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摘要: 针对杂波环境下多机动扩展目标跟踪问题, 提出一种基于高斯过程的变结构多模型联合概率数据关联方法.首先, 采用期望模型扩展方法构建自适应模型集, 并对各个扩展目标状态进行初始化.其次, 基于高斯过程建立联合跟踪门以选择有效量测, 形成联合关联矩阵.然后, 拆分联合关联矩阵得到可行关联矩阵并求解关联事件概率.最后, 利用联合概率数据关联滤波器更新各个扩展目标的状态和协方差, 并将更新的状态进行融合, 得到最终的状态估计.仿真验证了所提方法的有效性.Abstract: Aiming at the problem of multiple maneuvering extended target tracking in clutter, a variable structure multiple model joint probabilistic data association method based on Gaussian process is proposed. Firstly, the adaptive model set is constructed by the expecting model augmentation method, and each extended target state is initialized. Secondly, based on the Gaussian process, the joint validation gate of extended target is established to select the valid measurements and to form the joint association matrix. Then, the joint association matrix is splitted to obtain the feasible association matrix and the probabilities of association events are calculated. Finally, the joint probabilistic data association filter is used to update the state and covariance of each extended target, and the updated states are fused to obtain the final state estimation. Simulation result verifies the effectiveness of the algorithm.
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Key words:
- Gaussian process /
- multiple maneuvering extended target /
- expecting model augmentation /
- variable structure multiple model /
- joint probabilistic data association
1) 本文责任编委 赖剑煌 -
表 1 不同参数下两种方法的位置估计误差(m)
Table 1 Position estimation error of two algorithms against different parameters (m)
参数 参数值 IMM-RM GP-VSMM-JPDA $P_D$ 0.65 0.7890 0.6531 0.80 0.4307 0.3358 0.90 0.3189 0.2375 $\sigma_2$ 1.0 0.3189 0.2375 2.0 0.5735 0.4518 4.0 0.8306 0.7331 
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表 2 不同参数下两种方法的速度估计误差(m/s)
Table 2 Velocity estimation error of two algorithms against different parameters (m/s)
参数 参数值 IMM-RM GP-VSMM-JPDA $P_D$ 0.65 0.7890 0.6531 0.80 0.4307 0.3358 0.90 0.3189 0.2375 $\sigma_2$ 1.0 0.3189 0.2375 2.0 0.5735 0.4518 4.0 0.8306 0.7331
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表 3 三种方法在不同参数下的中心点位置估计误差(m)
Table 3 Position estimation error of three algorithms against different parameters (m)
参数 参数值 ET-GM-PHD GPR-MM-ETT GP-VSMM-JPDA $P_D$ 目标1 目标2 目标3 目标1 目标2 目标3 目标1 目标2 目标3 0.65 1.3134 1.1359 1.1021 1.3025 0.9516 0.9383 0.9859 0.8447 0.8103 0.80 0.7723 0.6106 0.5863 0.5517 0.4731 0.4419 0.4561 0.4091 0.3947 0.95 0.6865 0.4563 0.4416 0.4330 0.3616 0.3501 0.2304 0.2197 0.2053 $\lambda_c\, /{\rm m}^{-2}$ 0.0001 0.5947 0.4132 0.3958 0.3245 0.2919 0.2767 0.2038 0.1825 0.1807 0.0002 0.6865 0.4563 0.4331 0.4330 0.3616 0.3501 0.2304 0.2197 0.2053 0.0004 1.1647 1.0537 0.9873 0.9107 0.8491 0.7904 0.7537 0.6735 0.6691
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表 4 三种方法在不同参数下的速度估计误差
Table 4 Velocity estimation error of three algorithms against different parameters (m/s)
参数 参数值 ET-GM-PHD GPR-MM-ETT GP-VSMM-JPDA $P_D$ 目标1 目标2 目标3 目标1 目标2 目标3 目标1 目标2 目标3 0.65 0.8051 0.7340 0.7021 0.6418 0.5622 0.5141 0.5827 0.5136 0.4835 0.80 0.5380 0.5027 0.4715 0.4135 0.3947 0.3691 0.3968 0.3429 0.3152 0.95 0.4127 0.3901 0.3684 0.3241 0.3028 0.2731 0.2719 0.2708 0.2493 $\lambda_c\, /{\rm m}^{-2}$ 0.0001 0.3865 0.3310 0.3174 0.2907 0.2347 0.2109 0.2576 0.2178 0.1844 0.0002 0.4127 0.3901 0.3684 0.3241 0.3028 0.2731 0.2719 0.2708 0.2493 0.0004 0.7261 0.6317 0.5715 0.5108 0.4410 0.3947 0.4631 0.4147 0.3716
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表 5 三种方法在不同参数下的正确航迹率
Table 5 Correct track probability of three algorithms against different parameters
参数 参数值 ET-GM-PHD GPR-MM-ETT GP-VSMM-JPDA $P_D$ 目标1 目标2 目标3 目标1 目标2 目标3 目标1 目标2 目标3 0.65 0.65 0.73 0.79 0.76 0.85 0.88 0.81 0.85 0.87 0.80 0.77 0.81 0.85 0.87 0.91 0.91 0.90 0.93 0.91 0.95 0.82 0.84 0.90 0.91 0.94 0.93 0.93 0.96 0.95 $\lambda_c\, /{\rm m}^{-2}$ 0.0001 0.88 0.93 0.93 0.93 0.97 0.94 0.95 0.97 0.96 0.0002 0.82 0.84 0.90 0.91 0.94 0.93 0.93 0.96 0.95 0.0004 0.71 0.77 0.85 0.82 0.85 0.87 0.84 0.88 0.87
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