基于随机集理论的被动多传感器多目标跟踪
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摘要
被动多传感器多目标跟踪技术是多传感器数据融合系统的重要研究内容之一，在军事和民用领域具有广阔的应用前景，备受国内外专家学者的关注。本论文结合国家自然科学基金（No.60677040，No.60871074），主要研究随机集理论在被动多传感器多目标跟踪领域的应用，取得的主要成果如下：
1.针对被动多传感器量测数据关联中的代价函数选取问题，提出了一种基于距离加权最小二乘的改进代价函数，将距离信息融入最小二乘估计中，并在代价函数中考虑了融合方差的影响，提高了关联精度。在此基础上，针对拉格朗日松弛算法运算量过大的问题，提出了一种基于统计量检验的快速关联算法，通过两次基于指示函数的统计量检验对候选关联集进行化简，在保证较高关联精度的同时，提高了计算效率。最后将改进的代价函数运用于快速关联算法中，有效改善了算法的综合性能。
2.针对乘积形式的多传感器PHD滤波中存在的缩放比例失衡问题，提出一种改进算法，将似然和缩放比例分离开来考虑，先采用乘积形式计算联合似然，再采用求和形式计算缩放比例，有效解决了该问题。然后，针对机动目标跟踪问题，提出一种改进的多模型粒子PHD滤波算法，用粒子拟合目标状态的模型条件PHD强度，通过重采样实现对存活粒子的输入交互，有效解决了模型概率过小时的粒子退化问题。在此基础上，采用Rao-Blackwellized的思想进一步提高采样效率，改善了混合马尔可夫系统下的跟踪性能。
3.针对CPHD滤波中存在的目标漏检问题，提出一种改进算法，首先采用高斯分量标记法进行估计与航迹关联，然后通过对修剪合并后各个高斯分量的权值进行再分配，有效解决了目标漏检问题。在此基础上，针对GMP-CPHD滤波中存在的权值过估问题，提出一种改进算法，在高斯混合框架下，通过一组求积分点传播目标状态估计的均值和方差，在解决观测非线性的同时，避免了粒子滤波可能带来的问题。
4.针对MeMBer滤波中存在的目标数过估问题以及CBMeMBer滤波中存在的量测新息弱化问题，提出了一种IMeMBer算法，通过对漏检目标的多贝努利RFS进行修正，在解决目标数过估问题的同时，避免了CBMeMBer滤波可能导致的量测新息弱化问题。在此基础上，将高斯粒子滤波引入IMeMBer算法中，通过一组高斯粒子近似多贝努利随机集中元素的概率分布，改善了被动测角情况下的跟踪性能。
5.针对随机集滤波的航迹管理问题，提出一种基于模糊聚类的航迹管理算法。该算法充分利用多帧信息，由不同时刻的滤波状态对当前时刻状态进行n步预测，并根据惯性进行加权，最后利用模糊聚类求得当前估计属于每条航迹的隶属度，从而得到最终的航迹。与传统的估计与航迹关联算法不同，该算法在更新每条航迹信息时，不仅仅是简单地对相邻帧之间的对数似然比进行求和，而是通过加权聚类等操作综合考虑了多帧信息，有效提高了航迹维持性能。
The techniques of passive multi-sensor multi-target tracking are important topicsin multi-sensor data fusion systems. Because of the wide applications in both militaryand civil areas, much attention has been paid to their developments by worldwilderesearchers and engineers. Sponsored by the National Natural Science Foundation ofChina, the dissertation mainly investigates the applications of the random finite settheory in the field of passive multi-sensor multi-target tracking. The main contributionsof the dissertation are as follows:
1. To construct a proper cost function for the multi-sensor data associationproblem, a modified cost function is proposed based on the distance weighted leastsquares, which takes the distance information and the fusion covariance into account,with a great improvement of correlation accuracy. Then, to improve the computationalefficiency of the Lagrangian relaxation algorithm, a fast relaxation algorithm isproposed, which directly picks out a part of correct pairs by two statistic tests withoutredundant relaxation and enforcement processes. Finally, the modified cost function isemployed into the fast relaxation algorithm, which efficiently improves the correlationaccuracy and computational efficiency.
2. For the problem of scale unbalance in the product multi-sensor PHD filter, animproved algorithm is proposed, which calculates the joint likelihood function in theproduct form while the scale factor in the summation form, respectively. Then, to solvethe particle degeneration problem in the multiple-model PHD filter for trackingmaneuvering targets, an interacting multiple-model PHD filter is proposed, whichapproximates the model conditional PHD of target states by particles, and makes theinteraction of survival targets by resampling. Finally, the idea of Rao-Blackwellized isintroduced into the improved algorithm to further enhance the performance for jumpMarkov systems with mixed linear/nonlinear state space models.
3. For the problem of missed detection in the CPHD filter, an improved algorithmis proposed, which minimizes the effect of the weight shifting and subsequentestimation errors by a dynamic reweighting scheme after pruning and merging. Then,to solve the weight over estimation problem in the GMP-CPHD filter, a novel CPHDalgorithm based on nonlinear Gaussian filter is proposed, which propagates the meansand covariances of the Gaussian components by a group of quadrature points, and improves the tracking accuracy and computational efficiency.
4. For the problems of target number over estimation in the MeMBer filter and themeasurement innovation weakening in the CBMeMBer filter, respectively, anIMeMBer filter is proposed by modifying the legacy rather than the measurementupdated tracks parameters, which can solve both the problems effectively. Then, toprovide a closed-form solution to the nonlinear problem occurred in the passivebearings-only multi-target tracking system, a set of Gaussian particles is employed toapproximate the distributions of the multi-Bernoulli RFS.
5. For the problem of track management in the RFS based filters, an improvedestimate-to-track association algorithm is proposed. Firstly, a multi-step prediction ofcurrent target states is made, and the weighted labels are assigned to them according tothe inertia. Secondly, the fuzzy membership degrees of the predicted state estimatesbelonging to the current state estimates are obtained by utilizing the maximum entropyfuzzy clustering. Different from the traditional methods, the proposed algorithm doesnot update the track information by simply summing the log likelihood ratios betweenadjacent frames, but takes the entire multi-frame information into account, thus anexcellent performance of track continuity.
1.针对被动多传感器量测数据关联中的代价函数选取问题，提出了一种基于距离加权最小二乘的改进代价函数，将距离信息融入最小二乘估计中，并在代价函数中考虑了融合方差的影响，提高了关联精度。在此基础上，针对拉格朗日松弛算法运算量过大的问题，提出了一种基于统计量检验的快速关联算法，通过两次基于指示函数的统计量检验对候选关联集进行化简，在保证较高关联精度的同时，提高了计算效率。最后将改进的代价函数运用于快速关联算法中，有效改善了算法的综合性能。
2.针对乘积形式的多传感器PHD滤波中存在的缩放比例失衡问题，提出一种改进算法，将似然和缩放比例分离开来考虑，先采用乘积形式计算联合似然，再采用求和形式计算缩放比例，有效解决了该问题。然后，针对机动目标跟踪问题，提出一种改进的多模型粒子PHD滤波算法，用粒子拟合目标状态的模型条件PHD强度，通过重采样实现对存活粒子的输入交互，有效解决了模型概率过小时的粒子退化问题。在此基础上，采用Rao-Blackwellized的思想进一步提高采样效率，改善了混合马尔可夫系统下的跟踪性能。
3.针对CPHD滤波中存在的目标漏检问题，提出一种改进算法，首先采用高斯分量标记法进行估计与航迹关联，然后通过对修剪合并后各个高斯分量的权值进行再分配，有效解决了目标漏检问题。在此基础上，针对GMP-CPHD滤波中存在的权值过估问题，提出一种改进算法，在高斯混合框架下，通过一组求积分点传播目标状态估计的均值和方差，在解决观测非线性的同时，避免了粒子滤波可能带来的问题。
4.针对MeMBer滤波中存在的目标数过估问题以及CBMeMBer滤波中存在的量测新息弱化问题，提出了一种IMeMBer算法，通过对漏检目标的多贝努利RFS进行修正，在解决目标数过估问题的同时，避免了CBMeMBer滤波可能导致的量测新息弱化问题。在此基础上，将高斯粒子滤波引入IMeMBer算法中，通过一组高斯粒子近似多贝努利随机集中元素的概率分布，改善了被动测角情况下的跟踪性能。
5.针对随机集滤波的航迹管理问题，提出一种基于模糊聚类的航迹管理算法。该算法充分利用多帧信息，由不同时刻的滤波状态对当前时刻状态进行n步预测，并根据惯性进行加权，最后利用模糊聚类求得当前估计属于每条航迹的隶属度，从而得到最终的航迹。与传统的估计与航迹关联算法不同，该算法在更新每条航迹信息时，不仅仅是简单地对相邻帧之间的对数似然比进行求和，而是通过加权聚类等操作综合考虑了多帧信息，有效提高了航迹维持性能。
The techniques of passive multi-sensor multi-target tracking are important topicsin multi-sensor data fusion systems. Because of the wide applications in both militaryand civil areas, much attention has been paid to their developments by worldwilderesearchers and engineers. Sponsored by the National Natural Science Foundation ofChina, the dissertation mainly investigates the applications of the random finite settheory in the field of passive multi-sensor multi-target tracking. The main contributionsof the dissertation are as follows:
1. To construct a proper cost function for the multi-sensor data associationproblem, a modified cost function is proposed based on the distance weighted leastsquares, which takes the distance information and the fusion covariance into account,with a great improvement of correlation accuracy. Then, to improve the computationalefficiency of the Lagrangian relaxation algorithm, a fast relaxation algorithm isproposed, which directly picks out a part of correct pairs by two statistic tests withoutredundant relaxation and enforcement processes. Finally, the modified cost function isemployed into the fast relaxation algorithm, which efficiently improves the correlationaccuracy and computational efficiency.
2. For the problem of scale unbalance in the product multi-sensor PHD filter, animproved algorithm is proposed, which calculates the joint likelihood function in theproduct form while the scale factor in the summation form, respectively. Then, to solvethe particle degeneration problem in the multiple-model PHD filter for trackingmaneuvering targets, an interacting multiple-model PHD filter is proposed, whichapproximates the model conditional PHD of target states by particles, and makes theinteraction of survival targets by resampling. Finally, the idea of Rao-Blackwellized isintroduced into the improved algorithm to further enhance the performance for jumpMarkov systems with mixed linear/nonlinear state space models.
3. For the problem of missed detection in the CPHD filter, an improved algorithmis proposed, which minimizes the effect of the weight shifting and subsequentestimation errors by a dynamic reweighting scheme after pruning and merging. Then,to solve the weight over estimation problem in the GMP-CPHD filter, a novel CPHDalgorithm based on nonlinear Gaussian filter is proposed, which propagates the meansand covariances of the Gaussian components by a group of quadrature points, and improves the tracking accuracy and computational efficiency.
4. For the problems of target number over estimation in the MeMBer filter and themeasurement innovation weakening in the CBMeMBer filter, respectively, anIMeMBer filter is proposed by modifying the legacy rather than the measurementupdated tracks parameters, which can solve both the problems effectively. Then, toprovide a closed-form solution to the nonlinear problem occurred in the passivebearings-only multi-target tracking system, a set of Gaussian particles is employed toapproximate the distributions of the multi-Bernoulli RFS.
5. For the problem of track management in the RFS based filters, an improvedestimate-to-track association algorithm is proposed. Firstly, a multi-step prediction ofcurrent target states is made, and the weighted labels are assigned to them according tothe inertia. Secondly, the fuzzy membership degrees of the predicted state estimatesbelonging to the current state estimates are obtained by utilizing the maximum entropyfuzzy clustering. Different from the traditional methods, the proposed algorithm doesnot update the track information by simply summing the log likelihood ratios betweenadjacent frames, but takes the entire multi-frame information into account, thus anexcellent performance of track continuity.
引文
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