一种基于马尔科夫链的冲突证据组合方法

李新德; 董清泉; 王丰羽; 雒超民

doi:10.16383/j.aas.2015.c140681

一种基于马尔科夫链的冲突证据组合方法

doi: 10.16383/j.aas.2015.c140681

1.
东南大学自动化学院复杂工程测量与控制教育部重点实验室南京 210096 中国;
2.
底特律大学电子与计算机工程系密歇根美国

基金项目:

国家自然科学基金(60804063, 61175091), 航空基金 (20140169002), 江苏省 "青蓝工程" 资助计划, 江苏省 "六大高峰人才" 资助计划资助

详细信息

作者简介:
董清泉东南大学自动化学院硕士研究生. 主要研究方向为信息融合和不确定推理. E-mail: 374561475@qq.com

通讯作者:
李新德东南大学自动化学院副教授.主要研究方向为智能机器人, 人机交互,机器感知, 信息融合, 不确定推理和机器视觉. E-mail: xindeli@seu.edu.cn

计量
- 文章访问数: 2672
- HTML全文浏览量: 95
- PDF下载量: 936
- 被引次数: 0
出版历程
- 收稿日期: 2014-09-25
- 修回日期: 2015-01-19
- 刊出日期: 2015-05-20

A Method of Conflictive Evidence Combination Based on the Markov Chain

1.
Key Laboratory of Measurement and Control (School of Automation, Southeast University), Ministry of Education, Nanjing 210096, China;
2.
Department of Electrical and Computer Engineering, University of Detroit Mercy, Michigan, USA

Funds:

Supported by National Natural Science Foundation of China (60804063, 61175091), Aeronautical Science Foundation of China (20140169002), Qing Lan Project of Jiangsu Province, and Six Major Top-talent Plan of Jiangsu Province

摘要

摘要: 针对智能信息处理中Dempster组合规则不能处理高度冲突的问题,考虑到序贯证据的序列性具有高效的抗干扰性能,因此本文提出了一种基于马尔科夫链的冲突证据组合方法. 首先,从经典马尔科夫链中的确定性状态描述扩展到不确定性状态描述;然后,以滑动窗口宽度l对序贯历史证据进行采样, 并利用相似性测度计算的权重来修正它们,从而对修正后的历史证据进行马尔科夫建模,并根据转移概率矩阵,计算证据代表;最后,利用Murphy组合规则对该证据代表组合l-1次. 当然,本文方法也比较适合批量同步融合. 大量的仿真实验对比分析表明,该方法优势比较明显, 有效地解决了冲突证据合成出现的问题,并能有效兼顾合成结果的鲁棒性和灵敏性.
- 证据推理 /
- 冲突 /
- 马尔科夫链 /
- 状态不确定性 /
- 组合规则
Abstract: Aiming at the problem that highly conflictive evidence can not be processed by Dempster rule in intelligent information processing, a method of conflictive evidence combination based on Markov chain is proposed by considering the high-efficiency anti-interference performance for the sequentiality of sequential evidences. At first, the deterministic state description in the classic Markov chain is extended to nondeterministic state description. And then, the past evidences are sampled sequentially according to the sliding window width l, which could be amended according to the weight computed by utilizing the similarity measure. A Markov model is established on these past evidences amended so that a transition probability matrix could be obtained, which is used to compute the evidential representative. Finally, this representative is combined with itself for l-1 times according to the Murphy's combination method. Of course, this method also fits parallel fuse in a step. Through simulation experiments, the comparisive analysis show that the new method's advantage is obvious. That is to say, it efficiently solves the problem of the combination of conflictive evidences; moreover, it keeps robustness and sensibility of combinational result.
- Evidence reasoning /
- conflict /
- Markov chain /
- state-uncertainty /
- combination rule

HTML全文

参考文献(34)

[1]	Shafer G. A Mathematical Theory of Evidence. Princeton: Princeton University Press, 1976.
[2]	[2] Smarandache F, Dezert J. Advances and Applications of DSmT for Information Fusion, Collected Works. USA: American Research Press, 2004/2006/2009, Vol.1-3
[3]	Li Xin-De, Dezert J, Huang Xin-Han, Meng Zheng-Da, Wu Xue-Jian. A fast approximate reasoning method in hierarchical DSmT (A). Acta Electronica Sinica, 2010, 38(11): 2566-2572(李新德, Dezert J, 黄心汉, 孟正大, 吴雪建. 一种快速分层递阶DSmT近似推理融合方法(A). 电子学报, 2010, 38(11): 2566-2572)
[4]	Li Xin-De, Yang Wei-Dong, Wu Xue-Jian, Dezert J. A fast approximate reasoning method in hierarchical DSmT (B). Acta Electronica Sinica, 2011, 39(3A): 31-36(李新德, 杨伟东, 吴雪建, Dezert J. 一种快速分层递阶DSmT近似推理融合方法(B). 电子学报, 2011, 39(3A): 31-36)
[5]	Li Xin-De, Yang Wei-Dong, Dezert J. An airplane image target's multi-feature fusion recognition method. Acta Automatica Sinica, 2012, 38(8): 1298-1307(李新德, 杨伟东, Dezert J. 一种飞机图像目标多特征信息融合识别方法. 自动化学报, 2012, 38(8): 1298-1307)
[6]	Li Xin-De, Pan Jin-Dong, Dezert J. A target recognition algorithm for sequential aircraft based on DSmT and HMM. Acta Automatica Sinica, 2014, 40(12): 2862-2876(李新德, 潘锦东, Dezert J. 一种基于DSmT和HMM的序列飞机目标识别算法. 自动化学报, 2014, 40(12): 2862-2876)
[7]	[7] Lefevre E, Colot O, Vannoorenberghe P. Belief function combination and conflict management. Information Fusion, 2002, 3(2): 149-162
[8]	[8] Yager R R. On the dempster-shafer framework and new combination rules. Information Sciences, 1987, 41(2): 93-137
[9]	[9] Liu W R. Analyzing the degree of conflict among belief functions. Artificial Intelligence, 2006, 170(11): 909-924
[10]	Wang Dong, Li Qi, Jiang Wen, Xu Xiao-Bin, Deng Yong. New method to combine conflict evidence based on pignistic probability distance. Infrared and Laser Engineering, 2009, 38(1): 149-154(王栋, 李齐, 蒋雯, 徐晓滨, 邓勇. 基于Pignistic概率距离的冲突证据合成方法. 红外与激光工程, 2009, 38(1): 149-154)
[11]	Deng Yong, Wang Dong, Li Qi, Zhang Ya-Juan. A new method to analyze evidence conflict. Control Theory Applications, 2011, 28(6): 839-844(邓勇, 王栋, 李齐, 章雅娟. 一种新的证据冲突分析方法. 控制理论与应用, 2011, 28(6): 839-844)
[12]	Quan Wen, Wang Xiao-Dan, Wang Jian, Zhang Yu-Xi. New combination rule of DST based on local conflict distribution strategy. Acta Electronica Sinica, 2012, 40(9): 1880-1884(权文, 王晓丹, 王坚, 张玉玺. 一种基于局部冲突分配的DST组合规则. 电子学报, 2012, 40(9): 1880-1884)
[13]	Yang J B, Xu D L. Evidential reasoning rule for evidence combination. Artificial Intelligence, 2013, 205: 1-29
[14]	Hu Li-Fang, Guan Xin, Deng Yong, He You. Cause-analysis for conflicting evidences in the generalized power space. Control Theory Applications, 2011, 28(12): 1717-1722(胡丽芳, 关欣, 邓勇, 何友. 广义幂集空间中证据冲突的原因分析. 控制理论与应用, 2011, 28(12): 1717-1722)
[15]	Xiong Yan-Ming, Yang Zhan-Ping, Qu Xin-Fen. Novel combination method of conflict evidence based on evidential model modification. Control and Decision, 2011, 26(6): 883-887(熊彦铭, 杨战平, 屈新芬. 基于模型修正的冲突证据组合新方法. 控制与决策, 2011, 26(6): 883-887)
[16]	Lu Zheng-Cai, Qin Zheng. General framework for evidence combination and its approach to highly conflicting evidence fusion. Journal of Tsinghua University (Science and Technology), 2011, 51(11): 1161-1615, 1626(卢正才, 覃征. 证据合成的一般框架及高度冲突证据合成方法. 清华大学学报(自然科学版), 2011, 51(11): 1161-1165, 1626)
[17]	Han De-Qiang, Han Chong-Zhao, Deng Yong, Yang Yi. Weighted combination of conflicting evidence based on evidence variance. Acta Electronica Sinica, 2011, 39(3A): 153-157(韩德强, 韩崇昭, 邓勇, 杨艺. 基于证据方差的加权证据组合. 电子学报, 2011, 39(3A): 153-157)
[18]	Jiang Wen, Zhang An, Deng Yong. A novel information fusion method based on our evidence conflict representation. Journal of Northwestern Polytechnical University, 2010, 28(1): 27-32(蒋雯, 张安, 邓勇. 基于新的证据冲突表示的信息融合方法研究. 西北工业大学学报, 2010, 28(1): 27-32)
[19]	Markov A A. Extension of the limit theorems of probability theory to a sum of variables connected in a chain. Dynamic Probabilistic Systems, Volume 1: Markov Models. New York: John Wiley and Sons, 1971.
[20]	Norris J R. Markov Chains. Cambridge: Cambridge University Press, 1999.
[21]	Zadeh L A. Review of books: a mathematical theory of evidence. The AI Magazine, 1984, 5(3): 81-83
[22]	Papoulis A, Pillai S U. Probability, Random Variables and Stochastic Processes (4th Edition). Xi'an: Xi'an Jiaotong University Press, 2012.(帕普里斯 A,佩莱 S U. 概率、随机变量与随机过程(第4版). 西安: 西安交通大学出版社. 2012.)
[23]	Deng Xin-Yang, Deng Yong, Zhang Ya-Juan, Liu Qi. A belief Markov model and its application. Acta Automatica Sinica, 2012, 38(4): 666-672(邓鑫洋, 邓勇, 章雅娟, 刘琪. 一种信度马尔科夫模型及应用. 自动化学报, 2012, 38(4): 666-672)
[24]	Jousselme A L, Maupin P. Distances in evidence theory: comprehensive survey and generalizations. International Journal of Approximate Reasoning, 2012, 53(2): 118-145
[25]	Jousselme A L, Grenier D, Boss E. A new distance between two bodies of evidence. Information Fusion, 2001, 2(2): 91-101
[26]	Li X D, Dezert J, Smarandache F, Huang X H. Evidence supporting measure of similarity for reducing the complexity in information fusion. Information Sciences, 2011, 181(10): 1818-1835
[27]	Smets P. Data Fusion in the transferable belief model. In: Proceedings of the 3rd International Conference on Information Fusion. Paris, France: IEEE, 2000. 21-33
[28]	Wen C L, Wang Y C, Xu X B. Fuzzy information fusion algorithm of fault diagnosis based on similarity measure of evidence. Advances in Neural Networks, Lecture Notes in Computer Science vol. 5264, Berlin: Springer Berlin Heidelberg, 2008. 506-515
[29]	Liu Z G, Dezert J, Pan Q, Mercier G. Combination of sources of evidence with different discounting factors based on a new dissimilarity measure. Decision Support Systems, 2011, 52(1): 133-141
[30]	Smets P, Kennes R. The transferable belief model. Artificial Intelligence, 1994, 66(2): 191-243
[31]	Smets P. Decision making in the TBM: the necessity of the pignistic transformation. International Journal of Approximate Reasoning, 2005, 38(2): 133-147
[32]	Murphy C K. Combining belief functions when evidence conflicts. Decision Support Systems, 2000, 29(1): 1-9
[33]	Li Wen-Li, Guo Kai-Hong. Combination rules of D-S evidence theory and conflict problem. Systems Engineering-Theory Practice, 2010, 30(8): 1422-1432(李文立, 郭凯红. D-S证据理论合成规则及冲突问题. 系统工程理论与实践, 2010, 30(8): 1422-1432)
[34]	Li Xin-De, Wang Feng-Yu. A method of evidence reasoning based on ISODATA clustering and improved similarity measure. Acta Automatica Sinica, 2015, 41(3): 575-590(李新德, 王丰羽. 一种基于ISODATA聚类和改进相似度的证据推理方法. 自动化学报, 2015, 41(3): 575-590)