Information Fusion Progress: Joint Optimization Based on Variational Bayesian Theory
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摘要: 通过梳理近年信息融合理论的发展，分析了复杂目标跟踪系统中存在的非线性、多模式、深耦合、网络化、高维数和未知扰动输入等问题，指出现阶段目标跟踪系统中联合优化的必要性.继而，讨论了解决联合优化问题的主要方法，包括联合检测与估计，联合聚类与估计，联合关联与估计及联合决策与估计等.同时，着重介绍了变分贝叶斯辨识、估计和优化的统一框架和以其为基础的目标跟踪联合一体优化方法，并以天波超视距雷达为应用背景，给出在多路径多模式多目标跟踪场景下算法的一般性描述.最后，讨论了变分贝叶斯理论在目标跟踪领域的开放问题和未来研究方向.Abstract: By reviewing the development of information fusion theory in recent years, this paper analyzes the problems of target tracking systems, such as nonlinearity, multi-mode, deep coupling, networking, high-dimensionality and unknown disturbance input, and points out the necessity of joint optimization in target tracking system. Furthermore, several joint optimization methods, including the joint detection and estimation, joint clustering and estimation, joint association and estimation, joint decision and estimation are discussed. Meanwhile, we emphatically introduce the integrated optimization method based on the variational Bayesian theory that provides a unified framework of joint identification and estimation. Taking over-the-horizon radar as an application background, we give a general joint optimization method for the multi-path multi-mode multi-target tracking system in this paper. In addition, future research directions of the variational Bayesian theory in the field of target tracking are discussed.1) 本文责任编委 穆朝絮
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表 1 研究背景统计比例表
Table 1 Statistical proportion of research backgrounds
研究背景 军事应用 民事应用 理论及综合类 比例(%) 2015年 38.65 25.18 36.17 2016年 26.10 39.70 34.20 2017年 38.15 32.22 39.63 
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表 2 数学工具统计比例表
Table 2 Statistical proportion of mathematics tools
研究背景 概率论 随机集 证据推理 神经网络和
机器学习其他 比例(%) 2015年 47.72 8.07 7.72 9.82 26.67 2016年 48.2 8.2 9.1 11.4 23.1 2017年 51.95 11.72 7.43 14.45 14.45
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[1] 潘泉, 程咏梅, 梁彦, 杨峰, 王小旭.多源信息融合理论及应用.北京:清华大学出版社, 2013.Pan Quan, Cheng Yong-Mei, Liang Yan, Yang Feng, Wang Xiao-Xu. Multisource Information Fusion Theory and Application. Beijing: Tsinghua University Press, 2013. [2] Llinas J, Waltz E. Multisensor Data Fusion. Norwood, MA: Artech House Publisher, 1990. [3] 何友, 修建娟, 关欣.雷达数据处理及应用.第3版.北京:电子工业出版社, 2013.He You, Xiu Jian-Juan, Guan Xin. Radar Data Processing with Applications (Third Edition). Beijing: Publishing House of Electronics Industry, 2013. [4] Hall D L, Llinas J. Handbook of Multisensor Data Fusion. Danvers: CRC Press, 2001. [5] 周宏仁, 敬忠良, 王培德.机动目标跟踪.北京:国防工业出版社, 1991.Zhou Hong-Ren, Jing Zhong-Liang, Wang Pei-De. Maneuvering Target Tracking. Beijing: National Defense Industry Press, 1991. [6] Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software. New York: John Wiley and Sons, 2004. [7] 王增福, 潘泉, 梁彦, 刘慧霞.天波超视距雷达数据处理算法综述.中国电子科学研究院学报, 2011, 6(5): 477-484 doi: 10.3969/j.issn.1673-5692.2011.05.008Wang Zeng-Fu, Pan Quan, Liang Yan, Liu Hui-Xia. A review of data processing algorithms for Over-The-Horizon radar. Journal of China Academy of Electronics and Information Technology, 2011, 6(5): 477-484 doi: 10.3969/j.issn.1673-5692.2011.05.008 [8] Yadav S, Shroff G, Hassan E, Agarwal P. Business data fusion. In: Proceedings of the 18th IEEE Conference on Information Fusion. Washington, DC, USA: IEEE, 2015. 1876-1885 [9] Chang Y F, Chen C C, Lin S C. An intelligent context-aware communication system for one single autonomic region to realize smart living. Information Fusion, 2015, 21: 57-67 doi: 10.1016/j.inffus.2013.03.002 [10] Liu Y, Chen X, Cheng J, Peng H. A medical image fusion method based on convolutional neural networks. In: Proceedings of the 20th IEEE Conference on Information Fusion. Xi'an, China: IEEE, 2017. 1070-1077 [11] Bosman H H W J, Iacca G, Tejada A, Wörtche H J, Liotta A. Spatial anomaly detection in sensor networks using neighborhood information. Information Fusion, 2017, 33: 41-56 doi: 10.1016/j.inffus.2016.04.007 [12] Anderson C, Breimyer P, Foster S, Geyer K, Griffith J D, Heier A, et al. A network science approach to open source data fusion and analytics for disaster response. In: Proceedings of the 2015 18th International Conference on Information Fusion. Washington, DC, USA: IEEE, 2015: 207-214 [13] 潘泉, 于昕, 程咏梅, 张洪才.信息融合理论的基本方法与进展.自动化学报, 2003, 29(4): 599-615 http://www.aas.net.cn/CN/abstract/abstract13929.shtmlPan Quan, Yu Xin, Cheng Yong-Mei, Zhang Hong-Cai. Essential methods and progress of information fusion theory. Acta Automatica Sinica, 2003, 29(4): 599-615 http://www.aas.net.cn/CN/abstract/abstract13929.shtml [14] 潘泉, 王增福, 梁彦, 杨峰, 刘准钆.信息融合理论的基本方法与进展(Ⅱ).控制理论与应用, 2012, 29(10): 1233-1244 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy201210001Pan Quan, Wang Zeng-Fu, Liang Yan, Yang Feng, Liu Zhun-Ga. Basic methods and progress of information fusion (Ⅱ). Control Theory and Applications, 2012, 29(10): 1233-1244 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy201210001 [15] Li X R, Jilkov V P. Survey of maneuvering target tracking. Part V: multiple-model methods. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1255-1321 doi: 10.1109/TAES.2005.1561886 [16] Gustafsson F, Hendeby G. Some relations between extended and unscented Kalman filters. IEEE Transactions on Signal Processing, 2012, 60(2): 545-555 doi: 10.1109/TSP.2011.2172431 [17] Julier S, Uhlmann J, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482 doi: 10.1109/9.847726 [18] Arulampalam M S, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188 doi: 10.1109/78.978374 [19] Frank A, Smyth P, Ihler A. Beyond MAP estimation with the track-oriented multiple hypothesis tracker. IEEE Transactions on Signal Processing, 2014, 62(9): 2413-2423 doi: 10.1109/TSP.2014.2311962 [20] Li Q, Sun J P, Sun W. An efficient multiple hypothesis tracker using max product belief propagation. In: Proceedings of the 20th International Conference on Information Fusion. Xi'an, China: IEEE, 2017. 1042-1049 [21] Li X H, Willett P, Baum M, Li Y A. PMHT approach for underwater bearing-only multisensor—multitarget tracking in clutter. IEEE Journal of Oceanic Engineering, 2016, 41(4): 831-839 doi: 10.1109/JOE.2015.2506220 [22] Song T, Kim H, Musicki D. Iterative joint integrated probabilistic data association for multitarget tracking. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51(1): 642-653 doi: 10.1109/TAES.2014.130571 [23] Oh J, Russell S, Sastry S. Markov chain Monte Carlo data association for multi-target tracking. IEEE Transactions on Automatic Control, 2009, 54(3): 481-497 doi: 10.1109/TAC.2009.2012975 [24] Williams J L. Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51(3): 1664-1687 doi: 10.1109/TAES.2015.130550 [25] Mahler R. A survey of PHD filter and CPHD filter implementations. In: Proceedings of Signal Processing, Sensor Fusion, and Target Recognition XVI. Orlando, Florida, United States: SPIE, 2007. [26] Vo B T, Vo B N, Hoseinnezhad R, Mahler R P S. Robust multi-Bernoulli filtering. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(3): 399-409 doi: 10.1109/JSTSP.2013.2252325 [27] 陈辉, 韩崇昭. CBMeMBer滤波器序贯蒙特卡罗实现新方法的研究.自动化学报, 2016, 42(1): 26-36 http://www.aas.net.cn/CN/abstract/abstract18793.shtmlChen Hui, Han Chong-Zhao. A new sequential Monte Carlo implementation of cardinality balanced multi-target multi-Bernoulli filter. Acta Automatica Sinica, 2016, 42(1): 26-36 http://www.aas.net.cn/CN/abstract/abstract18793.shtml [28] Kamen E W. Multiple target tracking based on symmetric measurement equations. IEEE Transactions on Automatic Control, 1989, 37(3): 371-374 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=e2d444e88774d3b4f8b9e78fee1bc182 [29] Baum M, Noack B, Hanebeck U D. Kalman filter-based SLAM with unknown data association using symmetric measurement equations. In: Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems. New York, USA: IEEE, 2015. 49-53 [30] Fortmann T E, Bar-Shalom Y, Scheffe M. Multi-target tracking using joint probabilistic data association. In: Proceedings of the 19th IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes. New York, USA: IEEE, 1980. 807-812 [31] Blackman S S. Multiple hypothesis tracking for multiple target tracking. IEEE Aerospace and Electronic Systems Magazine, 2004, 19(1): 5-18 doi: 10.1109/MAES.2004.1263228 [32] Lan H, Wang X Z, Pan Q, Yang F, Wang Z F, Liang Y. A survey on joint tracking using expectation-maximization based techniques. Information Fusion, 2016, 30: 52-68 doi: 10.1016/j.inffus.2015.11.008 [33] Ruan Y H, Willett P. The turbo PMHT. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(4): 1388-1398 doi: 10.1109/TAES.2004.1386891 [34] Ruan Y H, Willett P. Multiple model PMHT and its application to the second benchmark radar tracking problem. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(4): 1337-1350 doi: 10.1109/TAES.2004.1386885 [35] Mahler R P S. Multitarget Bayes filtering via first-order multitarget moments. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1152-1178 doi: 10.1109/TAES.2003.1261119 [36] Mahler R. PHD filters of higher order in target number. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1523-1543 doi: 10.1109/TAES.2007.4441756 [37] Ristic B, Vo B T, Vo B N, Farina A. A tutorial on Bernoulli filters: theory, implementation and applications. IEEE Transactions on Signal Processing, 2013, 61(13): 3406-3430 doi: 10.1109/TSP.2013.2257765 [38] Vo B T, Vo B N. Labeled random finite sets and multi-object conjugate priors. IEEE Transactions on Signal Processing, 2013, 61(13): 3460-3475 doi: 10.1109/TSP.2013.2259822 [39] Vo B N, Mallick M, Bar-Shalom Y, Coraluppi S, Osborne Ⅲ R, Mahler R, Vo B T. Multitarget Tracking. New York: John Wiley and Sons, Inc., 2015. [40] 杨峰, 王永齐, 梁彦, 潘泉.基于概率假设密度滤波方法的多目标跟踪技术综述.自动化学报, 2013, 39(11): 1944-1956 http://www.aas.net.cn/CN/abstract/abstract18233.shtmlYang Feng, Wang Yong-Qi, Liang Yan, Pan Quan. A survey of PHD filter based multi-target tracking. Acta Automatica Sinica, 2013, 39(11): 1944-1956 http://www.aas.net.cn/CN/abstract/abstract18233.shtml [41] Lee Y J, Kamen E W. SME filter approach to multiple target tracking with false and missing measurements. In: Proceedings of Conference on Signal and Data Processing of Small Targets. New York, USA: SPIE, 1993. 574-586 [42] Leven W F, Lanterman A D. Multiple target tracking with symmetric measurement equations revisited: unscented Kalman filters, particle filters, and Taylor series expansions. In: Proceedings of International Society for Optical Engineering. New York, USA: SPIE, 2005. 56-67 [43] Hanebeck U D, Baum M, Willett P. Symmetrizing measurement equations for association-free multi-target tracking via point set distances. In: Proceedings of Conference of Signal Processing, Sensor/Information Fusion, and Target Recognition. New York, USA: SPIE, 2017. 1-14 [44] 吴潇, 黄树彩, 凌强, 钟宇.基于改进对称量测方程的多目标跟踪.系统工程与电子技术, 2016, 38(1): 21-25 http://d.old.wanfangdata.com.cn/Periodical/xtgcydzjs201601004Wu Xiao, Huang Shu-Cai, Ling Qiang, Zhong Yu. Multiple targets tracking using modified symmetric measurement equations. Systems Engineering and Electronics, 2016, 38(1): 21-25 http://d.old.wanfangdata.com.cn/Periodical/xtgcydzjs201601004 [45] Baum M, Hanebeck U D. The kernel-SME filter for multiple target tracking. Computer Science, 2012. 288-295 [46] Baum M, Yang S S, Hanebeck U D. The kernel-SME filter with false and missing measurements. In: Proceedings of the 19th IEEE International Conference on Information Fusion. Heidelberg, Germany: IEEE, 2016. 424-428 [47] Hu X Q, Bao M, Zhang X P, Guan L Y, Hu Y H. Generalized iterated Kalman filter and its performance evaluation. IEEE Transactions on Signal Processing, 2015, 63(12): 3204-3217 doi: 10.1109/TSP.2015.2423266 [48] Cappe O, Godsill S J, Moulines E. An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE, 2007, 95(5): 899-924 doi: 10.1109/JPROC.2007.893250 [49] Schön T B, Wills A, Ninness B. System identification of nonlinear state-space models. Automatica, 2011, 47(1): 39-49 doi: 10.1016/j.automatica.2010.10.013 [50] Kantas N, Doucet A, Singh S S, Maciejowski J, Chopin N. On Particle methods for parameter estimation in state-space models. Statistical Science, 2015, 30(3): 328-351 doi: 10.1214/14-STS511 [51] Dahlin J, Schön T B. Getting started with particle Metropolis-Hastings for inference in nonlinear dynamical models. arXiv: 1511.01707v7, 2017. [52] Schön T B, Lindsten F, Dahlin J, Waagberg J, Naesseth C A, Svensson A, et al. Sequential Monte Carlo Methods for system identification. IFAC Papers On Line, 2015, 48(28): 775-786 doi: 10.1016/j.ifacol.2015.12.224 [53] Daum F, Huang J. Particle flow with non-zero diffusion for nonlinear filters. In: Proceedings of Signal Processing, Sensor Fusion, and Target Recognition. Baltimore, Maryland, United States: SPIE, 2013. 1072-1079 [54] Bunch P, Godsill S. Approximations of the optimal importance density using Gaussian particle flow importance sampling. Journal of the American Statistical Association, 2016, 111(514): 748-762 doi: 10.1080/01621459.2015.1038387 [55] Nurminen H, Piche R, Godsill S. Gaussian flow sigma point filter for nonlinear Gaussian state-space models. In: Proceedings of the 20th IEEE International Conference on Information Fusion. Xi'an, China: IEEE, 2017. 445-452 [56] Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269 doi: 10.1109/TAC.2009.2019800 [57] Norgaard M, Poulsen N K, Ravn O. New developments in state estimation for nonlinear systems. Automatica, 2000, 36(11): 1627-1638 doi: 10.1016/S0005-1098(00)00089-3 [58] Smidl V, Quinn A. Variational Bayesian filtering. IEEE Transactions on Signal Processing, 2008, 56(10): 5020-5030 doi: 10.1109/TSP.2008.928969 [59] Wang X X, Liang Y, Pan Q, Wang Z F. General equivalence between two kinds of noise-correlation filters. Automatica, 2014, 50(12): 3316-3318 doi: 10.1016/j.automatica.2014.10.040 [60] Wang X X, Liang Y, Pan Q, Zhao C H, Yang F. Nonlinear Gaussian smoothers with colored measurement noise. IEEE Transactions on Automatic Control, 2015, 60(3): 870-876 doi: 10.1109/TAC.2014.2337991 [61] Geng H, Liang Y, Zhang X J. Linear-minimum-mean-square-error observer for multi-rate sensor fusion with missing measurements. IET Control Theory and Applications, 2014, 8(14): 1375-1383 doi: 10.1049/iet-cta.2013.0972 [62] Wang X X, Liang Y, Pan Q, Zhao C H. Gaussian filter for nonlinear systems with one-step randomly delayed measurements. Automatica, 2013, 49(4): 976-986 doi: 10.1016/j.automatica.2013.01.012 [63] Geng H, Liang Y, Liu Y R, Alsaadi F E. Bias estimation for asynchronous multi-rate multi-sensor fusion with unknown inputs. Information Fusion, 2018, 39: 139-153 doi: 10.1016/j.inffus.2017.03.002 [64] Geng H, Liang Y, Yang F, Xu L F, Pan Q. The joint optimal filtering and fault detection for multi-rate sensor fusion under unknown inputs. Information Fusion, 2016, 29: 57-67 doi: 10.1016/j.inffus.2015.10.003 [65] Qin Y M, Liang Y, Yang Y B, Wang Z F, Wang F. Adaptive filter of non-linear systems with generalised unknown disturbances. IET Radar, Sonar and Navigation, 2014, 8(4): 307-317 doi: 10.1049/iet-rsn.2013.0031 [66] Yang Y B, Liang Y, Pan Q, Qin Y M, Yang F. Distributed fusion estimation with square-root array implementation for Markovian jump linear systems with random parameter matrices and cross-correlated noises. Information Sciences, 2016, 370-371: 446-462 doi: 10.1016/j.ins.2016.08.020 [67] Sinopoli B, Schenato L, Franceschetti M, Poolla K, Jordan M I, Sastry S S. Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control, 2004, 49(9): 1453-1464 doi: 10.1109/TAC.2004.834121 [68] Sun S L, Xie L H, Xiao W D, Xiao N. Optimal filtering for systems with multiple packet dropouts. IEEE Transactions on Circuits and Systems-Ⅱ: Express Briefs, 2008, 55(7): 695-699 doi: 10.1109/TCSII.2008.921576 [69] Wang Z D, Yang F W, Ho D W C, Liu X H. Robust H∞ control for networked systems with random packet losses. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, 2007, 37(4): 916-924 doi: 10.1109/TSMCB.2007.896412 [70] Zhang H, Shi Y, Mehr A S. Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors. International Journal of Adaptive Control and Signal Processing, 2011, 25(4): 313-330 doi: 10.1002/acs.v25.4 [71] Lu X, Zhang H S, Wang W, Teo K L. Kalman filtering for multiple time-delay systems. Automatica, 2005, 41(8): 1455-1461 doi: 10.1016/j.automatica.2005.03.018 [72] Dey S, Leong A S, Evans J S. Kalman filtering with faded measurements. Automatica, 2009, 45(10): 2223-2233 doi: 10.1016/j.automatica.2009.06.025 [73] Garcia R, Puig J, Ridao P, Cufi X. Augmented state Kalman filtering for AUV navigation. In: Proceedings of the 2002 Conference on Robotics and Automation. Washington, DC, USA: IEEE, 2002. 4010-4015 [74] Ghaoui L E, Calafiore G. Robust filtering for discrete-time systems with bounded noise and parametric uncertainty. IEEE Transactions on Automatic Control, 2001, 46(7): 1084-1089 doi: 10.1109/9.935060 [75] Li X R, Jikov V P, Ru J. Multiple-model estimation with variable structure-part Ⅵ: expectation-mode augmentation. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(3): 853-867 doi: 10.1109/TAES.2005.1541435 [76] Bishop C M. Pattern Recognition and Machine Learning. New York, USA: Springer, 2007. [77] Sung J, Ghahramani Z, Bang S Y. Latent-space variational Bayes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008, 30(12): 2236-2242 doi: 10.1109/TPAMI.2008.157 [78] Tzikas D G, Likas A C, Galatsanos N P. The variational approximation for Bayesian inference. IEEE Signal Processing Magazine, 2008, 25(6): 131-146 doi: 10.1109/MSP.2008.929620 [79] Thormann K, Sigges F, Baum M. Learning an object tracker with a random forest and simulated measurements. In: Proceedings of the 20th IEEE Conference on Information Fusion. Xi'an, China: IEEE, 2017. 390-394 [80] Song K, Kim S H, Tak J, Choi H L, Moon I C. Data-driven ballistic coefficient learning for future state prediction of high-speed vehicles. In: Proceedings of the 19th International Conference on Information Fusion. Heidelberg, Germany: IEEE, 2016. 17-24 [81] Hexeberg S, Flaten A L, Eriksen B O H, Brekke E F. AIS-based vessel trajectory prediction. In: Proceedings of the 20th International Conference on Information Fusion. Xi'an, China: IEEE, 2017. 1019-1026 [82] Aprile A, Grossi E, Lops M, Venturino L. Track-before-detect for sea clutter rejection: tests with real data. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(3): 1035-1045 doi: 10.1109/TAES.2016.140851 [83] De Laet T, Bruyninckx H, De Schutter J. Shape-based online multitarget tracking and detection for targets causing multiple measurements: variational Bayesian clustering and lossless data association. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(12): 2477-2491 doi: 10.1109/TPAMI.2011.83 [84] Willett P, Ruan Y, Streit R. PMHT: problems and some solutions. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(3): 738-754 doi: 10.1109/TAES.2002.1039396 [85] Li X R. Optimal bayes joint decision and estimation. In: Proceedings of the 10th IEEE International Conference on Information Fusion. Quebec, Canada: IEEE, 2007. 1-8 [86] Saul L K, Jordan M I. Exploiting tractable substructures in intractable networks. In: Proceedings of Advances in Neural Information Processing Systems. Cambridge: MIT Press, 1995. 486-492 [87] Lan H, Liang Y, Pan Q, Yang F, Guan C. An EM algorithm for multipath state estimation in OTHR target tracking. IEEE Transactions on Signal Processing, 2014, 62(11): 2814-2826 doi: 10.1109/TSP.2014.2318134 [88] Beal M J. Variational algorithms for approximate Bayesian inference[Ph.D. thesis], University of London, UK, 2003. [89] Lan H, Pan Q, Yang F, Sun S, Li L. Variational Bayesian approach for joint multitarget tracking of multiple detection systems. In: Proceedings of the 19th IEEE International Conference on Information Fusion. Heidelberg, Germany: IEEE, 2016. [90] Jordan M I, Ghahramani Z, Jaakkola T S, Saul L K. An introduction to variational methods for graphical models. Machine Learning, 1999, 37(2): 183-233 doi: 10.1023/A:1007665907178 [91] Hoffman M D, Blei D M, Wang C, Paisley J. Stochastic variational inference. The Journal of Machine Learning Research, 2013, 14(1): 1303-1347 http://d.old.wanfangdata.com.cn/Periodical/jsjkxjsxb-e201602014 [92] Johnson M J, Willsky A S. Stochastic variational inference for Bayesian time series models. In: Proceedings of the 31st International Conference on Machine Learning. Beijing, China: ICML, 2014. 1854-1862 [93] Salimans T, Kingma D P, Welling M. Markov chain Monte Carlo and variational inference: bridging the gap. arxiv: 1014.6460v4, 2014. [94] Pearl J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, California: Morgan Kaufmann, 1988. [95] Pearl J. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 1986, 29(3): 241-288 doi: 10.1016/0004-3702(86)90072-X [96] Berrou C, Glavieux A, Thitimajshima P. Near Shannon limit error-correcting coding and decoding: turbo-codes. In: Proceedings of International Conference on Communications. New York, USA: IEEE, 1993. [97] Forney G D. Codes on graphs: Normal realizations. IEEE Transactions on Information Theory, 2001, 47(2): 520-548 doi: 10.1109/18.910573 [98] Kschischang F R, Frey B J, Loeliger H A. Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory, 2001, 47(2): 498-519 doi: 10.1109/18.910572 [99] Yedidia J S, Freeman W T, Weiss Y. Generalized belief propagation. In: Proceedings of Annual Conference on Neural Information Processing Systems. New York, USA: MIT Press, 2000. 689-695 [100] Yedidia J S, Freeman W T, Weiss Y. Constructing free-energy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory, 2005, 51(7): 2282-2312 doi: 10.1109/TIT.2005.850085 [101] Mooij J M, Kappen H J. On the properties of the Bethe approximation and loopy belief propagation on binary networks. Journal of Statistical Mechanics Theory and Experiment, 2005, 2005(11): Article No.P11012 [102] Koller D, Friedman N. Probabilistic Graphical Models: Principle and Technique. Cambridge: MIT Press, 2009. [103] Särkkä S, Nummenmaa A. Recursive noise adaptive Kalman filtering by variational Bayesian approximations. IEEE Transactions on Automatic Control, 2009, 54(3): 596-600 doi: 10.1109/TAC.2008.2008348 [104] Särkkä S, Hartikainen J. Non-linear noise adaptive Kalman filtering via variational Bayes. In: Proceedings of the 2013 IEEE International Workshop on Machine Learning for Signal Processing. New York, USA: IEEE, 2013. 1-6 [105] Agamennoni G, Nieto J I, Nebot E M. Approximate inference in state-space models with heavy-tailed noise. IEEE Transactions on Signal Processing, 2012, 60(10): 5024-5037 doi: 10.1109/TSP.2012.2208106 [106] Li W L, Sun S H, Jia Y M, Du J P. Robust unscented Kalman filter with adaptation of process and measurement noise covariances. Digital Signal Processing, 2016, 48: 93-103 doi: 10.1016/j.dsp.2015.09.004 [107] Li W L, Jia Y M, Du J P, Zhang J. PHD filter for multi-target tracking with glint noise. Signal Processing, 2014, 94: 48-56 doi: 10.1016/j.sigpro.2013.06.012 [108] Ardeshiri T, Özkan E, Orguner U, Gustafsson F. Approximate Bayesian smoothing with unknown process and measurement noise covariances. IEEE Signal Processing Letters, 2015, 22(12): 2450-2454 doi: 10.1109/LSP.2015.2490543 [109] Huang Y L, Zhang Y G, Wu Z M, Li N, Chambers J. A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices. IEEE Transactions on Automatic Control, 2018, 63(2): 594-601 doi: 10.1109/TAC.2017.2730480 [110] Wang C, Blei D M. Variational inference in nonconjugate models. The Journal of Machine Learning Research, 2013, 14(4): 1005-1031 http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1209.4360 [111] Piché R, Särkkä S, Hartikainen J. Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution. In: Proceedings of the 2012 International Workshop on Machine Learning for Signal Processing. Santander, Spain: IEEE, 2012: 1-6 [112] Nurminen H, Ardeshiri T, Piché R, Gustafsson F. Robust inference for state-space models with skewed measurement noise. IEEE Signal Processing Letters, 2015, 22(11): 1898-1902 doi: 10.1109/LSP.2015.2437456 [113] Turner R, Bottone S, Stanek C. Online variational approximations to non-exponential family change point models: with application to radar tracking. In: Proceedings of the 26th Annual Conference on Neural Information Processing Systems. New York, USA: MIT Press, 2013. 306-314 [114] Blei D M, Kucukelbir A, McAuliffe J D. Variational inference: a review for statisticians. Journal of the American Statistical Association, 2017112(518): 859-877 doi: 10.1080/01621459.2017.1285773 [115] Lázaro G M, van Vaerenbergh S, Lawrence N D. Overlapping mixtures of Gaussian processes for the data association problem. Pattern Recognition, 2012, 45(4): 1386-1395 doi: 10.1016/j.patcog.2011.10.004 [116] Turner R D, Bottone S, Avasarala B. A complete variational tracker. In: Proceedings of the 2014 Advances in Neural Information Processing Systems. Cambridge: MIT Press, 2014. 496-504 [117] Williams J L, Lau R A. Data association by loopy belief propagation. In: Proceedings of the 13th International Conference on Information Fusion. Edinburgh, UK: IEEE, 2010. 1-8 [118] Meyer F, Braca P, Willett P, Hlawatsch F. Tracking an unknown number of targets using multiple sensors: A belief propagation method. In: Proceedings of the 19th IEEE International Conference on Information Fusion. Heidelberg, Germany: IEEE, 2016. [119] 兰华.基于期望最大法联合估计与辨识的远程预警数据处理[博士学位论文], 西北工业大学, 中国, 2014.Lan Hua. Joint estimation and identification based on expectation maximization for data processing of distance early warning[Ph.D. thesis], Northwestern Polytechnical University, China, 2014. [120] Lan H, Sun S, Wang Z F, Pan Q, Zhang Z S. Joint detection and tracking for multipath targets: a variational Bayesian approach. arXiv: 1610.08616, 2016. [121] Ranganath R, Gerrish S, Blei D M. Black box variational inference. arXiv: 1401.0118, 2014. [122] Haykin S. Cognitive radar: a way of the future. IEEE Signal Processing Magazine, 2006, 23(1): 30-40 doi: 10.1109/MSP.2006.1593335 -
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