多传感器分布式检测和估计融合
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摘要
随着科学和工业的发展,信息科学领域涌现出许多应用数学科学问题,这些问题的研究拓宽和加速了基础数学理论的研究.另一方面,基础数学理论的进展以及在信息科学领域的成功应用也促使了工业领域的蓬勃发展.数学与其他学科的相互渗透已成为当今应用数学的主要特点之一,如在2010年ICM(国际数学家大会)上有2个分别关于控制和图像科学的1小时大会报告、7个关于"Mathematical Aspects of Computer Science"的特邀报告和8个关于"Mathematics in Science and Technology"的特邀报告.多源信息融合是数学和信息科学结合的一个重要研究方向.本文主要考虑其中两类基本问题:多传感器检测融合和估计融合,主要创新点包括:(1)对一般传感器观测相关条件下的多传感器分布式检测融合系统,获得同时搜索最优传感器律和最优融合律的高效算法;(2)对失序观测、错误观测和异步观测多传感器分布式估计融合系统,给出统一的全航迹(不仅仅校正当前状态估计)全局最优估计融合公式和算法;(3)对有偏不确定系统估计融合提出极小化Euclid误差准则,并基于多传感器和多算法估计融合获得极小化Euclid误差的抗偏估计高效算法.
With the development of the science and industry,there are many applied mathematics problems emerging from information science felds. The studies on these problems broaden and accelerate the study of pure mathematical theory. On the other hand,the progresses of pure mathematical theories and their innovation applications in information science contribute to the rapid development of industrial areas. The mutual penetration between mathematics and other subjects has become one of the main features of applied mathematics. For example,in the International Congress of Mathematicians(2010),there are two plenary lectures about the control and the image science respectively,seven invited lectures about "Mathematical Aspects of Computer Science" and eight invited lectures about "Mathematics in Science and Technology". The multi-source information fusion is an important interdisciplinary research direction of mathematics and information science. In our thesis,we focus on two classes of basic problems: multi-sensor distributed detection fusion and multi-sensor distributed estimation fusion. The main innovations include:(1) For dependent measurements and the general multi-sensor distributed detection fusion systems,we derived an efcient algorithm to simultaneously search for optimal sensor rules and an optimal fusion rule.(2) For multi-sensor distributed estimation fusion systems with out-of-sequence measurements,error measurements and asynchronous measurements,we derived a unifed estimation fusion algorithm which updates the whole trajectory and is optimal.(3) For uncertain dynamic systems with biases,we presented the criterion of minimizing Euclidean error and obtained an efcient minimized-Euclidean-error algorithm to estimate states based on multi-sensor and multi-algorithm fusion.
With the development of the science and industry,there are many applied mathematics problems emerging from information science felds. The studies on these problems broaden and accelerate the study of pure mathematical theory. On the other hand,the progresses of pure mathematical theories and their innovation applications in information science contribute to the rapid development of industrial areas. The mutual penetration between mathematics and other subjects has become one of the main features of applied mathematics. For example,in the International Congress of Mathematicians(2010),there are two plenary lectures about the control and the image science respectively,seven invited lectures about "Mathematical Aspects of Computer Science" and eight invited lectures about "Mathematics in Science and Technology". The multi-source information fusion is an important interdisciplinary research direction of mathematics and information science. In our thesis,we focus on two classes of basic problems: multi-sensor distributed detection fusion and multi-sensor distributed estimation fusion. The main innovations include:(1) For dependent measurements and the general multi-sensor distributed detection fusion systems,we derived an efcient algorithm to simultaneously search for optimal sensor rules and an optimal fusion rule.(2) For multi-sensor distributed estimation fusion systems with out-of-sequence measurements,error measurements and asynchronous measurements,we derived a unifed estimation fusion algorithm which updates the whole trajectory and is optimal.(3) For uncertain dynamic systems with biases,we presented the criterion of minimizing Euclidean error and obtained an efcient minimized-Euclidean-error algorithm to estimate states based on multi-sensor and multi-algorithm fusion.
引文
1 沈晓静.多传感器分布式检测和估计融合.博士学位论文.成都:四川大学,2009
2 Tsitsiklis J N,Athans M.On the complexity of decentralized decision making and detection problems.IEEE Trans Automat Control,1985,30:440–446
3 Drakopoulos E,Lee C C.Optimum multisensor fusion of correlated local decisions.IEEE Trans Aerosp Electron Systems,1991,27:424–429
4 Kam I,Zhu Q,Gray W S,et al.Optimal data fusion of correlated local decisions in multiple sensor detection systems.IEEE Trans Aerosp Electron Systems,1992,28:916–920
5 Zhu Y,Blum R S,Luo Z-Q,et al.Unexpected properties and optimum-distributed sensor detectors for dependent observation cases.IEEE Trans Automat Control,2000,45:62–72
6 Chair Z,Varshney P K.Optimal data fusion in multiple sensor detection systems.IEEE Trans Aerosp Electron Systems,1986,1:98–101
7 Shen X,Zhu Y,He L,et al.A near-optimal iterative algorithm via alternately optimizing sensor and fusion rules in distributed decision systems.IEEE Trans Aerosp Electron Systems,2011,47:2514–2529
8 Shen X,Zhu Y,You Z.An efcient sensor quantization algorithm for decentralized estimation fusion.Automatica,2011,47:1053–1059
9 Bar-Shalom Y,Chen H,Mallick M.One-step solution for the multistep out-of-sequence measurement problem in tracking.IEEE Trans Aerosp Electron Systems,2004,1:27–37
10 Shen X,Luo Y,Zhu Y,et al.Globally optimal fight path update with adding or removing out-of-sequence measurements.Automatica,2010,46:1437–1442
11 Shen X,Luo Y,Zhu Y,et al.Globally optimal distributed Kalman fltering fusion.Sci China Inf Sci,2012,55:512–529
12 Bertsekas D P,Rhodes I B.Recursive state estimation for a setmembership description of uncertainty.IEEE Trans Automat Control,1971,16:117–128
13 Schweppe F C.Recursive state estimation:unknown but bounded errors and system inputs.IEEE Trans Automat Control,1968,13:22–28
14 Fan M K H,Tits A L,Doyle J C.Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics.IEEE Trans Automat Control,1991,36:25–38
15 El Ghaoui L,Calafore G.Robust fltering for discrete-time systems with bounded noise and parametric uncertainty.IEEE Trans Automat Control,2001,46:1084–1089
16 Zhu Y,Zhou J,Shen X,et al.Networked Multisensor Decision and Estimation Fusion:Based on Advanced Mathematical Methods.Boca Raton,FL:CRC Press,2012
17 Shen X,Zhu Y,Song E,et al.Minimizing Euclidean state estimation error for linear uncertain dynamic systems based on multisensor and multi-algorithm fusion.IEEE Trans Inform Theory,2011,57:7131–7146
18 Nesterov Y,Nemirovski A.Interior Point Polynomial Methods in Convex Programming:Theory and Applications.Philadelphia,PA:SIAM,1994
2 Tsitsiklis J N,Athans M.On the complexity of decentralized decision making and detection problems.IEEE Trans Automat Control,1985,30:440–446
3 Drakopoulos E,Lee C C.Optimum multisensor fusion of correlated local decisions.IEEE Trans Aerosp Electron Systems,1991,27:424–429
4 Kam I,Zhu Q,Gray W S,et al.Optimal data fusion of correlated local decisions in multiple sensor detection systems.IEEE Trans Aerosp Electron Systems,1992,28:916–920
5 Zhu Y,Blum R S,Luo Z-Q,et al.Unexpected properties and optimum-distributed sensor detectors for dependent observation cases.IEEE Trans Automat Control,2000,45:62–72
6 Chair Z,Varshney P K.Optimal data fusion in multiple sensor detection systems.IEEE Trans Aerosp Electron Systems,1986,1:98–101
7 Shen X,Zhu Y,He L,et al.A near-optimal iterative algorithm via alternately optimizing sensor and fusion rules in distributed decision systems.IEEE Trans Aerosp Electron Systems,2011,47:2514–2529
8 Shen X,Zhu Y,You Z.An efcient sensor quantization algorithm for decentralized estimation fusion.Automatica,2011,47:1053–1059
9 Bar-Shalom Y,Chen H,Mallick M.One-step solution for the multistep out-of-sequence measurement problem in tracking.IEEE Trans Aerosp Electron Systems,2004,1:27–37
10 Shen X,Luo Y,Zhu Y,et al.Globally optimal fight path update with adding or removing out-of-sequence measurements.Automatica,2010,46:1437–1442
11 Shen X,Luo Y,Zhu Y,et al.Globally optimal distributed Kalman fltering fusion.Sci China Inf Sci,2012,55:512–529
12 Bertsekas D P,Rhodes I B.Recursive state estimation for a setmembership description of uncertainty.IEEE Trans Automat Control,1971,16:117–128
13 Schweppe F C.Recursive state estimation:unknown but bounded errors and system inputs.IEEE Trans Automat Control,1968,13:22–28
14 Fan M K H,Tits A L,Doyle J C.Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics.IEEE Trans Automat Control,1991,36:25–38
15 El Ghaoui L,Calafore G.Robust fltering for discrete-time systems with bounded noise and parametric uncertainty.IEEE Trans Automat Control,2001,46:1084–1089
16 Zhu Y,Zhou J,Shen X,et al.Networked Multisensor Decision and Estimation Fusion:Based on Advanced Mathematical Methods.Boca Raton,FL:CRC Press,2012
17 Shen X,Zhu Y,Song E,et al.Minimizing Euclidean state estimation error for linear uncertain dynamic systems based on multisensor and multi-algorithm fusion.IEEE Trans Inform Theory,2011,57:7131–7146
18 Nesterov Y,Nemirovski A.Interior Point Polynomial Methods in Convex Programming:Theory and Applications.Philadelphia,PA:SIAM,1994