基于随机集理论的多目标跟踪技术研究
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摘要
目前大多数关于多传感器多目标跟踪的研究工作主要是对传统的数据关联算法的推广,这类算法存在约束条件苛刻、“组合爆炸”以及NP-Hard等问题。而随着近年来随机集理论在信息融合中的应用为多目标跟踪方法提供了系统、严格的数学基础,为解决多传感器多目标跟踪问题提供了强有力工具。基于随机集理论的概率假设密度滤波(PHDF)算法是近年来发展起来的一种非数据关联跟踪算法,该方法绕过了数据关联问题,克服了传统数据关联算法带来的一系列问题,它是多目标跟踪中的一种崭新算法。这类算法具有Bayes意义和较理想的近似结果,能解决复杂环境中的数目变化的多目标跟踪问题。因此,本文重点对随机集理论的PHDF算法展开研究:主要工作和贡献包括如下内容:
(1)在Bayes滤波方法的基础上,介绍了几种具有典型意义的多目标跟踪滤波算法,如kalman滤波(KF)、扩展Kalman滤波(EKF)、无迹Kalman滤波(UKF)以及粒子滤波(PF)。在随机集理论框架下,构建了多目标状态模型和多目标观测模型,并推导出了多目标状态的状态转移密度函数和多目标观测的似然函数。从数学原理上讨论了Bayes滤波和PHDF之间的本质联系,分析了PHDF算法及其评价指标。这部分工作为本文的算法研究做了铺垫。
(2)针对粒子概率假设密度滤波(P-PHDF)算法估计精度不高、滤波发散等问题,引入UKF算法,提出了无迹粒子概率假设密度滤波(UP-PHDF)算法。该算法有效地利用观测信息得到更优的重要性密度函数,在采样精确性上进一步得到提高,从根本上解决了P-PHDF算法由转移概率密度函数中采样所引起的滤波精度低、滤波发散及粒子退化等一些问题。该算法保持了良好的滤波性能,是一种适应性强、估计精度高的跟踪方法,鲁棒性和实时性也得到改善。
(3)为解决复杂环境下的多机动目标跟踪问题,提出了一种基于交互多模型(IMM)的无迹Kalman高斯混合概率假设密度滤波(UK-GMPHDF)算法。该算法结合了IMM算法对不同目标机动模型的自适应能力和UK-GMPHDF估计精度高、计算量小的优点,对处理机动目标跟踪问题显出了强大的优势。实现了在杂波环境下对多机动目标的精确跟踪,大大提高了多机动目标跟踪精度。
(4)为了确保一个多目标跟踪系统的可靠性和稳健性,考虑到PHDF算法的有效性,将PHDF算法从单传感器扩展到多传感器情况。针对集中式多传感器的序贯融合具有信息损失最小,可获得最佳的融合效果的优势,将集中式序贯多传感器与UP-PHDF算法结合,提出一种基于集中式的序贯多传感器多目标跟踪算法,不仅适用于任意的非线性非高斯系统,而且充分体现了异类传感器融合的优越性。
(5)为进一步提高多传感器融合的适用领域,本文将基于随机集的跟踪方法推广到分布式多传感器融合系统。提出了适用于分布式多传感器多目标跟踪的基于UK-GMPHDF的模糊C均值(FCM)聚类融合算法。用UK-GMPHDF完成局部传感器的局部状态估计,然后用FCM算法对这些局部状态进行融合处理,产生目标的全局状态估计。该算法能够处理杂波情况下目标数目不断变化的情况,增强了算法的鲁棒性,提高了算法的跟踪性能,具有一定的工程应用价值。
At present, most research on the multi-sensor multi-target tracking is mainly focusing on the traditional data association algorithm promotion. There are some difficulties such as harsh constraints,“combinatorial explosion”and the NP-Hard problems. With the random sets theory widely applied in information fusion, it provides systematic and rigorous mathematical foundation for multi-target tracking method, and is becoming a powerful tool to solve the multi-sensor multi-target tracking problem. The probability hypothesis density filter (PHDF) based on the random sets theory is one kind of non data association tracking algorithm developed in recent years. This method bypasses the data association question, and overcomes a series of questions caused by the traditional data association algorithm, and is becoming a brand-new algorithm in the multi-target tracking field. As this kind of algorithm has better Bayes significance and approximate result, it can solve number change multi-target tracking problem in the complex environment. Therefore, the article focuses on PHDF algorithm study based on the random sets theory. The prime tasks are as follows:
(1) On the basis of the Bayes filter, several typical multi-target tracking filter algorithms are introduced, such as Kalman filter (KF), extended Kalman filter (EKF), unscented Kalman filter (UKF) as well as particle filter (PF). The multi-target state model and observation model in the background of the random sets theory are constructed, by which the state transition probability density function and observation likelihood function are deduced. The intrinsic relationships between Bayes filter and PHDF are discussed based on mathematical principles, so that the PHDF algorithm and corresponding evaluation indicators are analyzed. This section mainly makes a good foundation for the following chapter's algorithm research.
(2) Considering the particle probability hypothesis density filter (P-PHDF) algorithm estimate precision lower, filter divergence and other issues, this chapter introduces the UKF algorithm, and proposes unscented particle probability hypothesis density (UP-PHDF) algorithm. This algorithm takes use of the observation information effectively to obtain more superior important density function, further improves the sampling accuracy, and fundamentally solves filter accuracy lower, filter divergence, particle degeneration and so on some questions caused by transition probability density sampling in the P-PHDF algorithm. This algorithm maintains a good filter performance, has stronger adaptability, higher tracking precision, and better robustness and timeliness.
(3) To solve multiple maneuvering targets tracking problem under the complex environment, unscented Kalman Gaussian mixture probability hypothesis density filter (UK-GMPHDF) algorithm based on interacting multiple models (IMM) is proposed. The algorithm combines the stronger adaptability of IMM with the higher estimation accuracy and less computation load of UK-GMPHDF to different target maneuvering model, realizes accurate tracking for multiple maneuvering targets under the clutter environment, and greatly improves the accuracy of multiple maneuvering targets tracking.
(4) In order to ensure reliability and robustness of the multi-target tracking system, the PHDF algorithm is ranging from a single sensor to multi-sensor case. Considering that the centralized multi-sensor sequential fusion algorithm has minimal information loss, and can achieve the best fusion effect, in this paper a algorithm combined the centralized sequential multi-sensor with the UP-PHDF algorithm is proposed. It is not only suitable for the random non-linear non-Gauss system, but also manifests heterogeneous sensor superiority.
(5) To improve the application field of the multi-sensor fusion, the fuzzy C-means (FCM) clustering fusion algorithm based on the UK-GMPHDF is proposed for the distributed multi-sensor multi-target tracking. In the algorithm, the UK-GMPHDF is used to complete local state estimation of local sensors, then the FCM algorithm is used to fuse the local state estimation and result global state estimation. This algorithm is able to enhance target number changing in the clutter situation, and has stronger robustness and higher tracking performance.
(1)在Bayes滤波方法的基础上,介绍了几种具有典型意义的多目标跟踪滤波算法,如kalman滤波(KF)、扩展Kalman滤波(EKF)、无迹Kalman滤波(UKF)以及粒子滤波(PF)。在随机集理论框架下,构建了多目标状态模型和多目标观测模型,并推导出了多目标状态的状态转移密度函数和多目标观测的似然函数。从数学原理上讨论了Bayes滤波和PHDF之间的本质联系,分析了PHDF算法及其评价指标。这部分工作为本文的算法研究做了铺垫。
(2)针对粒子概率假设密度滤波(P-PHDF)算法估计精度不高、滤波发散等问题,引入UKF算法,提出了无迹粒子概率假设密度滤波(UP-PHDF)算法。该算法有效地利用观测信息得到更优的重要性密度函数,在采样精确性上进一步得到提高,从根本上解决了P-PHDF算法由转移概率密度函数中采样所引起的滤波精度低、滤波发散及粒子退化等一些问题。该算法保持了良好的滤波性能,是一种适应性强、估计精度高的跟踪方法,鲁棒性和实时性也得到改善。
(3)为解决复杂环境下的多机动目标跟踪问题,提出了一种基于交互多模型(IMM)的无迹Kalman高斯混合概率假设密度滤波(UK-GMPHDF)算法。该算法结合了IMM算法对不同目标机动模型的自适应能力和UK-GMPHDF估计精度高、计算量小的优点,对处理机动目标跟踪问题显出了强大的优势。实现了在杂波环境下对多机动目标的精确跟踪,大大提高了多机动目标跟踪精度。
(4)为了确保一个多目标跟踪系统的可靠性和稳健性,考虑到PHDF算法的有效性,将PHDF算法从单传感器扩展到多传感器情况。针对集中式多传感器的序贯融合具有信息损失最小,可获得最佳的融合效果的优势,将集中式序贯多传感器与UP-PHDF算法结合,提出一种基于集中式的序贯多传感器多目标跟踪算法,不仅适用于任意的非线性非高斯系统,而且充分体现了异类传感器融合的优越性。
(5)为进一步提高多传感器融合的适用领域,本文将基于随机集的跟踪方法推广到分布式多传感器融合系统。提出了适用于分布式多传感器多目标跟踪的基于UK-GMPHDF的模糊C均值(FCM)聚类融合算法。用UK-GMPHDF完成局部传感器的局部状态估计,然后用FCM算法对这些局部状态进行融合处理,产生目标的全局状态估计。该算法能够处理杂波情况下目标数目不断变化的情况,增强了算法的鲁棒性,提高了算法的跟踪性能,具有一定的工程应用价值。
At present, most research on the multi-sensor multi-target tracking is mainly focusing on the traditional data association algorithm promotion. There are some difficulties such as harsh constraints,“combinatorial explosion”and the NP-Hard problems. With the random sets theory widely applied in information fusion, it provides systematic and rigorous mathematical foundation for multi-target tracking method, and is becoming a powerful tool to solve the multi-sensor multi-target tracking problem. The probability hypothesis density filter (PHDF) based on the random sets theory is one kind of non data association tracking algorithm developed in recent years. This method bypasses the data association question, and overcomes a series of questions caused by the traditional data association algorithm, and is becoming a brand-new algorithm in the multi-target tracking field. As this kind of algorithm has better Bayes significance and approximate result, it can solve number change multi-target tracking problem in the complex environment. Therefore, the article focuses on PHDF algorithm study based on the random sets theory. The prime tasks are as follows:
(1) On the basis of the Bayes filter, several typical multi-target tracking filter algorithms are introduced, such as Kalman filter (KF), extended Kalman filter (EKF), unscented Kalman filter (UKF) as well as particle filter (PF). The multi-target state model and observation model in the background of the random sets theory are constructed, by which the state transition probability density function and observation likelihood function are deduced. The intrinsic relationships between Bayes filter and PHDF are discussed based on mathematical principles, so that the PHDF algorithm and corresponding evaluation indicators are analyzed. This section mainly makes a good foundation for the following chapter's algorithm research.
(2) Considering the particle probability hypothesis density filter (P-PHDF) algorithm estimate precision lower, filter divergence and other issues, this chapter introduces the UKF algorithm, and proposes unscented particle probability hypothesis density (UP-PHDF) algorithm. This algorithm takes use of the observation information effectively to obtain more superior important density function, further improves the sampling accuracy, and fundamentally solves filter accuracy lower, filter divergence, particle degeneration and so on some questions caused by transition probability density sampling in the P-PHDF algorithm. This algorithm maintains a good filter performance, has stronger adaptability, higher tracking precision, and better robustness and timeliness.
(3) To solve multiple maneuvering targets tracking problem under the complex environment, unscented Kalman Gaussian mixture probability hypothesis density filter (UK-GMPHDF) algorithm based on interacting multiple models (IMM) is proposed. The algorithm combines the stronger adaptability of IMM with the higher estimation accuracy and less computation load of UK-GMPHDF to different target maneuvering model, realizes accurate tracking for multiple maneuvering targets under the clutter environment, and greatly improves the accuracy of multiple maneuvering targets tracking.
(4) In order to ensure reliability and robustness of the multi-target tracking system, the PHDF algorithm is ranging from a single sensor to multi-sensor case. Considering that the centralized multi-sensor sequential fusion algorithm has minimal information loss, and can achieve the best fusion effect, in this paper a algorithm combined the centralized sequential multi-sensor with the UP-PHDF algorithm is proposed. It is not only suitable for the random non-linear non-Gauss system, but also manifests heterogeneous sensor superiority.
(5) To improve the application field of the multi-sensor fusion, the fuzzy C-means (FCM) clustering fusion algorithm based on the UK-GMPHDF is proposed for the distributed multi-sensor multi-target tracking. In the algorithm, the UK-GMPHDF is used to complete local state estimation of local sensors, then the FCM algorithm is used to fuse the local state estimation and result global state estimation. This algorithm is able to enhance target number changing in the clutter situation, and has stronger robustness and higher tracking performance.
引文
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