最优和自校正多传感器观测融合滤波方法和算法研究
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摘要
随着计算机技术、通信技术、微电子技术、精密机械制造技术以及控制技术的飞速发展,各种面向复杂应用背景的多传感器系统大量涌现。在多传感器系统中,由于信息表现出形式多样、数量巨大、关系复杂以及要求处理及时、准确和可靠等特征,为了提高信息的综合处理能力,一门由信息学科、控制学科等交叉、综合、拓展而产生的新兴学科——多传感器信息融合应运而生。
多传感器信息融合估计是多传感器信息融合的一个重要分支,其目的是如何利用多传感器提供的观测数据对系统状态或信号给出比基于单传感器更精确的估计,广泛应用于目标跟踪、军事、航天、制导、GPS定位、机器人等高技术领域,具有重要理论和应用意义。
本课题来源于国家自然科学基金项目“多传感器信息融合最优和自校正滤波新理论和新方法”(60374026)和“自校正信息融合滤波理论及其应用研究”(60874063)。
本文基于现代时间序列分析方法,以理论分析为主,以计算机仿真示例为辅,对多传感器线性随机系统的最优加权观测融合状态估计和自校正加权观测融合状态估计问题进行了深入研究。做了如下几方面工作：
首先,对于带未知噪声统计的多传感器系统,利用相关方法,提出了一种具有强一致性的信息融合噪声统计在线估值器,其中从采样相关函数线性方程组中任意选择非奇异的部分线性方程组求解得局部噪声统计估值器,然后取局部估值器的算术加权平均作为融合估值器,证明了它可被视为最小二乘融合器。用相关函数的遍历性证明了它以概率1收敛于真实的噪声统计。它的精度介于局部估值器中最高和最低的精度之间,因而具有较高的可信度。对于含有未知模型参数和噪声统计的多传感器ARMA(自回归滑动平均)系统,利用已有的ARMA模型参数估计方法,结合未知噪声统计的信息融合在线估值器,提出了多段信息融合辨识方法,并且提出了一种信息融合模型参数估值器概念,它是基于各传感器得到的局部模型参数估值器的算术平均,且从理论上严格证明了所提出的信息融合模型参数估值器的一致性。
其次,对带相关观测噪声和带相关噪声的多传感器线性离散定常随机系统,在线性无偏最小方差(LUMV)融合准则下,应用Lagrange乘数法和基于ARMA新息模型的滤波理论,分别提出了最优加权观测融合稳态Kalman滤波和Wiener滤波算法,其结果等同于基于加权最小二乘(WLS)融合准则的最优加权观测融合滤波算法,兼具完全功能等价性和渐近全局最优性。对于带不同观测阵、相关观测噪声的多传感器系统,应用矩阵分块方法,结合观测加权阵的约束条件,提出了降维观测融合算法,可以显著地减少求观测加权阵和融合观测误差方差阵的计算负担,给出的计算负担比较表从定量分析的角度支持了此论断。
第三,对于带有未知噪声统计、相关观测噪声和相关噪声的多传感器系统,将未知噪声统计的信息融合在线估值器代入稳态最优加权观测融合滤波器,分别提出了自校正加权观测融合Kalman滤波器和Wiener滤波器,及自校正降维观测融合滤波器。利用动态误差系统分析(DESA)方法证明了自校正融合器按实现收敛于相应的稳态全局最优融合器,即具有渐近全局最优性。
最后,对于带公共干扰噪声和含有未知噪声统计和未知模型参数的多传感器单通道自回归(AR)信号系统和ARMA信号系统,利用ARMA模型到状态空间模型的转化方法,将信号估计问题转化为状态估计问题。将模型参数和噪声统计的信息融合估值器代入稳态最优加权观测融合Wiener信号滤波器中,分别提出了自校正加权观测融合Wiener信号滤波器。应用动态误差系统分析(DESA)方法,严格证明了提出的自校正加权观测融合Wiener信号滤波器按实现收敛于相应的稳态全局最优滤波器,因而具有渐近全局最优性。
通篇用大量的在跟踪系统中和在信号处理中的仿真例子说明了所提出方法和算法的有效性。
With the rapid development in computer technology, communication technology, microelectonics technology, precision machine manufacture technology and control technology, all kinds of multisensor systems, suited to the complicated application backgrounds, come into being. In the multisensor systems, since the information has a lot of characters, for example, it has the various forms, the tremendous quantities, the complicated relationship, and it requires to be precise and reliable, and settled in time, in order to increase the synthesized handling ability, a new branch of science, multisensor information fusion, intersected, synthesized and expended by information subject and control subject, comes into being.
Multisensor information fusion estimation is an important branch of multisensor information fusion, and its aim is how to utilize the measurement data, provided by multisensor, to make more precise estimation to the state or signal of the systems than the estimation based on the single sensor. It is widely used in many high technology fields, such as target tracking, military affairs, space flight, guidance, GPS position and robotics.
This subject comes from the National Nature Science Foundation under Grant 60374026, New Theories and New Methods for Multisensor Information Fusion Optimal and Self-tuning Filtering, and Grant 60874063, Research on Self-tuning Information Fusion Filtering Theory and Its Applications.
Based on modern time series analysis method, for multisensor linear stochastic systems, this paper makes the theoretical analysis primarily, the computation simulation examples secondarily, and the deep researches on the state estimation problems of optimal weighted measurement fusion and self-tuning weighted measurement fusion. The main works are as follows:
First, for the multisensor systems with unknown noise statistics, applying the correlation method, the information fusion noise statistics on-line estimators, which have the strong consistence, are presented, where the nonsingular partial linear equations are selected from the sampled correlation function linear equations to be solved to obtain the local noise statistics estimators, then the fused estimators are obtained by making the weighted arithmetic average of the local estimators, and it is proved that the fused estimators can be viewed as the least squares fusers. Using the ergodicity of the correlation function, it is proved that the fused estimators converge to the true noise statistics with probability one. Since the accuracy of each fused estimator falls in between the highest and lowest accuracies of the local estimators, it has the higher reliability. For the multisensor autoregressive moving average (ARMA) systems with unknown model parameters and noise statistics, applying the existing estimation methods for ARMA model parameters, combining the information fusion on-line estimators of the unknown noise statistics, the multi-stage information fusion identification methods and the concept of the information fusion model parameter estimators are presented. The information fusion model parameter estimators are obtained by taking the average of the local model parameter estimators obtained from each sensor. In theory, the consistence of the proposed information fusion model parameter estimators is rigorously proved.
Second, for the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises and correlated noises, under the linear unbiased minimum variance (LUMV) criterion, applying Lagrange multiplier method and the filtering theories based on ARMA innovation model, the optimal weighted measurement fusion steady-state Kalman filtering and Wiener filtering algorithms are presented respectively, and theirs results are equal to those of the optimal weighted measurement fusion filtering algorithms based on the weighted least squares (WLS) fusion criterion, that is, they have the completely functional equivalence and the asymptotical global optimality. For the multisensor systems with different measurement matrices and correlated measurement noises, using the matrix partitioning method, combining the constraint condition of the measurement weight matrices, the reduced dimension measurement fusion algorithm is presented, which can remarkably reduce the computational burdens of computing the measurement weight matrices and the fused measurement error variance matrices. The presented comparison table of the computational burden supports this inference from the view point of quantitative analysis.
Third, for the multisensor systems with unknown noise statistics, correlated measurement noises and correlated noises, by substituting the information fusion on-line estimators of unknown noise statistics into the steady-state optimal weighted measurement fusion filters, the self-tuning weighted measurement fusion Kalman filters and Wiener filters, and the self-tuning reduced dimension measurement fusion filters are presented respectively. Applying the dynamic error system analysis (DESA) method, it is proved that the proposed self-tuning fusers converge to the corresponding steady-state globally optimal fusers in a realization, that is, they have the asymptotical global optimality.
Last, for the multisensor single channel autoregressive (AR) signal systems and ARMA signal systems with the common disturbance noise, unknown noise statistics and unknown model parameters, using the transformation method from ARMA model to the state space model, the signal estimation problem is transformed into the state estimation problem. By substituting the information fusion estimators of model parameters and noise statistics into the steady-state optimal weighted measurement fusion Wiener signal filters, the self-tuning weighted measurement fusion Wiener signal filters are presented respectively. By DESA method, it is rigorously proved that the proposed self-tuning weighted measurement fusion Wiener signal filters converge to the corresponding steady-state globally optimal filters in a realization, so they have the asymptotical global optimality.
In the whole paper, a lot of simulation examples in the tracking system and the signal processing show the effectiveness of the proposed methods and algorithms.
多传感器信息融合估计是多传感器信息融合的一个重要分支,其目的是如何利用多传感器提供的观测数据对系统状态或信号给出比基于单传感器更精确的估计,广泛应用于目标跟踪、军事、航天、制导、GPS定位、机器人等高技术领域,具有重要理论和应用意义。
本课题来源于国家自然科学基金项目“多传感器信息融合最优和自校正滤波新理论和新方法”(60374026)和“自校正信息融合滤波理论及其应用研究”(60874063)。
本文基于现代时间序列分析方法,以理论分析为主,以计算机仿真示例为辅,对多传感器线性随机系统的最优加权观测融合状态估计和自校正加权观测融合状态估计问题进行了深入研究。做了如下几方面工作：
首先,对于带未知噪声统计的多传感器系统,利用相关方法,提出了一种具有强一致性的信息融合噪声统计在线估值器,其中从采样相关函数线性方程组中任意选择非奇异的部分线性方程组求解得局部噪声统计估值器,然后取局部估值器的算术加权平均作为融合估值器,证明了它可被视为最小二乘融合器。用相关函数的遍历性证明了它以概率1收敛于真实的噪声统计。它的精度介于局部估值器中最高和最低的精度之间,因而具有较高的可信度。对于含有未知模型参数和噪声统计的多传感器ARMA(自回归滑动平均)系统,利用已有的ARMA模型参数估计方法,结合未知噪声统计的信息融合在线估值器,提出了多段信息融合辨识方法,并且提出了一种信息融合模型参数估值器概念,它是基于各传感器得到的局部模型参数估值器的算术平均,且从理论上严格证明了所提出的信息融合模型参数估值器的一致性。
其次,对带相关观测噪声和带相关噪声的多传感器线性离散定常随机系统,在线性无偏最小方差(LUMV)融合准则下,应用Lagrange乘数法和基于ARMA新息模型的滤波理论,分别提出了最优加权观测融合稳态Kalman滤波和Wiener滤波算法,其结果等同于基于加权最小二乘(WLS)融合准则的最优加权观测融合滤波算法,兼具完全功能等价性和渐近全局最优性。对于带不同观测阵、相关观测噪声的多传感器系统,应用矩阵分块方法,结合观测加权阵的约束条件,提出了降维观测融合算法,可以显著地减少求观测加权阵和融合观测误差方差阵的计算负担,给出的计算负担比较表从定量分析的角度支持了此论断。
第三,对于带有未知噪声统计、相关观测噪声和相关噪声的多传感器系统,将未知噪声统计的信息融合在线估值器代入稳态最优加权观测融合滤波器,分别提出了自校正加权观测融合Kalman滤波器和Wiener滤波器,及自校正降维观测融合滤波器。利用动态误差系统分析(DESA)方法证明了自校正融合器按实现收敛于相应的稳态全局最优融合器,即具有渐近全局最优性。
最后,对于带公共干扰噪声和含有未知噪声统计和未知模型参数的多传感器单通道自回归(AR)信号系统和ARMA信号系统,利用ARMA模型到状态空间模型的转化方法,将信号估计问题转化为状态估计问题。将模型参数和噪声统计的信息融合估值器代入稳态最优加权观测融合Wiener信号滤波器中,分别提出了自校正加权观测融合Wiener信号滤波器。应用动态误差系统分析(DESA)方法,严格证明了提出的自校正加权观测融合Wiener信号滤波器按实现收敛于相应的稳态全局最优滤波器,因而具有渐近全局最优性。
通篇用大量的在跟踪系统中和在信号处理中的仿真例子说明了所提出方法和算法的有效性。
With the rapid development in computer technology, communication technology, microelectonics technology, precision machine manufacture technology and control technology, all kinds of multisensor systems, suited to the complicated application backgrounds, come into being. In the multisensor systems, since the information has a lot of characters, for example, it has the various forms, the tremendous quantities, the complicated relationship, and it requires to be precise and reliable, and settled in time, in order to increase the synthesized handling ability, a new branch of science, multisensor information fusion, intersected, synthesized and expended by information subject and control subject, comes into being.
Multisensor information fusion estimation is an important branch of multisensor information fusion, and its aim is how to utilize the measurement data, provided by multisensor, to make more precise estimation to the state or signal of the systems than the estimation based on the single sensor. It is widely used in many high technology fields, such as target tracking, military affairs, space flight, guidance, GPS position and robotics.
This subject comes from the National Nature Science Foundation under Grant 60374026, New Theories and New Methods for Multisensor Information Fusion Optimal and Self-tuning Filtering, and Grant 60874063, Research on Self-tuning Information Fusion Filtering Theory and Its Applications.
Based on modern time series analysis method, for multisensor linear stochastic systems, this paper makes the theoretical analysis primarily, the computation simulation examples secondarily, and the deep researches on the state estimation problems of optimal weighted measurement fusion and self-tuning weighted measurement fusion. The main works are as follows:
First, for the multisensor systems with unknown noise statistics, applying the correlation method, the information fusion noise statistics on-line estimators, which have the strong consistence, are presented, where the nonsingular partial linear equations are selected from the sampled correlation function linear equations to be solved to obtain the local noise statistics estimators, then the fused estimators are obtained by making the weighted arithmetic average of the local estimators, and it is proved that the fused estimators can be viewed as the least squares fusers. Using the ergodicity of the correlation function, it is proved that the fused estimators converge to the true noise statistics with probability one. Since the accuracy of each fused estimator falls in between the highest and lowest accuracies of the local estimators, it has the higher reliability. For the multisensor autoregressive moving average (ARMA) systems with unknown model parameters and noise statistics, applying the existing estimation methods for ARMA model parameters, combining the information fusion on-line estimators of the unknown noise statistics, the multi-stage information fusion identification methods and the concept of the information fusion model parameter estimators are presented. The information fusion model parameter estimators are obtained by taking the average of the local model parameter estimators obtained from each sensor. In theory, the consistence of the proposed information fusion model parameter estimators is rigorously proved.
Second, for the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises and correlated noises, under the linear unbiased minimum variance (LUMV) criterion, applying Lagrange multiplier method and the filtering theories based on ARMA innovation model, the optimal weighted measurement fusion steady-state Kalman filtering and Wiener filtering algorithms are presented respectively, and theirs results are equal to those of the optimal weighted measurement fusion filtering algorithms based on the weighted least squares (WLS) fusion criterion, that is, they have the completely functional equivalence and the asymptotical global optimality. For the multisensor systems with different measurement matrices and correlated measurement noises, using the matrix partitioning method, combining the constraint condition of the measurement weight matrices, the reduced dimension measurement fusion algorithm is presented, which can remarkably reduce the computational burdens of computing the measurement weight matrices and the fused measurement error variance matrices. The presented comparison table of the computational burden supports this inference from the view point of quantitative analysis.
Third, for the multisensor systems with unknown noise statistics, correlated measurement noises and correlated noises, by substituting the information fusion on-line estimators of unknown noise statistics into the steady-state optimal weighted measurement fusion filters, the self-tuning weighted measurement fusion Kalman filters and Wiener filters, and the self-tuning reduced dimension measurement fusion filters are presented respectively. Applying the dynamic error system analysis (DESA) method, it is proved that the proposed self-tuning fusers converge to the corresponding steady-state globally optimal fusers in a realization, that is, they have the asymptotical global optimality.
Last, for the multisensor single channel autoregressive (AR) signal systems and ARMA signal systems with the common disturbance noise, unknown noise statistics and unknown model parameters, using the transformation method from ARMA model to the state space model, the signal estimation problem is transformed into the state estimation problem. By substituting the information fusion estimators of model parameters and noise statistics into the steady-state optimal weighted measurement fusion Wiener signal filters, the self-tuning weighted measurement fusion Wiener signal filters are presented respectively. By DESA method, it is rigorously proved that the proposed self-tuning weighted measurement fusion Wiener signal filters converge to the corresponding steady-state globally optimal filters in a realization, so they have the asymptotical global optimality.
In the whole paper, a lot of simulation examples in the tracking system and the signal processing show the effectiveness of the proposed methods and algorithms.
引文
[1]何友,关欣,王国宏.多传感器信息融合研究进展与展望[J].宇航学报,2005,26(4)：524-529.
[2]吕漫丽,孙灵芳.多传感器信息融合技术[J].自动化技术与应用,2008,27(2)： 79-82.
[3]T. Kailath, A. H. Sayed, B. Hassibi. Linear Estimation[M]. Upper Saddle River, New Jersey:Prentice Hall,2000.1-11.
[4]石莹.广义离散系统的状态估计[D].博士论文,哈尔滨工业大学,2007.
[5]李佩珊,许良英.20世纪科学技术简史,第二版[M].北京：科学出版社,2004.875-878.
[6]邹海林,徐建培.科学技术史概论[M].北京：科学出版社,2005.336-340.
[7]M. J. Grimble. Polynomial systems approach to optimal linear filtering and prediction[J]. Int. J, Control,1985,41(6):1545-1564.
[8]A. Ahlen, M. Sternad. Wiener filter design using polynomial equations [J]. IEEE Trans. Signal Processing,1991,39(11):2387-2399.
[9]邓自立.信息融合滤波理论及其应用[M].哈尔滨：哈尔滨工业大学出版社,2007.1-483.
[10]R. E. Kalman. A new approach to linear filtering and prediction problems[J]. Trans, of the ASME-Journal of Basic Engineering,1960, 82(Series D):35-45.
[11]Y. Bar-Shalom, X. R. Li, T. Kirubarajan. Estimation with Applications to Tracking and Navigation:Theory Algorithms and Software[M]. New York:John Wiley & Sons, Inc.,2001.199-536.
[12]C. K. Chui, G. Chen. Kalman Filtering with Real-Time Application, Fourth Edition[M]. Berlin:Springer,2008.108-177.
[13]B. D.O. Anderson, J. B. Moore. Optimal Filtering[M]. Englewood Cliffs, New Jersey:Prentice Hall, Inc.,1979.193-222.
[14]Y. Bar-Shalom, X. R. Li. Estimation and Tracking:Principles, Techniques and Software[M]. Boston, MA:Artech House,1993.1-493.
[15]王志胜,姜斌,甄子洋.融合估计与融合控制[M].北京：科学出版社,2009.1-127.
[16]邓自立,郭一新.现代时间序列分析及其应用——建模、滤波、去卷、预报和控制[M].北京：知识出版社,1989.54-127.
[17]张仲俊.一门新兴的边缘学科——现代时间序列分析[J].信息与控制,1988,17(4)：62-63.
[18]邓自立.最优滤波理论及其应用——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2000.1-247.
[19]邓自立.自校正滤波理论及其应用——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2003.1-342.
[20]邓自立.最优估计理论及其应用——建模、滤波、信息融合估计[M].哈尔滨：哈尔滨工业大学出版社,2005.1-489.
[21]邓自立.卡尔曼滤波与维纳滤波——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2001.1-237.
[22]P. Hagander, B. Wittenmark. A self-tuning filter for fixed-lag smoothing[J]. IEEE Trans. Information Theory,1977,23(3):377-384.
[23]Z. L. Deng. Multivariate self-tuning filter and smoother[C]. Proceedings of 6th IFAC Symp. on Identification and Parameter Estimation. Washington, DC, USA,1982.879-882.
[24]邓自立,郭一新.动态系统分析及其应用——建模、滤波、预报、控制的新方法和程序库[M].沈阳：辽宁科学技术出版社,1985.1-223.
[25]M. Gevers, W. R. E. Wouters. An innovations approach to the discrete-time stochastic realization problem[J]. Journal A,1978, 19(2):90-110.
[26]邓自立.估计MA参数的多维强Gevers-Wouters算法及其在构造ARMA新息模型中的应用[J].控制理论与应用,2001,18(5)：737-740.
[27]邓自立.纯量谱分解的Gevers-Wouters算法收敛性分析[J].科学技术与工程,2005,5(1)：7-13.
[28]邓自立.滑动平均模型参数估计的Gevers-Wouters算法的指数收敛性[J].科学技术与工程,2005,5(20)：1473-1498.
[29]Z. L. Deng, H. S. Zhang, S. J. Liu, L. Zhou. Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems[J]. Automatica,1996,32(2):199-216.
[30]邓自立,孙书利,许燕,石莹.基于稳态Riccati方程迭代解的ARMA新息模型的构造[J].科学技术与工程,2002,2(6)：12-13.
[31]邓自立,孙书利.基于Kalman滤波的Wiener状态估值器[J].自动化学报,2004,30(1)：116-120.
[32]邓自立.时域Wiener状态滤波新方法[J].控制理论与应用,2004,21(3)：367-372.
[33]邓自立.ARMA过程线性预报、滤波和平滑的新结果[C].全国控制理论及其应用学术交流会议论文集.北京：科学出版社,1981.164-169.
[34]K. Tajima. Estimation of steady-state Kalman filter gain[J]. IEEE Trans. Automatic Control,1978,23(5):944-945.
[35]邓自立.稳态Kalman滤波器增益的估计[J].控制理论与应用,1985,2(1)：122-126.
[36]Z. L. Deng, Y. Gao, L. Mao, Y. Li, G. Hao. New approach to information fusion steady-state Kalman filtering[J]. Automatica,2005,41(10): 1695-1707.
[37]Z. L. Deng, Y. Xu. Descriptor Wiener state estimators [J]. Automatica, 2000,36(9):1761-1766.
[38]Z. L. Deng, Y. M. Liu. Descriptor Kalman estimators [J]. International Journal of Systems Science,1999,30(11):1205-1212.
[39]何友,陆大琻,彭应宁.多传感器信息融合及其应用[M].北京：电子工业出版社,2007.1-60.
[40]韩崇昭,朱洪艳,段战胜.多源信息融合[M].北京：清华大学出版社,2006.1-488.
[41]王璇,李春升,周荫清.多传感器信息融合技术[J].北京航空航天大学学报,1994,20(4)：402-406.
[42]郁文贤,雍少为,郭桂蓉.多传感器信息融合技术述评[J].国防科技大学学报,1994,16(3)：1-8.
[43]吴新垣.信息融合及其智能化途径探讨[J].舰船科学技术,1996,3：42-46.
[44]潘泉,于昕,程咏梅,张洪才.信息融合理论的基本方法与进展[J].自动化学报,2003,29(4)：599-616.
[45]管天云.多传感器信息融合研究[D].博士论文,浙江大学,1998.
[46]杨露菁,耿伯英.多传感器数据融合手册[M].北京：电子工业出版社,2008.5-7.
[47]M. Piovoso, P. A. Laplante. Kalman filter recipes for real-time image processing[J]. Real-time Imaging,2003,9(6):433-439.
[48]F. Caron, E. Duflos, D. Pomorski, P.Vanheeghe. GPS/IMU data fusion using multisensor Kalman filtering:introduction of contextual aspects[J]. Information Fusion,2006,7(2):221-230.
[49]X. L. Ning, J. C. Fang. An autonomous celestial navigation method for LEO satellite based on unscented Kalman filter and information fusion[J]. Aerospace Science and Technology,2007,11(2):222-228.
[50]M. Mosallaei, K. Salahshoor, M. Bayat. Centralized and decentralized process and sensor fault monitoring using data fusion based on adaptive extended Kalman filter algorithm[J]. Measurement,2008, 41(10):1059-1076.
[51]A. Okatan, C. Hajiyev, U. Hajiyeva. Fault detection in sensor information fusion Kalman filter[J]. Int. J. Electronics and Communications,2009,63(9):762-768.
[52]Y. Morales, E. Takeuchi, T. Tsubouchi. Vehicle localization in outdoor woodland environments with sensor fault detection[C].2008 IEEE International Conference on Robotics and Automation. Pasadena, CA, USA,2008.449-454.
[53]C. W. Jang, J. C. Juang, F. C. Kung. Adaptive fault detection in real-time GPS positioning [J]. IEE Proc.-Radar, Sonar and Navigation, 2000,147(5):254-258.
[54]J. H. Kim, J. H. Oh. A land vehicle tracking algorithm using stand-alone GPS[J]. Control Engineering Practice,2000,8(10):1189-1196.
[55]S. Suranthiran, S. Jayasuriya. Optimal fusion of multiple nonlinear sensor data[J]. IEEE Sensors Journal,2004,4(5):651-663.
[56]U. D. Hanebeck, J. Horn. Fusing information simultaneously corrupted by uncertainties with known bounds and random noise with known distribution[J]. Information Fusion,2000,1(1):55-63.
[57]H. Rehbinder, X. M. Hu. Drift-free attitude estimation for accelerated rigid bodies[J]. Automatica,2004,40(4):653-659.
[58]A. Gning, P. Bonnifait. Constraints propagation techniques on intervals for a guaranteed localization using redundant data[J]. Automatica,2006,42(7):1167-1175.
[59]何友,陆大琻,彭应宁.多传感器数据融合算法综述[J].火力与指挥控制,1996,2l(1)：12-21.
[60]Y. Bar-Shalom, T. E. Fortmann. Tracking and Data Association[M]. San Diego, CA:Academic Press,1988.1-136.
[61]Y. Bar-Shalom, X. R. Li. Multitarget-Multisensor Tracking:Principles and Techniques[M]. Stoors, CT:YBS Publishing,1995.1-585.
[62]袁军,王敏,黄心汉,陈锦江.智能系统多传感器信息融合研究进展[J].控制理论与应用,1994,11(5)：513-518.
[63]王耀南,李树涛.多传感器信息融合及其应用综述[J].控制与决策,2001,16(5)：518-522.
[64]张池平,崔平远,杨涤.一种基于证据决策的航迹相关算法[J].北京理工大学学报,2006,26(8)：689-692.
[65]O. Basir, X. H. Yuan. Engine fault diagnosis based on multi-sensor information fusion using Dempster-Shafer evidence theory[J]. Information Fusion,2007,8(4):379-386.
[66]L. X. Dong, D. M. Xiao, Y. S. Liang, Y. L. Liu. Rough set and fuzzy wavelet neural network integrated with least square weighted fusion algorithm based fault diagnosis research for power transformers [J]. Electric Power Systems Research,2008,78(1):129-136.
[67]Y. N. Zhang, Q. W. Sun, H. Quan, Y. G. Jin, T. F. Quan. Uncertain information fusion with robust adaptive neural networks-fuzzy reasoning [J]. Journal of Systems Engineering and Electronics,2006, 17(3):495-501.
[68]Q. Gan, C. J. Harris. Comparison of two measurement fusion methods for Kalman filter-based multisensor data fusion[J]. IEEE Trans. Aerospace and Electronic Systems,2001,37(1):273-280.
[69]J. L. Speyer. Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem[J]. IEEE Trans. Automatic Control,1979,24(2):266-269.
[70]A. S. Willsky, M. G. Bello, D. A. Castanon, C. L. Bernard, C. V. George. Combining and updating of local estimates and regional maps along sets of one-dimensional tracks [J]. IEEE Trans. Automatic Control,1982, 27(4):799-813.
[71]H. R. Hashemipour, S. Roy, A. J. Laub. Decentralized structures for parallel Kalman filtering[J]. IEEE Trans. Automatic Control,1988, 33(1):88-93.
[72]N. A. Carlson. Federated square root filter for decentralized parallel processes[J]. IEEE Trans. Aerospace and Electronic Systems,1990, 26(3):517-525.
[73]B. S. Paik, J. H. Oh. Gain fusion algorithm for decentralised parallel Kalman filters[J]. IEE Proc.-Control Theory Applications,2000, 147(1):97-103.
[74]Y. M. Zhu, Z. S. You, J. Zhao, K. S. Zhang, X. R. Li. The optimality for the distributed Kalman filtering fusion with feedback[J], Automatica,2001,37(9):1489-1493.
[75]Y. Bar-Shalom. On the track-to-track correlation problem[J], IEEE Trans. Automatic Control,1981,26(2):571-572.
[76]R. K. Saha. Track to track fusion with dissimilar sensor[J]. IEEE Trans. Aerospace and Electronic Systems,1996,32(3):1021-1029.
[77]K. H. Kim. Development of track to track fusion algorithms[C]. Proceedings of the American Control Conference. Bedford, MA, USA,1994. 1037-1041.
[78]H. Chen, T. Kirubarajan, Y. Bar-Shalom. Performance limits of track-to-track fusion versus centralized estimation:theory and application[J]. IEEE Trans. Aerospace and Electronic System,2003, 39(2):386-398.
[79]邓自立,祁荣宾.多传感器信息融合次优稳态Kalman滤波器[J].中国学术期刊文摘(科技快报),2000,6(2)：183-184.
[80]S. L. Sun, Z. L. Deng. Multi-sensor optimal information fusion Kalman filter[J]. Automatica,2004,40(6):1017-1023.
[81]S. L. Sun. Multi-sensor information fusion white noise filter weighted by scalars based on Kalman Predictor[J]. Automatica,2004,40(8): 1447-1453.
[82]H. Z. Qiu, H. Y. Zhang, H. Jin. Fusion algorithm of correlated local estimates [J]. Aerospace Science and Technology,2004,8(7):619-626.
[83]孙书利,邓自立.多传感器线性最小方差最大信息融合准则[J].科学技术与工程,2004,4(5)：334-336.
[84]E. B. Song, Y. M. Zhu, J. Zhou, Z. S. You. Optimal Kalman filtering fusion with cross-correlated sensor noises[J]. Automatica,2007, 43(8):1450-1456.
[85]J. A. Roecker, C. D. Mcgillem. Comparison of two-sensor tracking method based on state vector fusion and measurement fusion [J]. IEEE Trans. Aerospace and Electronic Systems,1988,24(4):447-449.
[86]K. C. Chang. T. Zhi, R. K. Saha. Performance evaluation of track fusion with information matrix filter[J]. IEEE Trans. Aerospace and Electronic Systems,2002,38(2):455-466.
[87]邓自立,崔崇信,白敬刚.基于稳态Kalman滤波的两种观测融合方法的功能等价性[J].科学技术与工程,2004,4(11)：897-902.
[88]邓自立,郝钢,吴孝慧.两种加权观测融合算法的全局最优性和完全功能等价性[J].科学技术与工程,2005,5(13)：860-865.
[89]邓自立.两种最优观测融合方法的功能等价性[J].控制理论与应用,2006,23(2)：319-323.
[90]余安喜,胡卫东,周文辉.多传感器量测融合算法的性能比较[J].国防科技大学学报,2003,25(6)：39-44.
[91]S. Roy, R. A. Iltis. Decentralized linear estimation in correlated measurement noise [J]. IEEE Trans, on Aerospace and Electronic Systems, 1991,27(6):939-941.
[92]欧连军,邱红专,张洪钺.多个相关测量的融合算法及其最优性[J].信息与控制,2005,34(6)：690-695.
[93]X. R. Li, Y. M. Zhu, C. Z. Han. Unified optimal linear estimation fusion-part I:unified models and fusion rules[C]. Proc.2000 International Conf. On Information Fusion. USA,2000. MoC 2.10-MoC 2.17.
[94]X. R. Li, J. Wang. Unified optimal linear estimation fusion-part II: discussions and examples[C]. Proc.2000 International Conf. On Information Fusion. USA,2000. MoC 2.18-MoC 2.25.
[95]X. R. Li, P. Zhang. Optimal linear estimation fusion-part III: cross-correlation of local estimation errors[C]. Proc.2001 International Conf. On Information Fusion. USA,2001. WeB 1.11-WeB 1.18.
[96]X. R. Li, K. S. Zhang. Optimal linear estimation fusion-part IV: optimality and efficiency of distributed fusion[C]. Proc.2001 International Conf. On Information Fusion. USA,2001. WeB 1.19-WeB 1.26.
[97]X. R. Li, K. S. Zhang, J. Zhao, Y. M. Zhu. Optimal linear estimation fusion-part V:relationships[C]. Proc.2002 International Conf. On Information Fusion. USA,2002.497-504.
[98]X. R. Li, Y. M. Zhu, J. Wang, C. Z. Han. Optimal linear estimation fusion-part Ⅰ:unified fusion rules[J].2003,49(9):2192-2208.
[99]K. S. Zhang, X. R. Li, P. Zhang, H. F. Li. Optimal linear estimation fusion-part Ⅵ:sensor data compression[C]. Proc.2003 International Conf. On Information Fusion. USA,2003.221-228.
[100]X. R. Li. Optimal linear estimation fusion-part VII:dynamic systems [C]. Proc.2003 International Conf. On Information Fusion. USA, 2003.455-462.
[101]L. Guo, H. F. Chen. The Astrom-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers[J]. IEEE Trans. Automatic Control,1991,36(7):802-812.
[102]B. Wittenmark. A self-tuning predictor[J]. IEEE Trans. Automatic Control,1974,19(6):848-851.
[103]H. Hagander, B. Wittenmark. A self-tuning filter for fixed-lag smoothing[J]. IEEE Trans. Information Theory,1977,23(3):377-384.
[104]邓自立.应用于地震数据去卷的自校正白噪声估值器[J].自动化学报,1986,12(2)：156-161.
[105]邓自立,刘叔军.实时自校正白噪声去卷滤波器和平滑器[C].1994中国控制与决策学术年会论文集.沈阳,1994.285-288.
[106]邓自立,刘叔军.单通道自校正白噪声去卷平滑器[J].信息与控制,1995,24(3)：129-134.
[107]郝钢,邓自立.自校正观测融合Kalman滤波器[C]. Proceedings of the 6th World Congress on Intelligent Control and Automation.大连,2006.1571-1575.
[108]李云,郝钢,邓自立.自校正加权观测融合Kalman估值器[J].科学技术与过程,2006,6(2)：116-120.
[109]陈红,邓自立.自校正观测融合解耦Wiener状态预报器[J].科学技术与工程,2007,7(24)：6285-6290.
[110]孙书利.最优与自适应信息融合卡尔曼估值器及其应用[D].博士论文,哈尔滨工业大学,2004.
[111]S. L. Sun. Optimal and self-tuning information fusion Kalman multi-step predictor [J]. IEEE Trans. Aerospace and Electronic Systems, 2007,43(2):418-427.
[112]Z. L. Deng, C. B. Li. Self-tuning information fusion Kalman predictor weighted by diagonal matrices and its convergence analysis[J]. Acta Automatica Sinica,2007,33(2):156-163.
[113]贾文静,张鹏,邓自立.辨识动态系统噪声方差Q和R的新方法[J].科学技术与工程,2006,6(14)：2008-2011.
[114]邓自立,郝钢.自校正分布式观测融合Kalman滤波器[J].电子与信息学报,2007,29(8)：1850-1854.
[115]李云,李春波,邓自立.自校正标量加权信息融合Kalman滤波器[J].科学技术与工程,2005,5(22)：1696-1700.
[116]邓自立,李春波.自校正标量加权信息融合Kalman预报器[C]. Proceedings of the 6th World Congress on Intelligent Control and Automation.大连,2006.1487-1491.
[117]邓自立,李春波.自校正解耦信息融合Wiener状态预报器[J].系统工程与电子技术,2007,29(5)：805-809.
[118]邓自立,李春波.自校正信息融合Kalman平滑器[J].控制理论与应用,2007,24(2)：236-248.
[119]邓自立,李春波.自校正解耦信息融合Wiener状态估值器[J].控制理论与应用,2008,25(4)：753-758.
[120]S. L. Sun, Z. L. Deng. Distributed optimal fusion steady-state Kalman filter for systems with coloured measurement noises[J]. International Journal of Systems Science,2005,36(3):113-118.
[121]S. L. Sun. Optimal multi-sensor Kalman smoothing fusion for discrete multichannel ARMA signals[J]. Journal of Control Theory and Applications,2005,3(2):168-172.
[122]邓自立,高媛.按对角阵加权信息融合Kalman滤波器[J].控制理论与应用,2005,22(6)：870-874.
[123]邓自立,高媛.多通道ARMA信号信息融合Wiener滤波器[J].电子与信息学报,2005,27(9)：1416—1419.
[124]邓自立,高媛.快速信息融合Kalman滤波器[J].控制与决策,2005,20(1)：27-31.
[125]邓自立,高媛.基于Kalman滤波的自回归滑动平均信号信息融合Wiener滤波器[J].控制理论与应用,2005,22(4)：641-644.
[126]S. L. Sun. Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother[J]. Automatica,2005,41(12): 2153-2159.
[127]S. L. Sun. Multi-sensor optimal information fusion Kalman filters with applications [J]. Aerospace Science and Technology,2004,8(1):57-62.
[128]S. L. Sun. Multisensor optimal information fusion input white noise deconvolution estimators[J]. IEEE Trans. Systems, Man, and Cybernetics—Part B:Cybernetics,2004,34(4):1886-1893.
[129]Y. Bar-shalom, L. Campo. The effect of the common process noise on the two-sensor fusion-track convariance[J]. IEEE Trans, on Aerospace and Electronic Systems,1986,22(6):803-805.
[130]邓自立,郝钢.自校正多传感器观测融合Kalman估值器及其收敛性分析[J].控制理论与工程,2008,25(5)：845-852.
[131]C. J. Ran, G. L. Tao, J. F. Liu, Z. L. Deng. Self-tuning decoupled fusion Kalman predictor and its convergence analysis [J]. IEEE Sensor Journal,2009,9(12):2024-2032.
[132]C. J. Ran, Z. L. Deng. Self-tuning Measurement Fusion Kalman Filter based on the Information Matrix[C]. Proc.2009 IEEE International Conference on Mechatronics and Automation. Changchun,2009. 2506-2511.
[133]X. J. Sun, Z. L. Deng. Self-tuning white noise deconvolution fuser with correlated measurement noises[C]. Proc.2009 IEEE International Conference on Mechatronics and Automation. Changchun,2009. 2524-2529.
[134]X. J. Sun, Z. L. Deng. Optimal and self-tuning weighted measurement fusion Wiener filter for the multisensor multichannel ARMA signals [J]. Signal Processing,2009,89(5):738-752.
[135]L. Ljung. System Identification, Theory for the User, Second Edition[M], Beijing:Tsinghua University Press,1999.1-398.
[136]方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1988.173-142.
[137]W. Rudion. Principles of Mathematical Analysis,3rd Edition[M]. Beijing:China Machine Press,2004.23-189.
[138]S. L. Sun. Scalar weighting optimal fusion predictors for discrete multichannel ARMA signals [C].2004 8th International Conference on Control, Automation, Robotics and Vision. Kunming,2004.1626-1629.
[139]邓自立,毛琳.多传感器信息融合ARMA信号Wiener滤波器[J].系统工程与电子技术,2005,27(11)：1971-1974.
[140]S. L. Sun. Optimal component fusion steady-state smoothing for discrete multichannel ARMA signals[C]. Pro.6th World Congress on Intelligent Control and Automation. Dalian,2006.1438-1441.
[141]X. J. Sun, Z. L. Deng. Information fusion Wiener filter for the multisensor multichannel ARMA signals with time-delayed measurements [J]. IET Signal Process,2009,3(5):403-415.
[2]吕漫丽,孙灵芳.多传感器信息融合技术[J].自动化技术与应用,2008,27(2)： 79-82.
[3]T. Kailath, A. H. Sayed, B. Hassibi. Linear Estimation[M]. Upper Saddle River, New Jersey:Prentice Hall,2000.1-11.
[4]石莹.广义离散系统的状态估计[D].博士论文,哈尔滨工业大学,2007.
[5]李佩珊,许良英.20世纪科学技术简史,第二版[M].北京：科学出版社,2004.875-878.
[6]邹海林,徐建培.科学技术史概论[M].北京：科学出版社,2005.336-340.
[7]M. J. Grimble. Polynomial systems approach to optimal linear filtering and prediction[J]. Int. J, Control,1985,41(6):1545-1564.
[8]A. Ahlen, M. Sternad. Wiener filter design using polynomial equations [J]. IEEE Trans. Signal Processing,1991,39(11):2387-2399.
[9]邓自立.信息融合滤波理论及其应用[M].哈尔滨：哈尔滨工业大学出版社,2007.1-483.
[10]R. E. Kalman. A new approach to linear filtering and prediction problems[J]. Trans, of the ASME-Journal of Basic Engineering,1960, 82(Series D):35-45.
[11]Y. Bar-Shalom, X. R. Li, T. Kirubarajan. Estimation with Applications to Tracking and Navigation:Theory Algorithms and Software[M]. New York:John Wiley & Sons, Inc.,2001.199-536.
[12]C. K. Chui, G. Chen. Kalman Filtering with Real-Time Application, Fourth Edition[M]. Berlin:Springer,2008.108-177.
[13]B. D.O. Anderson, J. B. Moore. Optimal Filtering[M]. Englewood Cliffs, New Jersey:Prentice Hall, Inc.,1979.193-222.
[14]Y. Bar-Shalom, X. R. Li. Estimation and Tracking:Principles, Techniques and Software[M]. Boston, MA:Artech House,1993.1-493.
[15]王志胜,姜斌,甄子洋.融合估计与融合控制[M].北京：科学出版社,2009.1-127.
[16]邓自立,郭一新.现代时间序列分析及其应用——建模、滤波、去卷、预报和控制[M].北京：知识出版社,1989.54-127.
[17]张仲俊.一门新兴的边缘学科——现代时间序列分析[J].信息与控制,1988,17(4)：62-63.
[18]邓自立.最优滤波理论及其应用——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2000.1-247.
[19]邓自立.自校正滤波理论及其应用——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2003.1-342.
[20]邓自立.最优估计理论及其应用——建模、滤波、信息融合估计[M].哈尔滨：哈尔滨工业大学出版社,2005.1-489.
[21]邓自立.卡尔曼滤波与维纳滤波——现代时间序列分析方法[M].哈尔滨：哈尔滨工业大学出版社,2001.1-237.
[22]P. Hagander, B. Wittenmark. A self-tuning filter for fixed-lag smoothing[J]. IEEE Trans. Information Theory,1977,23(3):377-384.
[23]Z. L. Deng. Multivariate self-tuning filter and smoother[C]. Proceedings of 6th IFAC Symp. on Identification and Parameter Estimation. Washington, DC, USA,1982.879-882.
[24]邓自立,郭一新.动态系统分析及其应用——建模、滤波、预报、控制的新方法和程序库[M].沈阳：辽宁科学技术出版社,1985.1-223.
[25]M. Gevers, W. R. E. Wouters. An innovations approach to the discrete-time stochastic realization problem[J]. Journal A,1978, 19(2):90-110.
[26]邓自立.估计MA参数的多维强Gevers-Wouters算法及其在构造ARMA新息模型中的应用[J].控制理论与应用,2001,18(5)：737-740.
[27]邓自立.纯量谱分解的Gevers-Wouters算法收敛性分析[J].科学技术与工程,2005,5(1)：7-13.
[28]邓自立.滑动平均模型参数估计的Gevers-Wouters算法的指数收敛性[J].科学技术与工程,2005,5(20)：1473-1498.
[29]Z. L. Deng, H. S. Zhang, S. J. Liu, L. Zhou. Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems[J]. Automatica,1996,32(2):199-216.
[30]邓自立,孙书利,许燕,石莹.基于稳态Riccati方程迭代解的ARMA新息模型的构造[J].科学技术与工程,2002,2(6)：12-13.
[31]邓自立,孙书利.基于Kalman滤波的Wiener状态估值器[J].自动化学报,2004,30(1)：116-120.
[32]邓自立.时域Wiener状态滤波新方法[J].控制理论与应用,2004,21(3)：367-372.
[33]邓自立.ARMA过程线性预报、滤波和平滑的新结果[C].全国控制理论及其应用学术交流会议论文集.北京：科学出版社,1981.164-169.
[34]K. Tajima. Estimation of steady-state Kalman filter gain[J]. IEEE Trans. Automatic Control,1978,23(5):944-945.
[35]邓自立.稳态Kalman滤波器增益的估计[J].控制理论与应用,1985,2(1)：122-126.
[36]Z. L. Deng, Y. Gao, L. Mao, Y. Li, G. Hao. New approach to information fusion steady-state Kalman filtering[J]. Automatica,2005,41(10): 1695-1707.
[37]Z. L. Deng, Y. Xu. Descriptor Wiener state estimators [J]. Automatica, 2000,36(9):1761-1766.
[38]Z. L. Deng, Y. M. Liu. Descriptor Kalman estimators [J]. International Journal of Systems Science,1999,30(11):1205-1212.
[39]何友,陆大琻,彭应宁.多传感器信息融合及其应用[M].北京：电子工业出版社,2007.1-60.
[40]韩崇昭,朱洪艳,段战胜.多源信息融合[M].北京：清华大学出版社,2006.1-488.
[41]王璇,李春升,周荫清.多传感器信息融合技术[J].北京航空航天大学学报,1994,20(4)：402-406.
[42]郁文贤,雍少为,郭桂蓉.多传感器信息融合技术述评[J].国防科技大学学报,1994,16(3)：1-8.
[43]吴新垣.信息融合及其智能化途径探讨[J].舰船科学技术,1996,3：42-46.
[44]潘泉,于昕,程咏梅,张洪才.信息融合理论的基本方法与进展[J].自动化学报,2003,29(4)：599-616.
[45]管天云.多传感器信息融合研究[D].博士论文,浙江大学,1998.
[46]杨露菁,耿伯英.多传感器数据融合手册[M].北京：电子工业出版社,2008.5-7.
[47]M. Piovoso, P. A. Laplante. Kalman filter recipes for real-time image processing[J]. Real-time Imaging,2003,9(6):433-439.
[48]F. Caron, E. Duflos, D. Pomorski, P.Vanheeghe. GPS/IMU data fusion using multisensor Kalman filtering:introduction of contextual aspects[J]. Information Fusion,2006,7(2):221-230.
[49]X. L. Ning, J. C. Fang. An autonomous celestial navigation method for LEO satellite based on unscented Kalman filter and information fusion[J]. Aerospace Science and Technology,2007,11(2):222-228.
[50]M. Mosallaei, K. Salahshoor, M. Bayat. Centralized and decentralized process and sensor fault monitoring using data fusion based on adaptive extended Kalman filter algorithm[J]. Measurement,2008, 41(10):1059-1076.
[51]A. Okatan, C. Hajiyev, U. Hajiyeva. Fault detection in sensor information fusion Kalman filter[J]. Int. J. Electronics and Communications,2009,63(9):762-768.
[52]Y. Morales, E. Takeuchi, T. Tsubouchi. Vehicle localization in outdoor woodland environments with sensor fault detection[C].2008 IEEE International Conference on Robotics and Automation. Pasadena, CA, USA,2008.449-454.
[53]C. W. Jang, J. C. Juang, F. C. Kung. Adaptive fault detection in real-time GPS positioning [J]. IEE Proc.-Radar, Sonar and Navigation, 2000,147(5):254-258.
[54]J. H. Kim, J. H. Oh. A land vehicle tracking algorithm using stand-alone GPS[J]. Control Engineering Practice,2000,8(10):1189-1196.
[55]S. Suranthiran, S. Jayasuriya. Optimal fusion of multiple nonlinear sensor data[J]. IEEE Sensors Journal,2004,4(5):651-663.
[56]U. D. Hanebeck, J. Horn. Fusing information simultaneously corrupted by uncertainties with known bounds and random noise with known distribution[J]. Information Fusion,2000,1(1):55-63.
[57]H. Rehbinder, X. M. Hu. Drift-free attitude estimation for accelerated rigid bodies[J]. Automatica,2004,40(4):653-659.
[58]A. Gning, P. Bonnifait. Constraints propagation techniques on intervals for a guaranteed localization using redundant data[J]. Automatica,2006,42(7):1167-1175.
[59]何友,陆大琻,彭应宁.多传感器数据融合算法综述[J].火力与指挥控制,1996,2l(1)：12-21.
[60]Y. Bar-Shalom, T. E. Fortmann. Tracking and Data Association[M]. San Diego, CA:Academic Press,1988.1-136.
[61]Y. Bar-Shalom, X. R. Li. Multitarget-Multisensor Tracking:Principles and Techniques[M]. Stoors, CT:YBS Publishing,1995.1-585.
[62]袁军,王敏,黄心汉,陈锦江.智能系统多传感器信息融合研究进展[J].控制理论与应用,1994,11(5)：513-518.
[63]王耀南,李树涛.多传感器信息融合及其应用综述[J].控制与决策,2001,16(5)：518-522.
[64]张池平,崔平远,杨涤.一种基于证据决策的航迹相关算法[J].北京理工大学学报,2006,26(8)：689-692.
[65]O. Basir, X. H. Yuan. Engine fault diagnosis based on multi-sensor information fusion using Dempster-Shafer evidence theory[J]. Information Fusion,2007,8(4):379-386.
[66]L. X. Dong, D. M. Xiao, Y. S. Liang, Y. L. Liu. Rough set and fuzzy wavelet neural network integrated with least square weighted fusion algorithm based fault diagnosis research for power transformers [J]. Electric Power Systems Research,2008,78(1):129-136.
[67]Y. N. Zhang, Q. W. Sun, H. Quan, Y. G. Jin, T. F. Quan. Uncertain information fusion with robust adaptive neural networks-fuzzy reasoning [J]. Journal of Systems Engineering and Electronics,2006, 17(3):495-501.
[68]Q. Gan, C. J. Harris. Comparison of two measurement fusion methods for Kalman filter-based multisensor data fusion[J]. IEEE Trans. Aerospace and Electronic Systems,2001,37(1):273-280.
[69]J. L. Speyer. Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem[J]. IEEE Trans. Automatic Control,1979,24(2):266-269.
[70]A. S. Willsky, M. G. Bello, D. A. Castanon, C. L. Bernard, C. V. George. Combining and updating of local estimates and regional maps along sets of one-dimensional tracks [J]. IEEE Trans. Automatic Control,1982, 27(4):799-813.
[71]H. R. Hashemipour, S. Roy, A. J. Laub. Decentralized structures for parallel Kalman filtering[J]. IEEE Trans. Automatic Control,1988, 33(1):88-93.
[72]N. A. Carlson. Federated square root filter for decentralized parallel processes[J]. IEEE Trans. Aerospace and Electronic Systems,1990, 26(3):517-525.
[73]B. S. Paik, J. H. Oh. Gain fusion algorithm for decentralised parallel Kalman filters[J]. IEE Proc.-Control Theory Applications,2000, 147(1):97-103.
[74]Y. M. Zhu, Z. S. You, J. Zhao, K. S. Zhang, X. R. Li. The optimality for the distributed Kalman filtering fusion with feedback[J], Automatica,2001,37(9):1489-1493.
[75]Y. Bar-Shalom. On the track-to-track correlation problem[J], IEEE Trans. Automatic Control,1981,26(2):571-572.
[76]R. K. Saha. Track to track fusion with dissimilar sensor[J]. IEEE Trans. Aerospace and Electronic Systems,1996,32(3):1021-1029.
[77]K. H. Kim. Development of track to track fusion algorithms[C]. Proceedings of the American Control Conference. Bedford, MA, USA,1994. 1037-1041.
[78]H. Chen, T. Kirubarajan, Y. Bar-Shalom. Performance limits of track-to-track fusion versus centralized estimation:theory and application[J]. IEEE Trans. Aerospace and Electronic System,2003, 39(2):386-398.
[79]邓自立,祁荣宾.多传感器信息融合次优稳态Kalman滤波器[J].中国学术期刊文摘(科技快报),2000,6(2)：183-184.
[80]S. L. Sun, Z. L. Deng. Multi-sensor optimal information fusion Kalman filter[J]. Automatica,2004,40(6):1017-1023.
[81]S. L. Sun. Multi-sensor information fusion white noise filter weighted by scalars based on Kalman Predictor[J]. Automatica,2004,40(8): 1447-1453.
[82]H. Z. Qiu, H. Y. Zhang, H. Jin. Fusion algorithm of correlated local estimates [J]. Aerospace Science and Technology,2004,8(7):619-626.
[83]孙书利,邓自立.多传感器线性最小方差最大信息融合准则[J].科学技术与工程,2004,4(5)：334-336.
[84]E. B. Song, Y. M. Zhu, J. Zhou, Z. S. You. Optimal Kalman filtering fusion with cross-correlated sensor noises[J]. Automatica,2007, 43(8):1450-1456.
[85]J. A. Roecker, C. D. Mcgillem. Comparison of two-sensor tracking method based on state vector fusion and measurement fusion [J]. IEEE Trans. Aerospace and Electronic Systems,1988,24(4):447-449.
[86]K. C. Chang. T. Zhi, R. K. Saha. Performance evaluation of track fusion with information matrix filter[J]. IEEE Trans. Aerospace and Electronic Systems,2002,38(2):455-466.
[87]邓自立,崔崇信,白敬刚.基于稳态Kalman滤波的两种观测融合方法的功能等价性[J].科学技术与工程,2004,4(11)：897-902.
[88]邓自立,郝钢,吴孝慧.两种加权观测融合算法的全局最优性和完全功能等价性[J].科学技术与工程,2005,5(13)：860-865.
[89]邓自立.两种最优观测融合方法的功能等价性[J].控制理论与应用,2006,23(2)：319-323.
[90]余安喜,胡卫东,周文辉.多传感器量测融合算法的性能比较[J].国防科技大学学报,2003,25(6)：39-44.
[91]S. Roy, R. A. Iltis. Decentralized linear estimation in correlated measurement noise [J]. IEEE Trans, on Aerospace and Electronic Systems, 1991,27(6):939-941.
[92]欧连军,邱红专,张洪钺.多个相关测量的融合算法及其最优性[J].信息与控制,2005,34(6)：690-695.
[93]X. R. Li, Y. M. Zhu, C. Z. Han. Unified optimal linear estimation fusion-part I:unified models and fusion rules[C]. Proc.2000 International Conf. On Information Fusion. USA,2000. MoC 2.10-MoC 2.17.
[94]X. R. Li, J. Wang. Unified optimal linear estimation fusion-part II: discussions and examples[C]. Proc.2000 International Conf. On Information Fusion. USA,2000. MoC 2.18-MoC 2.25.
[95]X. R. Li, P. Zhang. Optimal linear estimation fusion-part III: cross-correlation of local estimation errors[C]. Proc.2001 International Conf. On Information Fusion. USA,2001. WeB 1.11-WeB 1.18.
[96]X. R. Li, K. S. Zhang. Optimal linear estimation fusion-part IV: optimality and efficiency of distributed fusion[C]. Proc.2001 International Conf. On Information Fusion. USA,2001. WeB 1.19-WeB 1.26.
[97]X. R. Li, K. S. Zhang, J. Zhao, Y. M. Zhu. Optimal linear estimation fusion-part V:relationships[C]. Proc.2002 International Conf. On Information Fusion. USA,2002.497-504.
[98]X. R. Li, Y. M. Zhu, J. Wang, C. Z. Han. Optimal linear estimation fusion-part Ⅰ:unified fusion rules[J].2003,49(9):2192-2208.
[99]K. S. Zhang, X. R. Li, P. Zhang, H. F. Li. Optimal linear estimation fusion-part Ⅵ:sensor data compression[C]. Proc.2003 International Conf. On Information Fusion. USA,2003.221-228.
[100]X. R. Li. Optimal linear estimation fusion-part VII:dynamic systems [C]. Proc.2003 International Conf. On Information Fusion. USA, 2003.455-462.
[101]L. Guo, H. F. Chen. The Astrom-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers[J]. IEEE Trans. Automatic Control,1991,36(7):802-812.
[102]B. Wittenmark. A self-tuning predictor[J]. IEEE Trans. Automatic Control,1974,19(6):848-851.
[103]H. Hagander, B. Wittenmark. A self-tuning filter for fixed-lag smoothing[J]. IEEE Trans. Information Theory,1977,23(3):377-384.
[104]邓自立.应用于地震数据去卷的自校正白噪声估值器[J].自动化学报,1986,12(2)：156-161.
[105]邓自立,刘叔军.实时自校正白噪声去卷滤波器和平滑器[C].1994中国控制与决策学术年会论文集.沈阳,1994.285-288.
[106]邓自立,刘叔军.单通道自校正白噪声去卷平滑器[J].信息与控制,1995,24(3)：129-134.
[107]郝钢,邓自立.自校正观测融合Kalman滤波器[C]. Proceedings of the 6th World Congress on Intelligent Control and Automation.大连,2006.1571-1575.
[108]李云,郝钢,邓自立.自校正加权观测融合Kalman估值器[J].科学技术与过程,2006,6(2)：116-120.
[109]陈红,邓自立.自校正观测融合解耦Wiener状态预报器[J].科学技术与工程,2007,7(24)：6285-6290.
[110]孙书利.最优与自适应信息融合卡尔曼估值器及其应用[D].博士论文,哈尔滨工业大学,2004.
[111]S. L. Sun. Optimal and self-tuning information fusion Kalman multi-step predictor [J]. IEEE Trans. Aerospace and Electronic Systems, 2007,43(2):418-427.
[112]Z. L. Deng, C. B. Li. Self-tuning information fusion Kalman predictor weighted by diagonal matrices and its convergence analysis[J]. Acta Automatica Sinica,2007,33(2):156-163.
[113]贾文静,张鹏,邓自立.辨识动态系统噪声方差Q和R的新方法[J].科学技术与工程,2006,6(14)：2008-2011.
[114]邓自立,郝钢.自校正分布式观测融合Kalman滤波器[J].电子与信息学报,2007,29(8)：1850-1854.
[115]李云,李春波,邓自立.自校正标量加权信息融合Kalman滤波器[J].科学技术与工程,2005,5(22)：1696-1700.
[116]邓自立,李春波.自校正标量加权信息融合Kalman预报器[C]. Proceedings of the 6th World Congress on Intelligent Control and Automation.大连,2006.1487-1491.
[117]邓自立,李春波.自校正解耦信息融合Wiener状态预报器[J].系统工程与电子技术,2007,29(5)：805-809.
[118]邓自立,李春波.自校正信息融合Kalman平滑器[J].控制理论与应用,2007,24(2)：236-248.
[119]邓自立,李春波.自校正解耦信息融合Wiener状态估值器[J].控制理论与应用,2008,25(4)：753-758.
[120]S. L. Sun, Z. L. Deng. Distributed optimal fusion steady-state Kalman filter for systems with coloured measurement noises[J]. International Journal of Systems Science,2005,36(3):113-118.
[121]S. L. Sun. Optimal multi-sensor Kalman smoothing fusion for discrete multichannel ARMA signals[J]. Journal of Control Theory and Applications,2005,3(2):168-172.
[122]邓自立,高媛.按对角阵加权信息融合Kalman滤波器[J].控制理论与应用,2005,22(6)：870-874.
[123]邓自立,高媛.多通道ARMA信号信息融合Wiener滤波器[J].电子与信息学报,2005,27(9)：1416—1419.
[124]邓自立,高媛.快速信息融合Kalman滤波器[J].控制与决策,2005,20(1)：27-31.
[125]邓自立,高媛.基于Kalman滤波的自回归滑动平均信号信息融合Wiener滤波器[J].控制理论与应用,2005,22(4)：641-644.
[126]S. L. Sun. Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother[J]. Automatica,2005,41(12): 2153-2159.
[127]S. L. Sun. Multi-sensor optimal information fusion Kalman filters with applications [J]. Aerospace Science and Technology,2004,8(1):57-62.
[128]S. L. Sun. Multisensor optimal information fusion input white noise deconvolution estimators[J]. IEEE Trans. Systems, Man, and Cybernetics—Part B:Cybernetics,2004,34(4):1886-1893.
[129]Y. Bar-shalom, L. Campo. The effect of the common process noise on the two-sensor fusion-track convariance[J]. IEEE Trans, on Aerospace and Electronic Systems,1986,22(6):803-805.
[130]邓自立,郝钢.自校正多传感器观测融合Kalman估值器及其收敛性分析[J].控制理论与工程,2008,25(5)：845-852.
[131]C. J. Ran, G. L. Tao, J. F. Liu, Z. L. Deng. Self-tuning decoupled fusion Kalman predictor and its convergence analysis [J]. IEEE Sensor Journal,2009,9(12):2024-2032.
[132]C. J. Ran, Z. L. Deng. Self-tuning Measurement Fusion Kalman Filter based on the Information Matrix[C]. Proc.2009 IEEE International Conference on Mechatronics and Automation. Changchun,2009. 2506-2511.
[133]X. J. Sun, Z. L. Deng. Self-tuning white noise deconvolution fuser with correlated measurement noises[C]. Proc.2009 IEEE International Conference on Mechatronics and Automation. Changchun,2009. 2524-2529.
[134]X. J. Sun, Z. L. Deng. Optimal and self-tuning weighted measurement fusion Wiener filter for the multisensor multichannel ARMA signals [J]. Signal Processing,2009,89(5):738-752.
[135]L. Ljung. System Identification, Theory for the User, Second Edition[M], Beijing:Tsinghua University Press,1999.1-398.
[136]方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1988.173-142.
[137]W. Rudion. Principles of Mathematical Analysis,3rd Edition[M]. Beijing:China Machine Press,2004.23-189.
[138]S. L. Sun. Scalar weighting optimal fusion predictors for discrete multichannel ARMA signals [C].2004 8th International Conference on Control, Automation, Robotics and Vision. Kunming,2004.1626-1629.
[139]邓自立,毛琳.多传感器信息融合ARMA信号Wiener滤波器[J].系统工程与电子技术,2005,27(11)：1971-1974.
[140]S. L. Sun. Optimal component fusion steady-state smoothing for discrete multichannel ARMA signals[C]. Pro.6th World Congress on Intelligent Control and Automation. Dalian,2006.1438-1441.
[141]X. J. Sun, Z. L. Deng. Information fusion Wiener filter for the multisensor multichannel ARMA signals with time-delayed measurements [J]. IET Signal Process,2009,3(5):403-415.