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摘要: 证据理论已广泛应用于时空信息融合领域，由于时域信息融合表现出明显的序贯性和动态性，为实现基于证据理论的时域信息融合，有效处理时域冲突信息，结合证据可靠性评估和证据折扣的思想，在直觉模糊框架内提出了一种基于复合可靠度的时域证据组合方法.首先定义一种基于可靠度的直觉模糊数排序方法，在此基础上提出一种基于直觉模糊多属性决策的证据可靠性评估方法;然后，基于此方法对时域信息序列中相邻时间节点的证据可靠性进行评估，得到时域证据的相对可靠性因子;最后，结合由时域证据可靠度衰减模型得到的实时可靠性因子，得到时域证据的复合可靠性因子，再基于证据折扣运算和Dempster证据组合规则提出一种基于复合可靠度的时域证据组合方法.数值算例和仿真表明，该方法具有较强的时间敏感性，充分体现了时域信息融合的动态性特点，可以较好地处理时域证据中的冲突信息，基于该方法构建的融合识别系统具有较强的抗干扰能力.Abstract: Evidence theory has been widely used in spatial and temporal information fusion. The sequential and dynamic characteristics of temporal fusion calls for a new combination rule of temporal evidence sources. In this paper, temporal evidence combination is analyzed in the framework of evidence reliability and evidence discounting. A method of temporal evidence combination is proposed based on the composite reliability factor of temporal evidence. A ranking method for intuitionistic fuzzy values is firstly presented, followed by the presentation of evidence reliability evaluation based on intuitionistic fuzzy multiple criteria decision making. Then the relative reliability factors of evidence sources in neighboring time nodes are evaluated. By combining the relative reliability factor and real-time reliability factor yielded by the credibility decay model, a composite reliability factor is obtained. Finally, according to evidence discounting and Dempster's combination rule, a method of temporal evidence combination based on the composite reliability factor is proposed. Numerical examples and simulation demonstrate that the proposed method is time sensitive, which can reflect the dynamic nature of temporal information fusion. Moreover, it is illustrated that this method can deal with conflict in temporal fusion well. The proposed temporal evidence combination rule can enhance the anti-interference performance of the target identification fusion system.
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图 1 基于复合可靠度的时空证据序贯组合流程
Fig. 1 The flowchart of spatial-temporal evidence combination based on TEC-CRF
图 2 基于Dempster组合方法的时域累积融合结果
Fig. 2 Temporal evidence accumulation results obtained by Dempster's rule
图 3 基于TEC-CRF方法的时域累积融合结果
Fig. 3 Temporal evidence accumulation results obtained by TEC-CRF
图 4 Dempster方法获得的Pignistic概率
Fig. 4 The Pignistic probability obtained by Dempster's rule
表 1 两种情况下TEC-CRF方法的融合结果
Table 1 The combination results obtained by TEC-CRF for two cases
$m_3$ RTRF ${m_{12}}$折扣后的BPA RRF CRF 最终融合结果 ${m_3}(\{{\theta_1}\})=0.5$ $m_{12}^{{\alpha_1}}(\{{\theta_1}\})=0.2815$ $m_{13}^{{\alpha_1}}(\{{\theta_1}\})=0.4930$ ${m_3}(\{{\theta_2}\})=0.3$ ${\alpha _1}=0.7408$ $m_{12}^{{\alpha_1}}(\{{\theta_2}\})=0.1630$ $r_1=1$ $c_1=0.7408$ $m_{13}^{{\alpha_1}}(\{{\theta_2}\})=0.2491$ ${m_3}(\{{\theta_3}\})=0.2$ ${\alpha _2} = 1$ $m_{12}^{{\alpha_1}}(\{{\theta_3}\})=0.1852$ $r_2=0.8785$ $c_2=0.8785$ $m_{13}^{{\alpha_1}}(\{{\theta_3}\})=0.1853$ ${m_3}(\Theta)=0$ $m_{12}^{{\alpha_1}}(\Theta)=0.4092$ $m_{13}^{{\alpha_1}}(\Theta)=0.0726$ ${m_3}(\{{\theta_1}\})=0.1$ $m_{12}^{{\alpha_1}}(\{{\theta_1}\})=0.2815$ $m_{13}^{{\alpha_1}}(\{{\theta_1}\})=0.2183$ ${m_3}(\{{\theta_2}\})=0.15$ ${\alpha _1}=0.7408$ $m_{12}^{{\alpha_1}}(\{{\theta_2}\})=0.1630$ $r_1=1 $ $c_1=0.7408$ $m_{13}^{{\alpha_1}}(\{{\theta_2}\})=0.3540$ ${m_3}(\{{\theta_3}\})=0.75$ ${\alpha _2} = 1$ $m_{12}^{{\alpha_1}}(\{{\theta_3}\})=0.1630$ $r_2=0.4806$ $c_2=0.4806$ $m_{13}^{{\alpha_1}}(\{{\theta_3}\})=0.1691$ ${m_3}(\Theta)=0$ $m_{12}^{{\alpha_1}}(\Theta)=0.4092$ $m_{13}^{{\alpha_1}}(\Theta)=0.2586$ 
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表 2 两种情况下Dempster方法的融合结果
Table 2 The combination results obtained by Dempster's rule for two cases
$m_3$ $t_{2}$时刻融合结果 $t_{3}$时刻融合结果 ${m_3}(\{{\theta_1}\})=0.5$ $m_{12}(\{{\theta_1}\})=0$ $m_{13}(\{{\theta_1}\})=0$ ${m_3}(\{{\theta_2}\})=0.3$ $m_{12}(\{{\theta_2}\})=0.57$ $m_{13}(\{{\theta_2}\})=0.67$ ${m_3}(\{{\theta_3}\})=0.2$ $m_{12}(\{{\theta_3}\})=0.43$ $m_{13}(\{{\theta_3}\})=0.33$ ${m_3}(\{{\theta_1}\})=0.1$ $m_{12}(\{{\theta_1}\})=0$ $m_{13}(\{{\theta_1}\})=0$ ${m_3}(\{{\theta_2}\})=0.15$ $m_{12}(\{{\theta_2}\})=0.57$ $m_{13}(\{{\theta_2}\})=0.87$ ${m_3}(\{{\theta_3}\})=0.75$ $m_{12}(\{{\theta_3}\})=0.43$ $m_{13}(\{{\theta_3}\})=0.13$
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表 3 两种情况下TEC-RTRF方法的融合结果
Table 3 The combination results obtained by TEC-RTRF for two cases
$m_3$ $t_{2}$时刻融合结果 $t_{3}$时刻融合结果 ${m_3}(\{{\theta_1}\})=0.5$ $m_{12}(\{{\theta_1}\})=0$ $m_{13}(\{{\theta_1}\})=0.35$ ${m_3}(\{{\theta_2}\})=0.3$ $m_{12}(\{{\theta_2}\})=0.71$ $m_{13}(\{{\theta_2}\})=0.44$ ${m_3}(\{{\theta_3}\})=0.2$ $m_{12}(\{{\theta_3}\})=0.29$ $m_{13}(\{{\theta_3}\})=0.21$ ${m_3}(\{{\theta_1}\})=0.1$ $m_{12}(\{{\theta_1}\})=0$ $m_{13}(\{{\theta_1}\})=0.05$ ${m_3}(\{{\theta_2}\})=0.15$ $m_{12}(\{{\theta_2}\})=0.71$ $m_{13}(\{{\theta_2}\})=0.83$ ${m_3}(\{{\theta_3}\})=0.75$ $m_{12}(\{{\theta_3}\})=0.29$ $m_{13}(\{{\theta_3}\})=0.12$
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表 4 各传感器在不同时间节点的识别结果
Table 4 Recognition results of each sensor at all time nodes
时间节点(s) BPM $S_{1}$ $S_{2}$ $S_{3}$ $S_{4}$ $S_{5}$ $S_{6}$ $m(\{{\theta_1}\})$ 0.250 0.300 0.211 0.333 0.629 0.305 $t_{1}=5$ $m(\{{\theta_2}\})$ 0.299 0.256 0.350 0.273 0.352 0.212 $m(\{{\theta_3}\})$ 0.451 0.444 0.429 0.394 0.019 0.483 $m(\{{\theta_1}\})$ 0.440 0.628 0.435 0.348 0.642 0.530 $t_{2}=8$ $m(\{{\theta_2}\})$ 0.323 0.136 0.325 0.262 0.252 0.118 $m(\{{\theta_3}\})$ 0.237 0.236 0.240 0.390 0.106 0.352 $m(\{{\theta_1}\})$ 0.251 0.454 0.269 0.460 0.623 0.124 $t_{3}=16$ $m(\{{\theta_2}\})$ 0.276 0.236 0.336 0.215 0.142 0.420 $m(\{{\theta_3}\})$ 0.473 0.310 0.395 0.325 0.235 0.456 $m(\{{\theta_1}\})$ 0.337 0.318 0.262 0.246 0.435 0.312 $t_{4}=23$ $m(\{{\theta_2}\})$ 0.303 0.269 0.203 0.262 0.259 0.342 $m(\{{\theta_3}\})$ 0.360 0.413 0.535 0.492 0.306 0.346 $m(\{{\theta_1}\})$ 0.336 0.346 0.241 0.368 0.330 0.303 $t_{5}=26$ $m(\{{\theta_2}\})$ 0.312 0.305 0.258 0.262 0.301 0.391 $m(\{{\theta_3}\})$ 0.352 0.349 0.501 0.370 0.369 0.306
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表 5 运用Dempster组合规则获得的空域融合结果
Table 5 Spatial evidence combination results obtained by Dempster's rule
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.5529 0.2850 0.1621 $t_{2}=8$ 0.9489 0.0077 0.0134 $t_{3}=16$ 0.3216 0.0829 0.5955 $t_{4}=23$ 0.1715 0.0703 0.7582 $t_{5}=26$ 0.2365 0.1737 0.5898
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表 6 运用EC-CF方法获得的空域融合结果
Table 6 Spatial evidence combination results obtained by EC-CF
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.2322 0.1299 0.6379 $t_{2}=8$ 0.9509 0.0189 0.0302 $t_{3}=16$ 0.4425 0.0993 0.5482 $t_{4}=23$ 0.1951 0.0920 0.7129 $t_{5}=26$ 0.2546 0.1956 0.5498
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表 7 运用Dempster组合规则获得的时域累积融合结果
Table 7 Spatial evidence combination results obtained by Dempster's rule
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.2322 0.1299 0.6379 $t_{2}=8$ 0.9105 0.0101 0.0794 $t_{3}=16$ 0.9151 0.0023 0.0827 $t_{4}=23$ 0.7512 0.0009 0.2480 $t_{5}=26$ 0.5835 0.0005 0.4160
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表 8 运用TEC-CRF方法获得的时域累积融合结果
Table 8 Temporal evidence accumulation results obtained by TEC-CRF
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $m(\Theta)$ $t_{1}=5$ 0.2322 0.1299 0.6379 0 $t_{2}=8$ 0.9414 0.0168 0.0418 0.1247 $t_{3}=16$ 0.6570 0.0360 0.1466 0.1633 $t_{4}=23$ 0.4241 0.0445 0.3610 0.1704 $t_{5}=26$ 0.2903 0.1275 0.5823 0
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表 9 各传感器在$t_{1}$和$t_{2}$时刻的识别结果
Table 9 Recognition results of each sensor at $t_{1}$ and $t_{2}$
时间节点(s) BPM $S_{1}$ $S_{2}$ $S_{3}$ $S_{4}$ $S_{5}$ $S_{6}$ $m(\{{\theta_1}\})$ 0.440 0.628 0.435 0.348 0.642 0.530 $t_{1}=5$ $m(\{{\theta_2}\})$ 0.323 0.136 0.325 0.262 0.252 0.118 $m(\{{\theta_3}\})$ 0.237 0.236 0.240 0.390 0.106 0.352 $m(\{{\theta_1}\})$ 0.250 0.300 0.211 0.333 0.629 0.305 $t_{2}=8$ $m(\{{\theta_2}\})$ 0.299 0.256 0.350 0.273 0.352 0.212 $m(\{{\theta_3}\})$ 0.451 0.444 0.429 0.394 0.019 0.483
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表 10 基于Dempster方法的空域融合结果
Table 10 Spatial evidence combination results based on Dempster's rule
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.9789 0.0077 0.0134 $t_{2}=8$ 0.5529 0.2850 0.1621 $t_{3}=16$ 0.3216 0.0829 0.5955 $t_{4}=23$ 0.1715 0.0703 0.7582 $t_{5}=26$ 0.2365 0.1737 0.5898
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表 11 基于EC-CF方法的空域融合结果
Table 11 Spatial evidence combination results based on EC-CF
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.9509 0.0189 0.0302 $t_{2}=8$ 0.2322 0.1299 0.6379 $t_{3}=16$ 0.4425 0.0993 0.5482 $t_{4}=23$ 0.1951 0.0920 0.7129 $t_{5}=26$ 0.2546 0.1956 0.5498
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表 12 基于Dempster方法的时域累积融合结果
Table 12 Temporal evidence combination results based on Dempster's rule
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $t_{1}=5$ 0.9509 0.0189 0.0302 $t_{2}=8$ 0.9105 0.0101 0.0794 $t_{3}=16$ 0.9151 0.0023 0.0827 $t_{4}=23$ 0.7512 0.0009 0.2480 $t_{5}=26$ 0.5835 0.0005 0.4160
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表 13 基于TEC-CRF方法的时域累积融合结果
Table 13 Temporal evidence accumulation results based on TEC-CRF
时间节点(s) $m({\theta _1})$ $m({\theta _2})$ $m({\theta _3})$ $m(\Theta)$ $t_{1}=5$ 0.9509 0.0189 0.0302 0 $t_{2}=8$ 0.5427 0.0751 0.3822 0 $t_{3}=16$ 0.4300 0.0558 0.3441 0.1701 $t_{4}=23$ 0.2854 0.0510 0.4868 0.1768 $t_{5}=26$ 0.2321 0.1158 0.6521 0
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