分量预测

1) 群目标GGIW分量的BFG近似预测

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2) STF修正

STF引入时变的渐消因子，迫使输出残差正交，自适应修正状态协方差矩阵，能够增强滤波器对目标状态变化的跟踪能力，提高对目标机动阶段的状态估计精度。多群目标跟踪需要将同一时刻测量得到的所有量测划分成若干子集，每个子集对应一个可能的群目标产生的量测。量测子集W通过STF引入强跟踪渐消因子对第j个GGIW分量的群目标质心运动状态预测协方差Pk|k-1(j, W)进行修正，可得

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2.2.2 GGIW分量更新

GGIW分量的待估状态ξk中，量测比率γk同质心状态xk和扩展状态Xk独立，其对量测子集W的似然函数的概率密度分布为

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j个GGIW分量的更新步骤为

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2.2.3 模型概率更新

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Ψk, rWΨkW的计算相似，不同的是：ΨkW是由BFG近似后的模型对GGIW分量的预测和更新参数计算得到，而Ψk, rW是由各模型分别对GGIW分量的预测和更新参数计算得到的。

3 GLMB分量的预测与更新

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pD(ξ, ℓ)=pD(ℓ)时

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4 仿真实验 4.1 仿真场景

 图 1 运动轨迹仿真背景及质心位置一次仿真估计结果 Fig. 1 Motion trajectory, background and estimated centroid position in one simulation
4.2 算法性能对比

 图 2 质心状态、扩展状态及量测比率OSPA距离及其一倍标准差 Fig. 2 OSPA distance of centroid state, extension state and measurement rate and their one standard deviation
 图 3 目标数目估计及其一倍标准差 Fig. 3 Target number estimation and its one standard deviation

 图 4 MM-GGIW-GLMB及GGIW-GLMB算法各时刻真实航迹频次 Fig. 4 Frequency of real track at each moment in MM-GGIW-GLMB and GGIW-GLMB algorithms
5 结论

1) 针对多机动群目标跟踪的问题，提出了MM-GGIW-GLMB算法，利用随机矩阵将群目标扩展外形建模为椭圆，用GGIW分量描述群目标状态。GLMB分量通过加标签方法产生加标签的航迹估计，引入BFG和STF算法增强对目标机动的跟踪能力。

2) BFG算法通过多模型融合，增强了算法对群目标机动模式的适应性，STF算法通过对预测协方差的修正，增强了算法对群目标机动跟踪的鲁棒性。将加标签正确率作为补充的算法性能度量标准，弥补了仅利用OSPA距离评估GLMB算法性能的不足。

3) 仿真结果表明，MM-GGIW-GLMB算法跟踪多机动群目标的精度、稳定性和航迹标签正确率皆优于文献[14]算法。

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#### 文章信息

GAN Linhai, LIU Jinmang, WANG Gang, LI Song

Maneuvering group target tracking with multi-model GGIW-GLMB algorithm

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(10): 2185-2192
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0053