概率假设密度滤波算法及其在多目标跟踪中的应用
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摘要
随着多目标跟踪理论的日益成熟与深入，多目标跟踪技术已经从军事领域的应用扩展到民用领域，解决多目标跟踪问题的算法也随之层出不穷。经典的数据关联算法对于简单的民用领域具有良好的应用效果，但对于为获取最理想的作战效果，需要对监控区域内的每个目标进行实时准确地跟踪与定位的现代复杂的军事作战系统来说已显得力不从心，因此目标跟踪算法的研究仍具有的重要的理论意义和应用价值。Mahler.R所提出的基于随机集理论的概率假设密度（probability hypothesis Density，PHD）滤波多目标跟踪算法，突破了传统的数据关联方法，具有严格的数学理论基础，大大降低了计算量，并具有估计精度高、易于实现等优点，开拓了多目标跟踪的研究领域。本文在此进基础上进行了深入研究，主要内容如下：
（1）介绍了几种经典的多目标跟踪方法，如Bayes滤波，Kalman滤波以及粒子滤波。在随机集理论的基础上建立了Bayes递推多目标跟踪模型。对目前适用于PHD滤波性能的评估指标进行比较分析，确定适合本文所研究的滤波性能评估方法。为后续的课题研究奠定了理论基础。
（2）对随机集理论在多目标跟踪应用中的可行性进行分析，给出了PHD滤波算法和CPHD滤波算法及其粒子滤波实现和高斯混合滤波实现。分析了基于随机集理论的多目标跟踪滤波算法各自的优缺点及适用的环境与范围，并且针对这些问题做出改进。
（3）针对高斯混合概率假设密度（GM-PHD）滤波算法在强杂波存在的情况下会出现对目标明显漏跟及误跟现象，以及计算量会随着杂波强度的增加而增加的问题，提出了基于核密度估计的高斯混合概率假设密度滤波算法。该算法在高斯混合PHD滤波算法的剪枝、合并步骤之后引入核密度估计理论的Mean-shift算法，对高斯混合PHD分布密度函数进行核密度估计，取代了高斯混合PHD滤波算法中的状态估计方法，选择估计后得到的峰值作为目标状态估计值，很好地达到了排除强杂波干扰、提高跟踪精度、降低运算量的目的。
（4）针对粒子PHD滤波估计精度不高，滤波发散以及CPHD滤波对于局部的目标数目估计存在漏检的问题，提出了SMC-CPHD滤波算法。此方法利用随机样本同时对PHD分布和基数分布进行逼近，解决了滤波运算过程中没有闭式解的难题，而且滤波过程中，随着样本粒子数量的增加，PHDF接近于Bayes最优估计，避免了当某个目标发生漏检时，PHD权值转移的问题。相比于粒子PHD与CPHD的滤波有更可靠的跟踪性能。
（5）针对单传感器只能获得局部、片面的信息，以及对于目标的衍生、消失所引起的目标数目的变化和目标突发的机动会使得单传感器应接不暇的问题。提出了基于自适应“当前”统计模型的多传感器多目标跟踪CPHD滤波算法。针对自适应“当前”统计模型对于目标发生强机动时有很好的自适应能力，而对于目标弱机动时，跟踪性能降低的问题，通过位于观测区域不同位置的3个同类传感器（雷达）的序贯融合实现多目标跟踪，相比于单传感器提高了目标在弱机动时刻的跟踪精度。很好的体现出多传感器信息融合的优势。
（6）将变结构多模型算法与基于随机集理论的高斯混合基数概率假设密度滤波算法相结合，运用到多机动目标跟踪系统中，提出了基于变结构多模型的GMCPHD滤波算法。此方法通过实时变化模型集合来剔除不必要的模型，不至于因为模型之间的“过度”竞争使得滤波性能降低，对于弱机动以及强机动目标的都达到了很好的跟踪效果。
With the multi-target tracking theory getting mature increasingly, the application of themulti-target tracking technique has been developed from military to civilian area. and themethods for solving the multi-target tracking problem emerge endlessly. The classical dataassociation algorithm which is efficient in the simple civilian area have become unsuitable formodern complex military combat system, which need to real-time track and localize everytarget accuratly in the monitor area to achieve the best fighting effectiveness. As a result, theresearch of multi-target tracking algorithm still has some of importance and urgency. Theprobability hypothesis density (PHD) filtering multi-target tracking algorithm based onrandom set theory is put forward by Mahler, which has strict mathematical theory foundationand high estimation precision, reduces the computation burden, can be realized easily, breaksthe traditional data association method and exploit the area of multi-target tracking research.On the basis of above theories, the study contents of this paper are expressed as follows:
(1)Some classical multi-target tracking methods, such as Bayes filtering, Kalmanfiltering and particle filtering, are introduced at first. Bayes recursive multi-target trackingmodel has been set up based on the foundation of random set theory. The evaluation indexcurrently applied to the PHD filtering performance is analyzed and the evaluation methodsuitable to the filtering in this paper is identified. The theoretical foundation is laid for thefollowing research.
(2)The feasibility of the random set theory application in multi-target tracking isanalyzed and the reasons and advantages of choosing random set theory for the multi-target isstated. Then PHD filtering algorithm, CPHD filtering algorithm and the realization of particlefiltering and Gaussian mixture filtering are given out briefly. At last, the filtering algorithmswhich based on random set theory for multi-target tracking are researched and analyzed;meanwhile the advantages, disadvantages, the applicable environment and the scope of eachalgorithm for these algorithms are discussed and some improvements are made.
(3)Because of the presence of strong clutter, Gaussian mixture probability hypothesisDensity filtering algorithm (GMPHDF) will miss targets or tracks wrong targets, and thecalculation burden will increases while the strength of the cluster get bigger. For this reason,the GMPHDF based on kernel density estimation is proposed. After pruning and merging inGaussian mixture PHD filtering algorithm, the Mean-shift algorithm is introduced to estimatekernel density of Gaussian mixture PHD distribution density function, which replaces the state estimation method of Gaussian mixture PHD filtering algorithm. By choosing theestimated peak value as the state estimation of targets, the purpose of ruling out strong clutterinterference is achieved well.
(4)Aiming at the low filtering estimation accuracy, filtering divergence of particlePHD and the undetected problem of local filter number, the SMC-CPHD filtering algorithmis proposed. By using random samples to approach the PHD distribution and the cardinaldistribution simultaneously, the problem that there is no closed solution in the filtering processcan be solved. The PHDF is close to Bayes optimal estimation with the increasing of theparticle sample number, which avoids the weight transfer problem of PHD filter when sometargets miss detection. Comparing with particle PHD and CPHD filtering, it has more reliabletracking ability.
(5)The single sensor can only get local and one-side information and the changing intarget number and the gusty maneuvering of the target caused by target derivation andmission will make single sensor lay off. Aiming at this problem, the CPHD filter algorithmwith multi-sensor for multi-target tracking based on the adaptive “current” statistic model isproposed. The adaptive “current” statistic model has a very good adaptive ability, but thetracking performance would reduce when the targets are in the weak maneuvering state.Therefore, three sensors (radar) set at different places in the observation area are used to takesequential fusion to realize target tracking. Compared to the single sensor method, thismethod increased the tracking accuracy, which reflects the advantage of the multi-sensorinformation fusion.
(6)The Variable Structure Multiple Model algorithm(VSMM) is combined withGaussian Mixture Cardinalized Probability Hypothesis Density (GMCPHD) filter algorithmand applied to the multiple marneuver targets tracking system, which leads to the propositionof filter algorithm based on VSMM. the real-time transform model is used to delete theunnecessary models. Because of excessive competition among the models leads to thereduction of filtering performance, the tracking effectiveness of the algorithm is achieved wellfor both strong maneuver and weak maneuver.
（1）介绍了几种经典的多目标跟踪方法，如Bayes滤波，Kalman滤波以及粒子滤波。在随机集理论的基础上建立了Bayes递推多目标跟踪模型。对目前适用于PHD滤波性能的评估指标进行比较分析，确定适合本文所研究的滤波性能评估方法。为后续的课题研究奠定了理论基础。
（2）对随机集理论在多目标跟踪应用中的可行性进行分析，给出了PHD滤波算法和CPHD滤波算法及其粒子滤波实现和高斯混合滤波实现。分析了基于随机集理论的多目标跟踪滤波算法各自的优缺点及适用的环境与范围，并且针对这些问题做出改进。
（3）针对高斯混合概率假设密度（GM-PHD）滤波算法在强杂波存在的情况下会出现对目标明显漏跟及误跟现象，以及计算量会随着杂波强度的增加而增加的问题，提出了基于核密度估计的高斯混合概率假设密度滤波算法。该算法在高斯混合PHD滤波算法的剪枝、合并步骤之后引入核密度估计理论的Mean-shift算法，对高斯混合PHD分布密度函数进行核密度估计，取代了高斯混合PHD滤波算法中的状态估计方法，选择估计后得到的峰值作为目标状态估计值，很好地达到了排除强杂波干扰、提高跟踪精度、降低运算量的目的。
（4）针对粒子PHD滤波估计精度不高，滤波发散以及CPHD滤波对于局部的目标数目估计存在漏检的问题，提出了SMC-CPHD滤波算法。此方法利用随机样本同时对PHD分布和基数分布进行逼近，解决了滤波运算过程中没有闭式解的难题，而且滤波过程中，随着样本粒子数量的增加，PHDF接近于Bayes最优估计，避免了当某个目标发生漏检时，PHD权值转移的问题。相比于粒子PHD与CPHD的滤波有更可靠的跟踪性能。
（5）针对单传感器只能获得局部、片面的信息，以及对于目标的衍生、消失所引起的目标数目的变化和目标突发的机动会使得单传感器应接不暇的问题。提出了基于自适应“当前”统计模型的多传感器多目标跟踪CPHD滤波算法。针对自适应“当前”统计模型对于目标发生强机动时有很好的自适应能力，而对于目标弱机动时，跟踪性能降低的问题，通过位于观测区域不同位置的3个同类传感器（雷达）的序贯融合实现多目标跟踪，相比于单传感器提高了目标在弱机动时刻的跟踪精度。很好的体现出多传感器信息融合的优势。
（6）将变结构多模型算法与基于随机集理论的高斯混合基数概率假设密度滤波算法相结合，运用到多机动目标跟踪系统中，提出了基于变结构多模型的GMCPHD滤波算法。此方法通过实时变化模型集合来剔除不必要的模型，不至于因为模型之间的“过度”竞争使得滤波性能降低，对于弱机动以及强机动目标的都达到了很好的跟踪效果。
With the multi-target tracking theory getting mature increasingly, the application of themulti-target tracking technique has been developed from military to civilian area. and themethods for solving the multi-target tracking problem emerge endlessly. The classical dataassociation algorithm which is efficient in the simple civilian area have become unsuitable formodern complex military combat system, which need to real-time track and localize everytarget accuratly in the monitor area to achieve the best fighting effectiveness. As a result, theresearch of multi-target tracking algorithm still has some of importance and urgency. Theprobability hypothesis density (PHD) filtering multi-target tracking algorithm based onrandom set theory is put forward by Mahler, which has strict mathematical theory foundationand high estimation precision, reduces the computation burden, can be realized easily, breaksthe traditional data association method and exploit the area of multi-target tracking research.On the basis of above theories, the study contents of this paper are expressed as follows:
(1)Some classical multi-target tracking methods, such as Bayes filtering, Kalmanfiltering and particle filtering, are introduced at first. Bayes recursive multi-target trackingmodel has been set up based on the foundation of random set theory. The evaluation indexcurrently applied to the PHD filtering performance is analyzed and the evaluation methodsuitable to the filtering in this paper is identified. The theoretical foundation is laid for thefollowing research.
(2)The feasibility of the random set theory application in multi-target tracking isanalyzed and the reasons and advantages of choosing random set theory for the multi-target isstated. Then PHD filtering algorithm, CPHD filtering algorithm and the realization of particlefiltering and Gaussian mixture filtering are given out briefly. At last, the filtering algorithmswhich based on random set theory for multi-target tracking are researched and analyzed;meanwhile the advantages, disadvantages, the applicable environment and the scope of eachalgorithm for these algorithms are discussed and some improvements are made.
(3)Because of the presence of strong clutter, Gaussian mixture probability hypothesisDensity filtering algorithm (GMPHDF) will miss targets or tracks wrong targets, and thecalculation burden will increases while the strength of the cluster get bigger. For this reason,the GMPHDF based on kernel density estimation is proposed. After pruning and merging inGaussian mixture PHD filtering algorithm, the Mean-shift algorithm is introduced to estimatekernel density of Gaussian mixture PHD distribution density function, which replaces the state estimation method of Gaussian mixture PHD filtering algorithm. By choosing theestimated peak value as the state estimation of targets, the purpose of ruling out strong clutterinterference is achieved well.
(4)Aiming at the low filtering estimation accuracy, filtering divergence of particlePHD and the undetected problem of local filter number, the SMC-CPHD filtering algorithmis proposed. By using random samples to approach the PHD distribution and the cardinaldistribution simultaneously, the problem that there is no closed solution in the filtering processcan be solved. The PHDF is close to Bayes optimal estimation with the increasing of theparticle sample number, which avoids the weight transfer problem of PHD filter when sometargets miss detection. Comparing with particle PHD and CPHD filtering, it has more reliabletracking ability.
(5)The single sensor can only get local and one-side information and the changing intarget number and the gusty maneuvering of the target caused by target derivation andmission will make single sensor lay off. Aiming at this problem, the CPHD filter algorithmwith multi-sensor for multi-target tracking based on the adaptive “current” statistic model isproposed. The adaptive “current” statistic model has a very good adaptive ability, but thetracking performance would reduce when the targets are in the weak maneuvering state.Therefore, three sensors (radar) set at different places in the observation area are used to takesequential fusion to realize target tracking. Compared to the single sensor method, thismethod increased the tracking accuracy, which reflects the advantage of the multi-sensorinformation fusion.
(6)The Variable Structure Multiple Model algorithm(VSMM) is combined withGaussian Mixture Cardinalized Probability Hypothesis Density (GMCPHD) filter algorithmand applied to the multiple marneuver targets tracking system, which leads to the propositionof filter algorithm based on VSMM. the real-time transform model is used to delete theunnecessary models. Because of excessive competition among the models leads to thereduction of filtering performance, the tracking effectiveness of the algorithm is achieved wellfor both strong maneuver and weak maneuver.
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