信息融合理论研究进展:基于变分贝叶斯的联合优化
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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.
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 multipath 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.
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 multipath 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.
引文
1 Pan Quan, Cheng Yong-Mei, Liang Yan, Yang Feng, Wang Xiao-Xu. Multisource Information Fusion Theory and Application. Beijing:Tsinghua University Press, 2013.(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.)
2 Llinas J, Waltz E. Multisensor Data Fusion. Norwood,MA:Artech House Publisher, 1990.
3 He You, Xiu Jian-Juan, Guan Xin. Radar Data Processing with Applications(Third Edition). Beijing:Publishing House of Electronics Industry, 2013.(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.)
4 Hall D L, Llinas J. Handbook of Multisensor Data Fusion.Danvers:CRC Press, 2001.
5 Zhou Hong-Ren, Jing Zhong-Liang, Wang Pei-De. Maneuvering Target Tracking. Beijing:National Defense Industry Press, 1991.(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.)
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 Wang 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(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)
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 contextaware communication system for one single autonomic region to realize smart living. Information Fusion, 2015, 21:57-67
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, Wortche H J, Liotta A. Spatial anomaly detection in sensor networks using neighborhood information. Information Fusion, 2017, 33:41-56
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 Pan 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(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)
14 Pan 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(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)
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
16 Gustafsson F, Hendeby G. Some relations between extended and unscented Kalman filters. IEEE Transactions on Signal Processing, 2012, 60(2):545-555
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
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
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
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
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
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
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
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
27 Chen 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(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)
28 Kamen E W. Multiple target tracking based on symmetric measurement equations. IEEE Transactions on Automatic Control, 1989, 37(3):371-374
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
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
33 Ruan Y H, Willett P. The turbo PMHT. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(4):1388-1398
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
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
36 Mahler R. PHD filters of higher order in target number.IEEE Transactions on Aerospace and Electronic Systems,2007, 43(4):1523-1543
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
38 Vo B T, Vo B N. Labeled random finite sets and multiobject conjugate priors. IEEE Transactions on Signal Processing, 2013, 61(13):3460-3475
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 Yang 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(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)
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 Wu 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(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)
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
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
49 Schon T B, Wills A, Ninness B. System identification of nonlinear state-space models. Automatica, 2011, 47(1):39-49
50 Kantas N, Doucet A, Singh S S, Maciejowski J, Chopin N. On Particle methods for parameter estimation in statespace models. Statistical Science, 2015, 30(3):328-351
51 Dahlin J, Schon T B. Getting started with particle Metropolis-Hastings for inference in nonlinear dynamical models. arXiv:1511.01707v7, 2017.
52 Schon 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
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
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
57 Norgaard M, Poulsen N K, Ravn O. New developments in state estimation for nonlinear systems. Automatica, 2000,36(11):1627-1638
58 Smidl V, Quinn A. Variational Bayesian filtering.IEEE Transactions on Signal Processing, 2008, 56(10):5020-5030
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
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
61 Geng H, Liang Y, Zhang X J. Linear-minimum-meansquare-error observer for multi-rate sensor fusion with missing measurements. IET Control Theory and Applications, 2014, 8(14):1375-1383
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
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
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
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
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
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
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
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
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
71 Lu X, Zhang H S, Wang W, Teo K L. Kalman filtering for multiple time-delay systems. Automatica, 2005, 41(8):1455-1461
72 Dey S, Leong A S, Evans J S. Kalman filtering with faded measurements. Automatica, 2009, 45(10):2223-2233
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
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
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
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
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-beforedetect for sea clutter rejection:tests with real data. IEEE Transactions on Aerospace and Electronic Systems, 2016,52(3):1035-1045
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
84 Willett P, Ruan Y, Streit R. PMHT:problems and some solutions. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(3):738-754
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
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
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
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
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
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
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 freeenergy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory,2005, 51(7):2282-2312
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 Sarkka S, Nummenmaa A. Recursive noise adaptive Kalman filtering by variational Bayesian approximations.IEEE Transactions on Automatic Control, 2009, 54(3):596-600
104 Sarkka S, Hartikainen J. Non-linear noise adaptive Kalman filtering via variational Bayes. In:Proceedings of the 2013IEEE 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
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
107 Li W L, Jia Y M, Du J P, Zhang J. PHD filter for multitarget tracking with glint noise. Signal Processing, 2014,94:48-56
108 Ardeshiri T,Ozkan E, Orguner U, Gustafsson F. Approximate Bayesian smoothing with unknown process and measurement noise covariances. IEEE Signal Processing Letters, 2015, 22(12):2450-2454
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
110 Wang C, Blei D M. Variational inference in nonconjugate models. The Journal of Machine Learning Research, 2013,14(4):1005-1031
111 Piche R, Sarkka S, Hartikainen J. Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution. In:Proceedings of the2012 International Workshop on Machine Learning for Signal Processing. Santander, Spain:IEEE, 2012:1-6
112 Nurminen H, Ardeshiri T, Piche R, Gustafsson F. Robust inference for state-space models with skewed measurement noise. IEEE Signal Processing Letters, 2015, 22(11):1898-1902
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 the26 th 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
115 Lazaro 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
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 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.(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.)
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
2 Llinas J, Waltz E. Multisensor Data Fusion. Norwood,MA:Artech House Publisher, 1990.
3 He You, Xiu Jian-Juan, Guan Xin. Radar Data Processing with Applications(Third Edition). Beijing:Publishing House of Electronics Industry, 2013.(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.)
4 Hall D L, Llinas J. Handbook of Multisensor Data Fusion.Danvers:CRC Press, 2001.
5 Zhou Hong-Ren, Jing Zhong-Liang, Wang Pei-De. Maneuvering Target Tracking. Beijing:National Defense Industry Press, 1991.(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.)
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 Wang 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(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)
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 contextaware communication system for one single autonomic region to realize smart living. Information Fusion, 2015, 21:57-67
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, Wortche H J, Liotta A. Spatial anomaly detection in sensor networks using neighborhood information. Information Fusion, 2017, 33:41-56
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 Pan 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(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)
14 Pan 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(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)
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
16 Gustafsson F, Hendeby G. Some relations between extended and unscented Kalman filters. IEEE Transactions on Signal Processing, 2012, 60(2):545-555
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
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
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
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
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
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
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
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
27 Chen 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(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)
28 Kamen E W. Multiple target tracking based on symmetric measurement equations. IEEE Transactions on Automatic Control, 1989, 37(3):371-374
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
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
33 Ruan Y H, Willett P. The turbo PMHT. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(4):1388-1398
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
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
36 Mahler R. PHD filters of higher order in target number.IEEE Transactions on Aerospace and Electronic Systems,2007, 43(4):1523-1543
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
38 Vo B T, Vo B N. Labeled random finite sets and multiobject conjugate priors. IEEE Transactions on Signal Processing, 2013, 61(13):3460-3475
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 Yang 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(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)
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 Wu 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(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)
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
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
49 Schon T B, Wills A, Ninness B. System identification of nonlinear state-space models. Automatica, 2011, 47(1):39-49
50 Kantas N, Doucet A, Singh S S, Maciejowski J, Chopin N. On Particle methods for parameter estimation in statespace models. Statistical Science, 2015, 30(3):328-351
51 Dahlin J, Schon T B. Getting started with particle Metropolis-Hastings for inference in nonlinear dynamical models. arXiv:1511.01707v7, 2017.
52 Schon 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
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
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
57 Norgaard M, Poulsen N K, Ravn O. New developments in state estimation for nonlinear systems. Automatica, 2000,36(11):1627-1638
58 Smidl V, Quinn A. Variational Bayesian filtering.IEEE Transactions on Signal Processing, 2008, 56(10):5020-5030
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
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
61 Geng H, Liang Y, Zhang X J. Linear-minimum-meansquare-error observer for multi-rate sensor fusion with missing measurements. IET Control Theory and Applications, 2014, 8(14):1375-1383
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
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
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
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
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
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
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
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
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
71 Lu X, Zhang H S, Wang W, Teo K L. Kalman filtering for multiple time-delay systems. Automatica, 2005, 41(8):1455-1461
72 Dey S, Leong A S, Evans J S. Kalman filtering with faded measurements. Automatica, 2009, 45(10):2223-2233
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
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
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
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
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-beforedetect for sea clutter rejection:tests with real data. IEEE Transactions on Aerospace and Electronic Systems, 2016,52(3):1035-1045
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
84 Willett P, Ruan Y, Streit R. PMHT:problems and some solutions. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(3):738-754
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
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
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
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
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
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
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 freeenergy approximations and generalized belief propagation algorithms. IEEE Transactions on Information Theory,2005, 51(7):2282-2312
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 Sarkka S, Nummenmaa A. Recursive noise adaptive Kalman filtering by variational Bayesian approximations.IEEE Transactions on Automatic Control, 2009, 54(3):596-600
104 Sarkka S, Hartikainen J. Non-linear noise adaptive Kalman filtering via variational Bayes. In:Proceedings of the 2013IEEE 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
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
107 Li W L, Jia Y M, Du J P, Zhang J. PHD filter for multitarget tracking with glint noise. Signal Processing, 2014,94:48-56
108 Ardeshiri T,Ozkan E, Orguner U, Gustafsson F. Approximate Bayesian smoothing with unknown process and measurement noise covariances. IEEE Signal Processing Letters, 2015, 22(12):2450-2454
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
110 Wang C, Blei D M. Variational inference in nonconjugate models. The Journal of Machine Learning Research, 2013,14(4):1005-1031
111 Piche R, Sarkka S, Hartikainen J. Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution. In:Proceedings of the2012 International Workshop on Machine Learning for Signal Processing. Santander, Spain:IEEE, 2012:1-6
112 Nurminen H, Ardeshiri T, Piche R, Gustafsson F. Robust inference for state-space models with skewed measurement noise. IEEE Signal Processing Letters, 2015, 22(11):1898-1902
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 the26 th 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
115 Lazaro 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
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 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.(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.)
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