目标跟踪中的粒子滤波与概率假设密度滤波研究
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摘要
点目标跟踪问题是指在杂波环境中,根据受噪声干扰的传感器测量序列,对可以忽略形状、颜色等外观信息的目标状态进行估计,并估计出目标航迹的过程。点目标跟踪在定位、导航、工业控制等军事和民用领域有着广泛的应用。
根据监测区域内目标的个数,点目标跟踪可以划分为单目标跟踪和多目标跟踪,单目标跟踪中如何利用测量进行有效的滤波,实时给出准确的状态估计是其研究的核心内容;根据目标数目的情况,多目标跟踪又分为数目已知且固定的多目标跟踪,数目未知且随时间变化的多目标跟踪,后者在实际中有着更为广泛的应用范围和更高的技术难度。在存在杂波对测量的干扰和影响的情况下,利用带有噪声的传感器测量,对运动方式复杂多变的目标进行连续跟踪具有很大的不确定性,是十分具有挑战性和具有重要研究价值的课题。
本文分别针对单目标和未知时变的多目标跟踪问题进行了研究。对于单目标跟踪问题,由于不必考虑测量与目标的关联关系,因此以跟踪算法即滤波算法研究为核心,针对具有典型非线性特征的雷达测角等测量模型,采用以粒子滤波为核心的滤波跟踪方法,重点解决粒子滤波算法中的计算效率问题,同时通过解决样本枯竭问题,降低重采样算法中的多样性损失,提高粒子滤波的估计精度,从而提高对单目标的跟踪性能;对于未知时变的多目标跟踪问题,则以基于概率假设密度(Probability Hypothesis Density, PHD)滤波的目标状态估计和连续跟踪方法为主要研究内容,通过推导权值域的单目标PHD分解形式来估计多个目标的状态,同时结合粒子标签和航迹管理来形成目标的连续航迹。
首先,在基于粒子滤波的单目标跟踪算法研究方面:
(1)针对粒子滤波为解决退化问题引入重采样而导致的样本枯竭和多样性损失问题,提出了基于准蒙特卡罗(Quasi-Monte Carlo, QMC)的采样重采样算法,用在大权重样本邻域内生成具有低差异性的QMC序列来代替一般重采样算法中对大权重样本的复制过程,一方面解决了重采样后样本的枯竭和多样性损失问题,降低样本的目标失跟概率;另一方面利用QMC序列的低差异性,获取高于一般蒙特卡罗采样方法的估计精度,从上述两个方面提高粒子滤波的跟踪精度。
(2)针对粒子滤波的样本容量大,跟踪效率受样本容量影响明显的问题,在多分辨粒子滤波的基础上,提出基于滤波系统状态检验的样本容量控制算法。利用粒子滤波的样本集在空间域中的多分辨分解形式,在相似样本中提取关键样本,以降低总样本容量。为了监测系统是否出现滤波失效,定义了粒子滤波的系统拟测量误差等相关统计量,通过检测系统状态,对样本容量进行自适应调节,保证滤波精度的稳定,同时提高粒子滤波的跟踪效率。
其次,在基于粒子概率假设密度滤波的多目标状态估计与连续跟踪方法研究方面:
(1)针对概率假设密度滤波过程仅输出多目标分布的概率密度,无法直接输出目标的状态估计的问题,提出粒子单目标PHD滤波方法,通过构造PHD样本权值向量,从PHD的状态预测和测量更新公式中推导出单目标的粒子PHD分解公式,从混合的多目标后验PHD中同时分离出单个目标的后验PHD形式,从而利用粒子权值分量描述的单目标PHD实现所有目标的状态提取,从原理层面上解决基于粒子概率假设密度滤波的多目标状态估计问题。
(2)针对PHD滤波的输出状态的集合无序性,无法给出目标时间域上的状态关联问题,在提出的单目标PHD滤波的基础上,提出一种结合标签的粒子层状态关联方法,定义了基于权值向量的状态间关联矩阵,同时建立了结合一步预测的关联规则,通过追踪样本权值向量在测量域上的移动来判定目标状态的前后帧关系,进而给出目标状态的标识,形成连续航迹;在包含杂波的广义状态估计的基础上,构建了状态假设、伪航迹剪枝、状态估计反馈的环状粒子概率假设密度滤波跟踪器模型,解决了数目未知时变的多目标的连续跟踪问题。
Punctual target tracking problem is to estimate the target states, whose appearance features such as shape and color can be ignored, and provide their trajectories from a discrete set of noisy measurements in clutter. Punctual target tracking are wildly applied in military and civil fields such as location, navigation, industrial control and so on.
Punctual target tracking is decomposed of single-target tracking and multiple target tracking according to the number of targets existing in the survillance region. Besides, multi-target tracking scene includes a fixed and known number of target tracking and a time-varying and unknown number of target tracking, obviously, the latter has a wilder application and is harder to resolve. Furthermore, when targets move complicatedly in clutter, it is a challenge and valuable issue to obtain their continuious trajectories from noisy measurements.
This dissertation mainly addresses the issues that single target and a time-varying unknown number of targets tracking problem. In single target tracking, since data association is not necessary to consider, the key issue is the tracking algorithm, that is, filter algorithm. This dissertation uses particle filter to handle target tracking problem with nonlinear or non-Gaussian dynamic model from some classical sensors such as radar. In order to improve the performance of particle filter in single target tracking, we resolve the sample impoverishment, improve the computational efficiency and reduce the loss of variation of samples in resampling step. In the field of an unknown time-varying number of targets tracking, this dissertation focuses on the probability hypothesis density (PHD) filter and mainly addresses the issues of multi-target state estimation and track continuity. The single-target PHD decomposition is constructed in weight domain. Based on single-target PHDs from particle-PHD filter, this dissertation estimates the states of targets and identifies target trajectories by combining particle-labelling association and track management.
Firstly, in single-target tracking based on particle filter,
(1) Aimming at the sample impoverishment caused by rempling algorithm, this dissertation proposes a new resampling algorithm exploiting quasi-Monte Carlo (QMC) method. This algorithm generates QMC sequences around the particles with heavy weights instead of multiplying them. This scheme improves the tracking performance of particle filter from two aspects, on one hand; it solves the impoverishment of samples caused by resampling and reduces the probability of target miss-tracking. On the other hand, the estimation accuracy can be improved by taking advantage of low-discrepancy of the QMC sequence.
(2) A large number of particles propogated in the iterations of particle filter result in low tracking efficiency. Based on multi-resolutional particle filter, this disserstein proposes a sample-size control method combining with filtering performance detecting. This algorithm extracts representative particles from all sets of similar particles and reduces the number of particles. Several statistic values are further defined, including quasi-measurement error, to detect whether the particle filter falls into failure. Based on these performance parameters, a sample set control algorithm for a multi-resolvational particle filter is proposd. In this scheme samples are increased if the failure has been proved to happen, which maintains the performance of filtering, and meanwhile improves the efficiency of tracking.
Secondly, in particle probability hypothesis density (PHD) filter for multi-target state estimation and track continuity,
(1) Particle filter implementation of the PHD filter has demonstrated a feasible suboptimal method for tracking multi-target in real-time. To obtain the target states, the peak-extraction from the posterior PHD particles needs to be implemented. This disserstein derives a decomposition of single-target PHD form. Based on it, a new state estimation method is proposed, which doesn’t need to extract the PHD peaks by clustering analysis. The method provides a single-target PHD expression derived from the updated PHD equation. The target states can be directly estimated from the single-target PHD sequentially.
(2) In the aspects of track continuity, PHD filter can not provide the track-valued estimates. It is a drawback of PHD filter when it is necessary to identify the individual target trajectories. State association among frames is needed to estimate the individual target trajectories. A new particle PHD filter tracker is proposed. The method extends particle-labeling association to the single-target PHD filter, associates target location estimates among time frames by combining particle-labeling association with state prediction. Furthermore, in order to filter out clutter, a new single-target PHD filter tracking model is constructed, which includes state candidate estimation, pruning, and state estimates feedback. This framework resolves the problem of multi-target tracking continuity.
根据监测区域内目标的个数,点目标跟踪可以划分为单目标跟踪和多目标跟踪,单目标跟踪中如何利用测量进行有效的滤波,实时给出准确的状态估计是其研究的核心内容;根据目标数目的情况,多目标跟踪又分为数目已知且固定的多目标跟踪,数目未知且随时间变化的多目标跟踪,后者在实际中有着更为广泛的应用范围和更高的技术难度。在存在杂波对测量的干扰和影响的情况下,利用带有噪声的传感器测量,对运动方式复杂多变的目标进行连续跟踪具有很大的不确定性,是十分具有挑战性和具有重要研究价值的课题。
本文分别针对单目标和未知时变的多目标跟踪问题进行了研究。对于单目标跟踪问题,由于不必考虑测量与目标的关联关系,因此以跟踪算法即滤波算法研究为核心,针对具有典型非线性特征的雷达测角等测量模型,采用以粒子滤波为核心的滤波跟踪方法,重点解决粒子滤波算法中的计算效率问题,同时通过解决样本枯竭问题,降低重采样算法中的多样性损失,提高粒子滤波的估计精度,从而提高对单目标的跟踪性能;对于未知时变的多目标跟踪问题,则以基于概率假设密度(Probability Hypothesis Density, PHD)滤波的目标状态估计和连续跟踪方法为主要研究内容,通过推导权值域的单目标PHD分解形式来估计多个目标的状态,同时结合粒子标签和航迹管理来形成目标的连续航迹。
首先,在基于粒子滤波的单目标跟踪算法研究方面:
(1)针对粒子滤波为解决退化问题引入重采样而导致的样本枯竭和多样性损失问题,提出了基于准蒙特卡罗(Quasi-Monte Carlo, QMC)的采样重采样算法,用在大权重样本邻域内生成具有低差异性的QMC序列来代替一般重采样算法中对大权重样本的复制过程,一方面解决了重采样后样本的枯竭和多样性损失问题,降低样本的目标失跟概率;另一方面利用QMC序列的低差异性,获取高于一般蒙特卡罗采样方法的估计精度,从上述两个方面提高粒子滤波的跟踪精度。
(2)针对粒子滤波的样本容量大,跟踪效率受样本容量影响明显的问题,在多分辨粒子滤波的基础上,提出基于滤波系统状态检验的样本容量控制算法。利用粒子滤波的样本集在空间域中的多分辨分解形式,在相似样本中提取关键样本,以降低总样本容量。为了监测系统是否出现滤波失效,定义了粒子滤波的系统拟测量误差等相关统计量,通过检测系统状态,对样本容量进行自适应调节,保证滤波精度的稳定,同时提高粒子滤波的跟踪效率。
其次,在基于粒子概率假设密度滤波的多目标状态估计与连续跟踪方法研究方面:
(1)针对概率假设密度滤波过程仅输出多目标分布的概率密度,无法直接输出目标的状态估计的问题,提出粒子单目标PHD滤波方法,通过构造PHD样本权值向量,从PHD的状态预测和测量更新公式中推导出单目标的粒子PHD分解公式,从混合的多目标后验PHD中同时分离出单个目标的后验PHD形式,从而利用粒子权值分量描述的单目标PHD实现所有目标的状态提取,从原理层面上解决基于粒子概率假设密度滤波的多目标状态估计问题。
(2)针对PHD滤波的输出状态的集合无序性,无法给出目标时间域上的状态关联问题,在提出的单目标PHD滤波的基础上,提出一种结合标签的粒子层状态关联方法,定义了基于权值向量的状态间关联矩阵,同时建立了结合一步预测的关联规则,通过追踪样本权值向量在测量域上的移动来判定目标状态的前后帧关系,进而给出目标状态的标识,形成连续航迹;在包含杂波的广义状态估计的基础上,构建了状态假设、伪航迹剪枝、状态估计反馈的环状粒子概率假设密度滤波跟踪器模型,解决了数目未知时变的多目标的连续跟踪问题。
Punctual target tracking problem is to estimate the target states, whose appearance features such as shape and color can be ignored, and provide their trajectories from a discrete set of noisy measurements in clutter. Punctual target tracking are wildly applied in military and civil fields such as location, navigation, industrial control and so on.
Punctual target tracking is decomposed of single-target tracking and multiple target tracking according to the number of targets existing in the survillance region. Besides, multi-target tracking scene includes a fixed and known number of target tracking and a time-varying and unknown number of target tracking, obviously, the latter has a wilder application and is harder to resolve. Furthermore, when targets move complicatedly in clutter, it is a challenge and valuable issue to obtain their continuious trajectories from noisy measurements.
This dissertation mainly addresses the issues that single target and a time-varying unknown number of targets tracking problem. In single target tracking, since data association is not necessary to consider, the key issue is the tracking algorithm, that is, filter algorithm. This dissertation uses particle filter to handle target tracking problem with nonlinear or non-Gaussian dynamic model from some classical sensors such as radar. In order to improve the performance of particle filter in single target tracking, we resolve the sample impoverishment, improve the computational efficiency and reduce the loss of variation of samples in resampling step. In the field of an unknown time-varying number of targets tracking, this dissertation focuses on the probability hypothesis density (PHD) filter and mainly addresses the issues of multi-target state estimation and track continuity. The single-target PHD decomposition is constructed in weight domain. Based on single-target PHDs from particle-PHD filter, this dissertation estimates the states of targets and identifies target trajectories by combining particle-labelling association and track management.
Firstly, in single-target tracking based on particle filter,
(1) Aimming at the sample impoverishment caused by rempling algorithm, this dissertation proposes a new resampling algorithm exploiting quasi-Monte Carlo (QMC) method. This algorithm generates QMC sequences around the particles with heavy weights instead of multiplying them. This scheme improves the tracking performance of particle filter from two aspects, on one hand; it solves the impoverishment of samples caused by resampling and reduces the probability of target miss-tracking. On the other hand, the estimation accuracy can be improved by taking advantage of low-discrepancy of the QMC sequence.
(2) A large number of particles propogated in the iterations of particle filter result in low tracking efficiency. Based on multi-resolutional particle filter, this disserstein proposes a sample-size control method combining with filtering performance detecting. This algorithm extracts representative particles from all sets of similar particles and reduces the number of particles. Several statistic values are further defined, including quasi-measurement error, to detect whether the particle filter falls into failure. Based on these performance parameters, a sample set control algorithm for a multi-resolvational particle filter is proposd. In this scheme samples are increased if the failure has been proved to happen, which maintains the performance of filtering, and meanwhile improves the efficiency of tracking.
Secondly, in particle probability hypothesis density (PHD) filter for multi-target state estimation and track continuity,
(1) Particle filter implementation of the PHD filter has demonstrated a feasible suboptimal method for tracking multi-target in real-time. To obtain the target states, the peak-extraction from the posterior PHD particles needs to be implemented. This disserstein derives a decomposition of single-target PHD form. Based on it, a new state estimation method is proposed, which doesn’t need to extract the PHD peaks by clustering analysis. The method provides a single-target PHD expression derived from the updated PHD equation. The target states can be directly estimated from the single-target PHD sequentially.
(2) In the aspects of track continuity, PHD filter can not provide the track-valued estimates. It is a drawback of PHD filter when it is necessary to identify the individual target trajectories. State association among frames is needed to estimate the individual target trajectories. A new particle PHD filter tracker is proposed. The method extends particle-labeling association to the single-target PHD filter, associates target location estimates among time frames by combining particle-labeling association with state prediction. Furthermore, in order to filter out clutter, a new single-target PHD filter tracking model is constructed, which includes state candidate estimation, pruning, and state estimates feedback. This framework resolves the problem of multi-target tracking continuity.
引文
[1]杨廷梧.基于多传感器的机动目标跟踪与融合技术综述[J].飞行试验. 2004, 20(2):2-8
[2]权太范.目标跟踪新理论与技术[M].北京:国防工业出版社.2009:1-2
[3] Takamitsu Okada, Shingo Tsujimichi, Yoshio Kosuge. Tracking of a Highly Maneuvering Target Using a Radar Multisensor and an Angle Sensor [J] .Electronics and Communications in Japan, Part 1. 2001, 84(2):99-109
[4] Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems [J]. Transaction of the ASME—Journal of Basic Engineering. 1960. 82:35-45
[5] Julier, SimonJ, Jeffrey K Uhlmann. A New extension of the Kalman filter to nonlinear systems [C]. Proceedings of SPIE Signal Processing, Sensor Fusion, and Target Recognition VI. Vol. 3068, p. 182-193.
[6] Eric A. Wan, Rudolph van der Merwe. The Unscented Kalman Filter for Nonlinear Estimation [C]. Proceedings of IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000. AS-SPCC. 153– 158
[7] Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. http://www.cim.mcgill.ca/~dudek/417/papers/kalman_intro.pdf
[8] N.J. Gordon, D.J. Salmond, A.F.M. Smith. Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation [J]. IEE Proceedings of Radar and Signal Processing- F .1993, 140(2): 107-111
[9] Mahler R. A Theoretical Foundation for the Stein Winter Probability Hypothesis Density (PHD) Multi-target Tracking Approach [C]. Processing of the MSS Symposium on Sensor and Data Fusion. 2000
[10] Mahler R. Multi-target Bayes Filtering via First-order Multi-target Moments [J]. IEEE Transactions on Aerospace and Electronic Systems .2003, 39(4):1152-1178
[11] K Panta, B. Vo, S. Singh, and A. Doucet. Probability hypothesis density versus multiple hypothesis tracking [J]. Signal Processing, Sensor Fusion and Target Recognition XIII, 5429:284–295, 2004
[12] Blom, H.A.P. Bar-Shalom, Y. The interacting multiple model algorithm for systems with Markovian switching coefficients [J]. IEEE Transactions on Automatic Control. 1988, 33(8):780– 783
[13] Bar-Shalom Yaakov, Challa Subhash, Blom Henk A.P. IMM estimator versus optimal estimator for hybrid systems [J]. IEEE Transactions on Aerospace and Electronic Systems. 2005, 41(3): 986-991
[14] B. Ristic, S. Arulampalam, N. Gordon .Beyond the Kalman Filter: Particle Filters for Tracking Applications [M]. Artech House. Boston, London. 2004:21-49
[15] R.Nordlund, P. J. Particle filters for positioning, navigation, and tracking [J]. IEEE Transactions on Signal Processing. 2002, 50(2): 425-43
[16] Yvo Boers. A Particle Filter Multi Target Track Before Detect Application: Some Special Aspects [C]. Proceedings of the Seventh International Conference on Information Fusion. 2004, 701-708
[17] Rudolph van der Merwe, Arnaud Doucet, Nando de Freitas, Eric Wan. The Unscented Particle Filter .Technical Report CUED/F-INFENG/TR 380. Cambridge University Department of Engineering, 2000
[18] L. Hong, Devert Wicker. A Spatial-domain Multiresolutional Particle Filter with Thresholded Wavelets [J]. Signal Processing, 2007, 87(6): 1384-1404
[19] L. Hong. A spatial domain multiresolutional particle filter [C]. 2007 Mediterranean Conference on Control and Automation, MED, Greece
[20] Zia Khan, Tucker Balch, Frank Dellaert. An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets [J]. Lecture Notes in Computer Science. 2004, 3024, 279-290
[21] Zia Khan, Tucker Balch, Frank Dellaert. MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2005, 27(11):1805-1918
[22] Rudolph van der Merwe, Nando de Freitas, Arnaud Doucet, Eric Wan. The Unscented Particle Filter [J]. Advances in Neural Information Processing Systems. 2001, 13
[23] R.Mahler Random-set approach to data fusion [C]. Proceedings of SPIE Automatic Object Recognition IV, 1994, 2234, 287-295
[24] R. Mahler. Statistics 101 for multitarget, multisensor data fusion [J]. IEEEAerospace and Electronic Systems Magazine, 2004, 19(1):53–64
[25] Jaco Vermaak, Simon J. Godsill, Patrick Perez. Monte Carlo filtering for multi-target tracking and data association [J]. IEEE Transactions on Aerospace and Electronic Systems. 2005, 41(1):309-332
[26] Y. Bar-Shalom, E. Tse. Tracking in a cluttered environment with probabilistic data association [J]. Automatica. 1975, 11(5):451-460
[27] Chen Z. Bayesian filtering: From Kalman filters to particle filters, and beyond [EB/OL]. http://soma.crl.mcmaster.ca/~zhechen/homepage.htm. 2003
[28] R .A. Singer, J. J. Stein. An Optimal Tracking Filter for Processing Sensor Data of Imprecisely Determined Origin in Surveillance Systems [C]. Proceedings of the IEEE Conference on Decision and Control, 1971:171-175
[29] Y. Bar-Shalom, Edison Tse. Tracking in a cluttered environment with probabilistic data association [J]. Automatica. 1975, 11(5):451-460
[30] T. E. Fortmann, Y. Bar-Shalom, M.Scheffe. Multi-target Tracking Using Joint Probabilistic Data Association [C]. Proceedings of the 19th IEEE Conference on Decision and Control.1980:807-812
[31] D. B. Reid. An Algorithm for Tracking Multiple Targets [J]. IEEE Transactions on Aerospace and Elect ronic Systems, 1979, 24: 843-854
[32]何佳洲,吴传利,周志华,陈世福.多假设跟踪技术综述[J].火力与指挥控制. 2004, 29(6):1-6
[33] S. Deb, M.Yeddanapudi, K.R. Pattipati, Y. Bar-Shalom. A Generalized S-D Assignment Algorithm for Multisensor-Multitarget State Estimation [J]. IEEE Transactions on Aerospace and Elect Systems. 1997, 33(2):523-538
[34] R.L. Popp, K. R. Pattipati, Y. Bar-Shalom. M-best SD Assignment Algorithm with Application to Multitarget Tracking [C]. Proceedings of SPIE Conference on Signal and Data of Small Targets 1998. 1998, Orlando, FL. 1998:475-495
[35] R.L. Popp, K. R. Pattipati, Y. Bar-Shalom. M-Best S-D assignment algorithm with application to multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2001, 37(1):22-39
[36] M.Moreland, S.Challa. A multi-target tracking algorithm based on random sets [C]. Proceedings of 6th International Conference on Information Fusion, Cairns, Australia, 2003
[37] R.Mahler. Multi-target moments and their application to multi-target tracking [C]. Proceedings Workshop on Estimation, Tracking and Fusion: Atribute to Yaakov Bar-Shalom. Monterey, 2001. 134-166
[38] R. Mahler. Multi-target Bayes Filtering via First-order Multi-target Moments [J]. IEEE Transactions on Aerospace and Electronic Systems .2003, 39(4):1152-1178
[39] H.Sidenbladh. Multi-target particle filtering for the probability hypothesis density [C]. Proceedings of 6th International Conference on Information Fusion, FUSION 2003, Cairns, Australia, 2003, 800-806
[40] T. Zajic, R.Mahler. A particle-systems implementation of the PHD multitarget tracking filter [C]. Proceedings of SPIE Signal Processing, Sensor Fusion, and Target Recognition XII, pp. 2003, 291-299
[41] Vo B., Singh S., Doucet A. Sequential Monte Carlo Implementation of the PHD Filter for Multi-target Tracking [C]. Processing of International Conference on Information Fusion.2003:792-799
[42] B, Vo, S. Singh, A. Doucet. Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets [J]. IEEE Transactions on aerospace and electronic systems, 2005, 41(4):1224-1245
[43] B. Ristic, D. Clark, B. N. Vo. Improved SMC mplementation of the PHD filter [C]. Proceedings of the 13th International Conference on Information Fusion, 2010
[44] B. Vo, W. Ma. A closed form solution for the probability hypothesis density filter [C]. Proceedings of 8th International Conference on Information Fusion, FUSION 2005, Philadephia, USA, 2005, (2):856-863
[45] Ba-Ngu Vo, Wing-Kin Ma. The Gaussian mixture probability hypothesis density filter [J]. IEEE Transactions on signal processing. 2006, 54(11):4091-4104
[46] B. Vo, A. Pasha, and H.D. Yuan. A Gaussian mixture PHD filter for nonlinear jump markov models [C]. Proceedings of the 45th IEEE Conference on Decision and Control, 2006, 1-14:6063–6068
[47] D.E. Clark and B. Vo. Convergence analysis of the Gaussian mixture PHD filter [J]. IEEE Transations on Signal Processing, 55:1204–1212, 2007
[48] Clark, D.E. Bell, J. Heriot-Watt. Multi-target state estimation and trackcontinuity for the particle PHD filter [J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1441-1453
[49] M. Tobias, A.D. Lanterman. Techniques for birth-particle placement in the probability hypothesis density particle filter applied to passive radar [J]. IET Radar Sonar Navigation, 2008, 2(5): 351–365
[50] Lin, L. Bar-Shalom, T. Kirubarajan. Track labeling and PHD filter for multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2006, 42(3): 778-795
[51] K.Panta, B. N. Vo, S. Singh. Improved probability hypothesis density (PHD) filter for multitarget tracking [C]. Proceedings of the Third International Conference on Intelligent Sensing and Information Processing, Chennai, India, 2005, 213-218
[52] Clark, D. E., Bell, J. Data Association for the PHD Filter [C]. IEEE Oceans Europe Conference, Brest, 2005.1: 265-270
[53] K. Panta, B. Vo, and D.E Clark. An efficient track management scheme for the gaussian-mixture probability hypothesis density tracker [C]. Proceedings of the Fourth International Conference on Intelligent Sensing and Information Processing, pages 230–235, 2006
[54] D.E. Clark, B. Vo, J. Bell. GM-PHD filter multi-target tracking in sonar images [J]. Signal Processing, Sensor Fusion and Target Recognition XV. 2006, 6253:2350-
[55] Kusha Panta, Clark, D. E, Ba-Ngu Vo. Data Association and Track Management for the Gaussian Mixture Probability Hypothesis Density Filter [J]. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3):1003-1016
[56] Kusha Panta, Clark, D. E, Bell, J. Novel data association schemes for the probability hypothesis density filter [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(2): 556-570
[57] Rajib Charkravorty, Subhash Challa. Multitarget tracking algorithm-Joint IPDA and Gaussian Mixture PHD filter [C]. Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,316-323
[58] F. Papi, G. Battistelli, L. Chisci, S. Morrocchi, A. Farina, A. Graziano. Multitarget tracking via joint PHD filtering and multiscan association [C].Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,1163-1170
[59] R. Mahler. Multitarget-moment filters for nonstandard measurement models [C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2008, 6968
[60] R. Mahler.The multisensor PHD filter, I: General solution via multitarget calculus [C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2009, 7336
[61] R. Mahler. The multisensor PHD filter, II: Erroneous solution via‘Poisson magic’[C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2009, 7336
[62] R. Mahler. CPHD and PHD filters for unknown backgrounds, I: Dynamic data clustering [C]. Proceedings of Sensors and Systems for Space Applications III, SPIE. 2009, 7330
[63] R. Mahler. CPHD and PHD filters for unknown backgrounds, II: Multitarget filtering in dynamic clutter [C]. Proceedings of Sensors and Systems for Space Applications III, SPIE. 2009, 7330
[64] R. Mahler. PHD filters for nonstandard targets, II: Extended Target [C]. Proceedings of the 12th International Conference on Information Fusion, FUSION 2009, 2009, 915-921
[65] R. Mahler. PHD filters for nonstandard targets, II: Unresolved Target [C]. Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,922-929
[66] M. Vihol. Rao-Blackwellised particle filter in random set multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(2): 689-705
[67] R. Mahler. PHD filters of higher order in target number [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(4):1523-1543
[68] B.T. Vo, B. Vo, A. Cantoni. The cardinalized probability hypothesis density filter for linear Gaussian multi-target models [J]. Proceedings of 40th Annual Conference on Information Sciences and Systems. 2006, 1-4:681–686
[69] B.T. Vo, B. Vo, A. Cantoni. Analytic implemenations of the cardinalized probability hypothesis density filter [J]. IEEE Transactions on SignalProcessing. 2007, 55:3553–3567
[70]连峰,韩崇昭,刘伟峰,元向辉.基于SMC-PHDF的部分可分辨的群目标跟踪算法[J].自动化学报,2010,36(5):731-741
[71]吴静静,胡士强.基于概率假设密度的多目标视频跟踪算法[J].控制与决策. 2010. 25(12): 1861-1865
[72]庄泽森,张建秋,尹建君.多目标跟踪的核粒子概率假设密度滤波算法[J].航空学报. 2009, 30 (7):1264-1270
[73] Ya-Dong Wang, Jian-Kang Wu, Ashraf A. Kassim, and Wei-Min Huang. Tracking a Variable Number of Human Groups in Video Using Probability Hypothesis Density [C]. Proceedings of 18th International Conference on Pattern Recognition, ICPR 2006, 2006,1127-1130
[74]欧阳成,姬红兵,张俊根.一种改进的CPHD多目标跟踪算法[J].电子与信息学报.2010,32(9):2113-2119
[75]杨柏胜,姬红兵,高小东.随机集粒子滤波的快速被动数据关联算法[J].西安电子科技大学学报(自然科学版).2010, 37( 4):655-659
[76]彭冬亮,文成林,徐晓滨,薛安克.随机集理论及其在信息融合中的应用[J].电子与信息学报, 2006,28(11):2199-2204
[77]田淑荣,王国宏,何友.多目标跟踪的概率假设密度粒子滤波[J].海军航空工程学院学报. 2007, 22(4):417-421
[78] Sarkka Simo,Vehtari Aki, Lampinen Jouko. Rao-Blackwellized Particle Filter for Multiple Target Tracking [J]. Information Fusion.2007, 8(1):2-15
[79] S.J.Julier, J.K. Uhlmann, H. E Durrant-Whyte. A new method for the nonlinear transformation of means and covariances in filters and estimators [J]. IEEE Transactions on Automatic Control. 2000, 45(3):477-482
[80] Arulampalam M S, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking [J]. IEEE Transactions on Signal Processing. 2002, 50(2):174-188
[81] Pierre Minvielie, Alan D. Marrs Simon Maskeli, Arnaud Doucet. Joint target tracking and identification: Part I: sequential Monte Carlo model-based approaches [C]. Proceedings of the 7th International Conference on Information Fusion. 2005, 259-266
[82] Hue, C, Le Cadre, J. P, Perez, P. Tracking multiple objects with particle filtering [J]. IEEE Transactions on Aerospace and Electronic Systems. 2002,38(3):791-812
[83] Smith, Kevin, Gatica-Perez, Daniel, Odobez, Jean-Marc. Using particles to track varying numbers of interacting people [C]. Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2005:962-969
[84] Y. Zhai, M. Yeary. Implementing Particle Filters with Metropolis-Hastings Algorithms [C]. Region 5 Conference: Annual Technical and Leadership Workshop, 2004:149-152
[85] Niederreiter H. Random number generation and quasi-Monte Carlo methods. CBMSNSF, SIAM, Philade lphia, 1992
[86] Phelim P. Boyle, Ken Seng Tan. Quasi-Monte Carlo methods [C]. Proceedings of the 7th International AFIR Colloquium. Cairns, Australia. 1997. 1-24
[87] Kenneth M. Hanson. Halftoning and Quasi-Monte Carlo [J]. Sensitivity Analysis of Model Output, K. M. Hanson and F. M. Hemez, eds.2005:430-442
[88] Gilks W R, Berzuini C. Following a moving target-Monte Carlo inference for dynamic Bayesian models [J]. Journal of the Royal Statistical Society: Series B, 2001, 63(1): 127-146
[89] Musso C, Oudjane N, LeGland F. Improving regularised particle filters. In Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001
[90] Fearnhead P. Using random quasi-Monte-Carlo within particle filters, with application to financial time series [J]. Computational and Graphical Statistics, 2005.1(14):751-769
[91] Perez C J, Martin J, Rufo MJl. Quasi-random sampling importance resampling [J]. Communications in Statistics- Simulation and Computation. 2005, 34 (1):97-112
[92] Guo D, Wang X D. Quasi-Monte Carlo filtering in nonlinear dynamic systems [J]. IEEE Transactions on Signal Processing. 2006, 54(6):2087-2098
[93] Daum Fred, Huang Jim. Nonlinear Filtering with Quasi-Monte Carlo Methods [C]. Proceedings of SPIE - The International Society for Optical Engineering, Signal and Data Processing of Small Targets 2003, 2004:458-479
[94] Stephen Joe, Frances Y. Kuo. Implementing Sobol’s quasi-random sequence generator [J]. ACM Transactions on Mathematical Software. 2003, 29(1): 49–57
[95] Hatem Ben Ameur, Pierre L’Ecuyer, Christiane Lemieux. Variance Reduction of Monte Carlo and Randomized Quasi-Monte Carlo Estimate for Stochastic Volatility Model in Finance [C].Winter Simulation Conference Proceedings.1999, 1: 336-343
[96] A. B.Owen. Latin supercube sampling for very high-dimensional simulations [J]. ACM Transactions on Modeling and Computer Simulation. 1998, 8(1):71-102
[97] Huang D M, Pan Q. A new nonlinear filter algorithm based on QMC quadrature [C]. Proceedings of the International Conference on Computer Science and Software Engineering. Wuhan, China: 2008:190-193
[98] L. Hong. Multiresolutional distributed filtering [J]. IEEE Transactions on Automation and Control. 1994, 39(4): 853-856
[99] L. Hong, N. Cui, M. Bakich, J. R. Layne. Multirate interacting multiple model particle filter with application to terrain-based ground target tracking [C]. IEE Proceedings of Control Theory Application. 2006, 153(6): 721-731
[100] L. Hong. Multirate interacting multiple model filtering for target tracking using multirate models [J]. IEEE Transactions on Automation and Control. 1999, 44(7): 1326-1340
[101]陶国智,卢荣胜,叶声华.动态测量误差的均方定义与组成成分分析.计量学报[J]. 2002, 23(3): 233-236
[102] Daniel Edward Clark, Judith Bell. Convergence results for the particle PHD filter [J]. IEEE Transactions on signal processing. 2006, 54(7):2652-2751.
[103] B.Vo, W. K. Ma, S.Singh. Locating an unknown time-varying number of speakers: a bayesian random finite set approach [C]. Proceeding of IEEE International Conference on Acoustics, Speech, Signal Processing, Philadelphia. 2005, 4:1073-1076
[104] Singer R .A, Sea R. G. A New Filter for Optimal Tracking in Dense Multi-target Environments [C]. Proceedings of the 9th Conference on Circuit and System Theory. 1971:201-211
[105] R. Mahler. A Survey of PHD filter and CPHD filter implementations [C]. Proceedings of SPIE .I. Kadar (ed.), Signal Processing, Sensor Fusion, and Target Recognization. XVI, 2007, 5809
[106] J. R. Hoffman, R. Mahler. Multitarget miss distance via optimal assignment [J]. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans. 2004, 34(3): 327-336
[107] F. Bourgeois, J. C. Lassalle. An extension of the Munkres algorithm for the assignment problem to rectangular matrices [J]. Communication of ACM. 1971, 14(12): 802-804
[2]权太范.目标跟踪新理论与技术[M].北京:国防工业出版社.2009:1-2
[3] Takamitsu Okada, Shingo Tsujimichi, Yoshio Kosuge. Tracking of a Highly Maneuvering Target Using a Radar Multisensor and an Angle Sensor [J] .Electronics and Communications in Japan, Part 1. 2001, 84(2):99-109
[4] Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems [J]. Transaction of the ASME—Journal of Basic Engineering. 1960. 82:35-45
[5] Julier, SimonJ, Jeffrey K Uhlmann. A New extension of the Kalman filter to nonlinear systems [C]. Proceedings of SPIE Signal Processing, Sensor Fusion, and Target Recognition VI. Vol. 3068, p. 182-193.
[6] Eric A. Wan, Rudolph van der Merwe. The Unscented Kalman Filter for Nonlinear Estimation [C]. Proceedings of IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000. AS-SPCC. 153– 158
[7] Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. http://www.cim.mcgill.ca/~dudek/417/papers/kalman_intro.pdf
[8] N.J. Gordon, D.J. Salmond, A.F.M. Smith. Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation [J]. IEE Proceedings of Radar and Signal Processing- F .1993, 140(2): 107-111
[9] Mahler R. A Theoretical Foundation for the Stein Winter Probability Hypothesis Density (PHD) Multi-target Tracking Approach [C]. Processing of the MSS Symposium on Sensor and Data Fusion. 2000
[10] Mahler R. Multi-target Bayes Filtering via First-order Multi-target Moments [J]. IEEE Transactions on Aerospace and Electronic Systems .2003, 39(4):1152-1178
[11] K Panta, B. Vo, S. Singh, and A. Doucet. Probability hypothesis density versus multiple hypothesis tracking [J]. Signal Processing, Sensor Fusion and Target Recognition XIII, 5429:284–295, 2004
[12] Blom, H.A.P. Bar-Shalom, Y. The interacting multiple model algorithm for systems with Markovian switching coefficients [J]. IEEE Transactions on Automatic Control. 1988, 33(8):780– 783
[13] Bar-Shalom Yaakov, Challa Subhash, Blom Henk A.P. IMM estimator versus optimal estimator for hybrid systems [J]. IEEE Transactions on Aerospace and Electronic Systems. 2005, 41(3): 986-991
[14] B. Ristic, S. Arulampalam, N. Gordon .Beyond the Kalman Filter: Particle Filters for Tracking Applications [M]. Artech House. Boston, London. 2004:21-49
[15] R.Nordlund, P. J. Particle filters for positioning, navigation, and tracking [J]. IEEE Transactions on Signal Processing. 2002, 50(2): 425-43
[16] Yvo Boers. A Particle Filter Multi Target Track Before Detect Application: Some Special Aspects [C]. Proceedings of the Seventh International Conference on Information Fusion. 2004, 701-708
[17] Rudolph van der Merwe, Arnaud Doucet, Nando de Freitas, Eric Wan. The Unscented Particle Filter .Technical Report CUED/F-INFENG/TR 380. Cambridge University Department of Engineering, 2000
[18] L. Hong, Devert Wicker. A Spatial-domain Multiresolutional Particle Filter with Thresholded Wavelets [J]. Signal Processing, 2007, 87(6): 1384-1404
[19] L. Hong. A spatial domain multiresolutional particle filter [C]. 2007 Mediterranean Conference on Control and Automation, MED, Greece
[20] Zia Khan, Tucker Balch, Frank Dellaert. An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets [J]. Lecture Notes in Computer Science. 2004, 3024, 279-290
[21] Zia Khan, Tucker Balch, Frank Dellaert. MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2005, 27(11):1805-1918
[22] Rudolph van der Merwe, Nando de Freitas, Arnaud Doucet, Eric Wan. The Unscented Particle Filter [J]. Advances in Neural Information Processing Systems. 2001, 13
[23] R.Mahler Random-set approach to data fusion [C]. Proceedings of SPIE Automatic Object Recognition IV, 1994, 2234, 287-295
[24] R. Mahler. Statistics 101 for multitarget, multisensor data fusion [J]. IEEEAerospace and Electronic Systems Magazine, 2004, 19(1):53–64
[25] Jaco Vermaak, Simon J. Godsill, Patrick Perez. Monte Carlo filtering for multi-target tracking and data association [J]. IEEE Transactions on Aerospace and Electronic Systems. 2005, 41(1):309-332
[26] Y. Bar-Shalom, E. Tse. Tracking in a cluttered environment with probabilistic data association [J]. Automatica. 1975, 11(5):451-460
[27] Chen Z. Bayesian filtering: From Kalman filters to particle filters, and beyond [EB/OL]. http://soma.crl.mcmaster.ca/~zhechen/homepage.htm. 2003
[28] R .A. Singer, J. J. Stein. An Optimal Tracking Filter for Processing Sensor Data of Imprecisely Determined Origin in Surveillance Systems [C]. Proceedings of the IEEE Conference on Decision and Control, 1971:171-175
[29] Y. Bar-Shalom, Edison Tse. Tracking in a cluttered environment with probabilistic data association [J]. Automatica. 1975, 11(5):451-460
[30] T. E. Fortmann, Y. Bar-Shalom, M.Scheffe. Multi-target Tracking Using Joint Probabilistic Data Association [C]. Proceedings of the 19th IEEE Conference on Decision and Control.1980:807-812
[31] D. B. Reid. An Algorithm for Tracking Multiple Targets [J]. IEEE Transactions on Aerospace and Elect ronic Systems, 1979, 24: 843-854
[32]何佳洲,吴传利,周志华,陈世福.多假设跟踪技术综述[J].火力与指挥控制. 2004, 29(6):1-6
[33] S. Deb, M.Yeddanapudi, K.R. Pattipati, Y. Bar-Shalom. A Generalized S-D Assignment Algorithm for Multisensor-Multitarget State Estimation [J]. IEEE Transactions on Aerospace and Elect Systems. 1997, 33(2):523-538
[34] R.L. Popp, K. R. Pattipati, Y. Bar-Shalom. M-best SD Assignment Algorithm with Application to Multitarget Tracking [C]. Proceedings of SPIE Conference on Signal and Data of Small Targets 1998. 1998, Orlando, FL. 1998:475-495
[35] R.L. Popp, K. R. Pattipati, Y. Bar-Shalom. M-Best S-D assignment algorithm with application to multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2001, 37(1):22-39
[36] M.Moreland, S.Challa. A multi-target tracking algorithm based on random sets [C]. Proceedings of 6th International Conference on Information Fusion, Cairns, Australia, 2003
[37] R.Mahler. Multi-target moments and their application to multi-target tracking [C]. Proceedings Workshop on Estimation, Tracking and Fusion: Atribute to Yaakov Bar-Shalom. Monterey, 2001. 134-166
[38] R. Mahler. Multi-target Bayes Filtering via First-order Multi-target Moments [J]. IEEE Transactions on Aerospace and Electronic Systems .2003, 39(4):1152-1178
[39] H.Sidenbladh. Multi-target particle filtering for the probability hypothesis density [C]. Proceedings of 6th International Conference on Information Fusion, FUSION 2003, Cairns, Australia, 2003, 800-806
[40] T. Zajic, R.Mahler. A particle-systems implementation of the PHD multitarget tracking filter [C]. Proceedings of SPIE Signal Processing, Sensor Fusion, and Target Recognition XII, pp. 2003, 291-299
[41] Vo B., Singh S., Doucet A. Sequential Monte Carlo Implementation of the PHD Filter for Multi-target Tracking [C]. Processing of International Conference on Information Fusion.2003:792-799
[42] B, Vo, S. Singh, A. Doucet. Sequential Monte Carlo Methods for Multi-Target Filtering with Random Finite Sets [J]. IEEE Transactions on aerospace and electronic systems, 2005, 41(4):1224-1245
[43] B. Ristic, D. Clark, B. N. Vo. Improved SMC mplementation of the PHD filter [C]. Proceedings of the 13th International Conference on Information Fusion, 2010
[44] B. Vo, W. Ma. A closed form solution for the probability hypothesis density filter [C]. Proceedings of 8th International Conference on Information Fusion, FUSION 2005, Philadephia, USA, 2005, (2):856-863
[45] Ba-Ngu Vo, Wing-Kin Ma. The Gaussian mixture probability hypothesis density filter [J]. IEEE Transactions on signal processing. 2006, 54(11):4091-4104
[46] B. Vo, A. Pasha, and H.D. Yuan. A Gaussian mixture PHD filter for nonlinear jump markov models [C]. Proceedings of the 45th IEEE Conference on Decision and Control, 2006, 1-14:6063–6068
[47] D.E. Clark and B. Vo. Convergence analysis of the Gaussian mixture PHD filter [J]. IEEE Transations on Signal Processing, 55:1204–1212, 2007
[48] Clark, D.E. Bell, J. Heriot-Watt. Multi-target state estimation and trackcontinuity for the particle PHD filter [J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1441-1453
[49] M. Tobias, A.D. Lanterman. Techniques for birth-particle placement in the probability hypothesis density particle filter applied to passive radar [J]. IET Radar Sonar Navigation, 2008, 2(5): 351–365
[50] Lin, L. Bar-Shalom, T. Kirubarajan. Track labeling and PHD filter for multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2006, 42(3): 778-795
[51] K.Panta, B. N. Vo, S. Singh. Improved probability hypothesis density (PHD) filter for multitarget tracking [C]. Proceedings of the Third International Conference on Intelligent Sensing and Information Processing, Chennai, India, 2005, 213-218
[52] Clark, D. E., Bell, J. Data Association for the PHD Filter [C]. IEEE Oceans Europe Conference, Brest, 2005.1: 265-270
[53] K. Panta, B. Vo, and D.E Clark. An efficient track management scheme for the gaussian-mixture probability hypothesis density tracker [C]. Proceedings of the Fourth International Conference on Intelligent Sensing and Information Processing, pages 230–235, 2006
[54] D.E. Clark, B. Vo, J. Bell. GM-PHD filter multi-target tracking in sonar images [J]. Signal Processing, Sensor Fusion and Target Recognition XV. 2006, 6253:2350-
[55] Kusha Panta, Clark, D. E, Ba-Ngu Vo. Data Association and Track Management for the Gaussian Mixture Probability Hypothesis Density Filter [J]. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3):1003-1016
[56] Kusha Panta, Clark, D. E, Bell, J. Novel data association schemes for the probability hypothesis density filter [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(2): 556-570
[57] Rajib Charkravorty, Subhash Challa. Multitarget tracking algorithm-Joint IPDA and Gaussian Mixture PHD filter [C]. Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,316-323
[58] F. Papi, G. Battistelli, L. Chisci, S. Morrocchi, A. Farina, A. Graziano. Multitarget tracking via joint PHD filtering and multiscan association [C].Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,1163-1170
[59] R. Mahler. Multitarget-moment filters for nonstandard measurement models [C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2008, 6968
[60] R. Mahler.The multisensor PHD filter, I: General solution via multitarget calculus [C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2009, 7336
[61] R. Mahler. The multisensor PHD filter, II: Erroneous solution via‘Poisson magic’[C]. Proceedings of Signal Processing, Sensor Fusion, and Targart Recognization. XVII, SPIE. 2009, 7336
[62] R. Mahler. CPHD and PHD filters for unknown backgrounds, I: Dynamic data clustering [C]. Proceedings of Sensors and Systems for Space Applications III, SPIE. 2009, 7330
[63] R. Mahler. CPHD and PHD filters for unknown backgrounds, II: Multitarget filtering in dynamic clutter [C]. Proceedings of Sensors and Systems for Space Applications III, SPIE. 2009, 7330
[64] R. Mahler. PHD filters for nonstandard targets, II: Extended Target [C]. Proceedings of the 12th International Conference on Information Fusion, FUSION 2009, 2009, 915-921
[65] R. Mahler. PHD filters for nonstandard targets, II: Unresolved Target [C]. Proceedings of 12th International Conference on Information Fusion, FUSION 2009, 2009,922-929
[66] M. Vihol. Rao-Blackwellised particle filter in random set multitarget tracking [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(2): 689-705
[67] R. Mahler. PHD filters of higher order in target number [J]. IEEE Transactions on Aerospace and Electronic Systems. 2007, 43(4):1523-1543
[68] B.T. Vo, B. Vo, A. Cantoni. The cardinalized probability hypothesis density filter for linear Gaussian multi-target models [J]. Proceedings of 40th Annual Conference on Information Sciences and Systems. 2006, 1-4:681–686
[69] B.T. Vo, B. Vo, A. Cantoni. Analytic implemenations of the cardinalized probability hypothesis density filter [J]. IEEE Transactions on SignalProcessing. 2007, 55:3553–3567
[70]连峰,韩崇昭,刘伟峰,元向辉.基于SMC-PHDF的部分可分辨的群目标跟踪算法[J].自动化学报,2010,36(5):731-741
[71]吴静静,胡士强.基于概率假设密度的多目标视频跟踪算法[J].控制与决策. 2010. 25(12): 1861-1865
[72]庄泽森,张建秋,尹建君.多目标跟踪的核粒子概率假设密度滤波算法[J].航空学报. 2009, 30 (7):1264-1270
[73] Ya-Dong Wang, Jian-Kang Wu, Ashraf A. Kassim, and Wei-Min Huang. Tracking a Variable Number of Human Groups in Video Using Probability Hypothesis Density [C]. Proceedings of 18th International Conference on Pattern Recognition, ICPR 2006, 2006,1127-1130
[74]欧阳成,姬红兵,张俊根.一种改进的CPHD多目标跟踪算法[J].电子与信息学报.2010,32(9):2113-2119
[75]杨柏胜,姬红兵,高小东.随机集粒子滤波的快速被动数据关联算法[J].西安电子科技大学学报(自然科学版).2010, 37( 4):655-659
[76]彭冬亮,文成林,徐晓滨,薛安克.随机集理论及其在信息融合中的应用[J].电子与信息学报, 2006,28(11):2199-2204
[77]田淑荣,王国宏,何友.多目标跟踪的概率假设密度粒子滤波[J].海军航空工程学院学报. 2007, 22(4):417-421
[78] Sarkka Simo,Vehtari Aki, Lampinen Jouko. Rao-Blackwellized Particle Filter for Multiple Target Tracking [J]. Information Fusion.2007, 8(1):2-15
[79] S.J.Julier, J.K. Uhlmann, H. E Durrant-Whyte. A new method for the nonlinear transformation of means and covariances in filters and estimators [J]. IEEE Transactions on Automatic Control. 2000, 45(3):477-482
[80] Arulampalam M S, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking [J]. IEEE Transactions on Signal Processing. 2002, 50(2):174-188
[81] Pierre Minvielie, Alan D. Marrs Simon Maskeli, Arnaud Doucet. Joint target tracking and identification: Part I: sequential Monte Carlo model-based approaches [C]. Proceedings of the 7th International Conference on Information Fusion. 2005, 259-266
[82] Hue, C, Le Cadre, J. P, Perez, P. Tracking multiple objects with particle filtering [J]. IEEE Transactions on Aerospace and Electronic Systems. 2002,38(3):791-812
[83] Smith, Kevin, Gatica-Perez, Daniel, Odobez, Jean-Marc. Using particles to track varying numbers of interacting people [C]. Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2005:962-969
[84] Y. Zhai, M. Yeary. Implementing Particle Filters with Metropolis-Hastings Algorithms [C]. Region 5 Conference: Annual Technical and Leadership Workshop, 2004:149-152
[85] Niederreiter H. Random number generation and quasi-Monte Carlo methods. CBMSNSF, SIAM, Philade lphia, 1992
[86] Phelim P. Boyle, Ken Seng Tan. Quasi-Monte Carlo methods [C]. Proceedings of the 7th International AFIR Colloquium. Cairns, Australia. 1997. 1-24
[87] Kenneth M. Hanson. Halftoning and Quasi-Monte Carlo [J]. Sensitivity Analysis of Model Output, K. M. Hanson and F. M. Hemez, eds.2005:430-442
[88] Gilks W R, Berzuini C. Following a moving target-Monte Carlo inference for dynamic Bayesian models [J]. Journal of the Royal Statistical Society: Series B, 2001, 63(1): 127-146
[89] Musso C, Oudjane N, LeGland F. Improving regularised particle filters. In Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001
[90] Fearnhead P. Using random quasi-Monte-Carlo within particle filters, with application to financial time series [J]. Computational and Graphical Statistics, 2005.1(14):751-769
[91] Perez C J, Martin J, Rufo MJl. Quasi-random sampling importance resampling [J]. Communications in Statistics- Simulation and Computation. 2005, 34 (1):97-112
[92] Guo D, Wang X D. Quasi-Monte Carlo filtering in nonlinear dynamic systems [J]. IEEE Transactions on Signal Processing. 2006, 54(6):2087-2098
[93] Daum Fred, Huang Jim. Nonlinear Filtering with Quasi-Monte Carlo Methods [C]. Proceedings of SPIE - The International Society for Optical Engineering, Signal and Data Processing of Small Targets 2003, 2004:458-479
[94] Stephen Joe, Frances Y. Kuo. Implementing Sobol’s quasi-random sequence generator [J]. ACM Transactions on Mathematical Software. 2003, 29(1): 49–57
[95] Hatem Ben Ameur, Pierre L’Ecuyer, Christiane Lemieux. Variance Reduction of Monte Carlo and Randomized Quasi-Monte Carlo Estimate for Stochastic Volatility Model in Finance [C].Winter Simulation Conference Proceedings.1999, 1: 336-343
[96] A. B.Owen. Latin supercube sampling for very high-dimensional simulations [J]. ACM Transactions on Modeling and Computer Simulation. 1998, 8(1):71-102
[97] Huang D M, Pan Q. A new nonlinear filter algorithm based on QMC quadrature [C]. Proceedings of the International Conference on Computer Science and Software Engineering. Wuhan, China: 2008:190-193
[98] L. Hong. Multiresolutional distributed filtering [J]. IEEE Transactions on Automation and Control. 1994, 39(4): 853-856
[99] L. Hong, N. Cui, M. Bakich, J. R. Layne. Multirate interacting multiple model particle filter with application to terrain-based ground target tracking [C]. IEE Proceedings of Control Theory Application. 2006, 153(6): 721-731
[100] L. Hong. Multirate interacting multiple model filtering for target tracking using multirate models [J]. IEEE Transactions on Automation and Control. 1999, 44(7): 1326-1340
[101]陶国智,卢荣胜,叶声华.动态测量误差的均方定义与组成成分分析.计量学报[J]. 2002, 23(3): 233-236
[102] Daniel Edward Clark, Judith Bell. Convergence results for the particle PHD filter [J]. IEEE Transactions on signal processing. 2006, 54(7):2652-2751.
[103] B.Vo, W. K. Ma, S.Singh. Locating an unknown time-varying number of speakers: a bayesian random finite set approach [C]. Proceeding of IEEE International Conference on Acoustics, Speech, Signal Processing, Philadelphia. 2005, 4:1073-1076
[104] Singer R .A, Sea R. G. A New Filter for Optimal Tracking in Dense Multi-target Environments [C]. Proceedings of the 9th Conference on Circuit and System Theory. 1971:201-211
[105] R. Mahler. A Survey of PHD filter and CPHD filter implementations [C]. Proceedings of SPIE .I. Kadar (ed.), Signal Processing, Sensor Fusion, and Target Recognization. XVI, 2007, 5809
[106] J. R. Hoffman, R. Mahler. Multitarget miss distance via optimal assignment [J]. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans. 2004, 34(3): 327-336
[107] F. Bourgeois, J. C. Lassalle. An extension of the Munkres algorithm for the assignment problem to rectangular matrices [J]. Communication of ACM. 1971, 14(12): 802-804
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