观测时滞系统的最优滤波
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摘要
线性估计问题是控制、通信、信号处理等领域一个重要的研究课题。20世纪60年代提出的Kalman滤波理论成为近几十年来估计和控制的主要研究工具,但是标准的Kalman滤波理论只能处理正常系统,而不适合时滞系统。时滞系统的估计和控制问题,由于实际的需要已引起人们广泛的关注,至今有些问题如含有时滞观测的线性系统的估计问题、输入带时滞的控制等问题还没有得到足够的研究。本论文将针对时滞观测的线性系统提出一种最优估计的新方法,即新息重组分析方法。其基本思想是将带有时滞的观测数据重新组合成为来自不同观测系统但无时滞的观测数据,然后对重组后的观测数据定义新息序列,由此提出全新的Kalman滤波公式,进而得到复杂的白噪声H_∞估计器、时滞鲁棒Kalman滤波器及时滞信息融合滤波。本文的主要工作如下:
研究了离散情况下时滞系统的Kalman滤波问题。引入离散系统的新息重组分析方法,分析了含有即时观测和单时滞观测的情况,得到了优化滤波器,进而推导出非常复杂的线性离散系统多时滞情况下的新息重组分析方法,给出此时的最优滤波器以及计算的流程图。该方法一个重要的优点是计算量比传统的系统增广方法大大减少了,文中给出了两种方法计算量上的比较,并通过两个例子进行了验证,根据一个仿真例子验证了所给方法的有效性。并将离散单时滞系统的结果应用到鲁棒和时滞信息融合滤波问题上,给出了一个时滞系统的鲁棒Kalman滤波器和时滞信息融合滤波器。
研究了连续情况下时滞系统的Kalman滤波问题。提出了连续时滞系统新息重组分析方法,对含有即时观测和单时滞观测的情况进行了深入地研究,进而将其推广到更一般的多时滞观测的情况,给出了含有即时观测和时滞观测情况下的最优滤波器,并利用实例和流程图直观得体现了算法的实现过程,方法中没有采用传统的偏微分方法,得到了显式解。
提出的新息重组分析方法可以用来处理很多复杂的问题,其中H_∞白噪声估计问题就是一个重要的应用。引入Krein空间,借助新息重组分析方法、射影定理,研究了线性系统(包括离散和连续情况)的白噪声估计问题,给出了H_∞估计器(主要是滤波器和固定时滞平滑器)及其存在的充要条件。揭示出H_∞白噪声滤波问题实际上等价于Krein空间内的H_2白噪声滤波问题,而H_∞白噪声固定时滞平滑问题实际上等价于Krein空间内含即时观测和单时滞观测的系统的H_2白噪声估计问题。本课题具有非常重要的理论价值和实际意义。
Linear Estimation is a key research topic in many fields such as control, communications, signal processing, and so on. In the 1960's, Kalman filtering was presented and has been a major tool of state estimation and control since then. However, the standard Kalman filtering can be only applicable to the normal systems without delays not to the delayed systems. Much interest has been attached to the case of time delays for the actual requirements. Some problems such as estimation for linear systems with delayed measurements and control for systems with input delay haven't been studied well up to the present. In this paper, we are concerned with the optimal estimation problem for linear systems systems with delayed measurements, and a new optimal approach, re-organization of innovation analysis, is then proposed. The main idea is to re-organize the delayed measurements into delay-free measurements from different systems, and the associated innovation sequence is given in according to the re-organized measurements, Kalman filtering formulations based on the new approach are thus given. With the new technique, the more complicated H_∞white noise estimator, robust time-delayed Kalman filter, and time-delayed information fusion filter are then given. The paper mainly includes the following parts:
Kalman filtering for linear discrete-time systems with delayed measurements. Reorganization of innovation analysis for discrete-time systems is introduced, and the case of systems with instantaneous measurement and delayed measurements is studied, the optimal filters are then given. Furthermore, the more complicated technique, re-organization of innovation analysis, is derived for discrete-time systems with multiple delayed measurements, and optimal filters and the flow chart are also given in the paper. Such an approach is much more computationally attractive which is a major advantage over the traditional system augmentation, and the comparison of the computation costs between the proposed re-organization of innovation analysis and the traditional augmentation method is also given, and two examples have been given to show this point. A numerical example is given to show the efficiency of the proposed approach. The proposed approach is further extended to the robust Kalman filtering for discrete-time systems with single delayed measurement and the time-delayed information fusion filtering problem, then the robust Kalman filter and the time-delayed information fusion filter are given.
Kalman filtering for linear continuous-time systems with delayed measurements. Reorganization of innovation analysis for continuous-time systems is presented, the case of systems with instantaneous measurement and delayed measurements is studied well, and the proposed approach is extended to the case of continuous-time systems with multiple delayed measurements, and optimal filters are given. Two numerical examples and the flowchart for the computation are given to show the process of the computation. Explicit solutions to the problem are given without resorting to traditional partial differential equations.
Re-organization of innovation analysis can be used to deal with many difficult problems, one of which is H_∞white noise estimation. In the paper, Krein space is introduced, and the H_∞white noise estimation for linear systems (including both discrete-time case and continuous-time case) is considered with the help of re-organization of innovation analysis and projection formulation in Krein space, thus the estimators (mainly filters and fixed-lag smoothers) and the associated sufficient and essential conditions are given. It is also shown that the white noise H_∞white noise filtering is equivalent to the H_2 white noise filtering in Krein space, and the H_∞white noise fixed-lag smoothing is in fact equivalent to an H_2 estimation problem for measurement delayed system in Krein space. The problem is much valuable both in theory and in practice.
研究了离散情况下时滞系统的Kalman滤波问题。引入离散系统的新息重组分析方法,分析了含有即时观测和单时滞观测的情况,得到了优化滤波器,进而推导出非常复杂的线性离散系统多时滞情况下的新息重组分析方法,给出此时的最优滤波器以及计算的流程图。该方法一个重要的优点是计算量比传统的系统增广方法大大减少了,文中给出了两种方法计算量上的比较,并通过两个例子进行了验证,根据一个仿真例子验证了所给方法的有效性。并将离散单时滞系统的结果应用到鲁棒和时滞信息融合滤波问题上,给出了一个时滞系统的鲁棒Kalman滤波器和时滞信息融合滤波器。
研究了连续情况下时滞系统的Kalman滤波问题。提出了连续时滞系统新息重组分析方法,对含有即时观测和单时滞观测的情况进行了深入地研究,进而将其推广到更一般的多时滞观测的情况,给出了含有即时观测和时滞观测情况下的最优滤波器,并利用实例和流程图直观得体现了算法的实现过程,方法中没有采用传统的偏微分方法,得到了显式解。
提出的新息重组分析方法可以用来处理很多复杂的问题,其中H_∞白噪声估计问题就是一个重要的应用。引入Krein空间,借助新息重组分析方法、射影定理,研究了线性系统(包括离散和连续情况)的白噪声估计问题,给出了H_∞估计器(主要是滤波器和固定时滞平滑器)及其存在的充要条件。揭示出H_∞白噪声滤波问题实际上等价于Krein空间内的H_2白噪声滤波问题,而H_∞白噪声固定时滞平滑问题实际上等价于Krein空间内含即时观测和单时滞观测的系统的H_2白噪声估计问题。本课题具有非常重要的理论价值和实际意义。
Linear Estimation is a key research topic in many fields such as control, communications, signal processing, and so on. In the 1960's, Kalman filtering was presented and has been a major tool of state estimation and control since then. However, the standard Kalman filtering can be only applicable to the normal systems without delays not to the delayed systems. Much interest has been attached to the case of time delays for the actual requirements. Some problems such as estimation for linear systems with delayed measurements and control for systems with input delay haven't been studied well up to the present. In this paper, we are concerned with the optimal estimation problem for linear systems systems with delayed measurements, and a new optimal approach, re-organization of innovation analysis, is then proposed. The main idea is to re-organize the delayed measurements into delay-free measurements from different systems, and the associated innovation sequence is given in according to the re-organized measurements, Kalman filtering formulations based on the new approach are thus given. With the new technique, the more complicated H_∞white noise estimator, robust time-delayed Kalman filter, and time-delayed information fusion filter are then given. The paper mainly includes the following parts:
Kalman filtering for linear discrete-time systems with delayed measurements. Reorganization of innovation analysis for discrete-time systems is introduced, and the case of systems with instantaneous measurement and delayed measurements is studied, the optimal filters are then given. Furthermore, the more complicated technique, re-organization of innovation analysis, is derived for discrete-time systems with multiple delayed measurements, and optimal filters and the flow chart are also given in the paper. Such an approach is much more computationally attractive which is a major advantage over the traditional system augmentation, and the comparison of the computation costs between the proposed re-organization of innovation analysis and the traditional augmentation method is also given, and two examples have been given to show this point. A numerical example is given to show the efficiency of the proposed approach. The proposed approach is further extended to the robust Kalman filtering for discrete-time systems with single delayed measurement and the time-delayed information fusion filtering problem, then the robust Kalman filter and the time-delayed information fusion filter are given.
Kalman filtering for linear continuous-time systems with delayed measurements. Reorganization of innovation analysis for continuous-time systems is presented, the case of systems with instantaneous measurement and delayed measurements is studied well, and the proposed approach is extended to the case of continuous-time systems with multiple delayed measurements, and optimal filters are given. Two numerical examples and the flowchart for the computation are given to show the process of the computation. Explicit solutions to the problem are given without resorting to traditional partial differential equations.
Re-organization of innovation analysis can be used to deal with many difficult problems, one of which is H_∞white noise estimation. In the paper, Krein space is introduced, and the H_∞white noise estimation for linear systems (including both discrete-time case and continuous-time case) is considered with the help of re-organization of innovation analysis and projection formulation in Krein space, thus the estimators (mainly filters and fixed-lag smoothers) and the associated sufficient and essential conditions are given. It is also shown that the white noise H_∞white noise filtering is equivalent to the H_2 white noise filtering in Krein space, and the H_∞white noise fixed-lag smoothing is in fact equivalent to an H_2 estimation problem for measurement delayed system in Krein space. The problem is much valuable both in theory and in practice.
引文
[1]Kohnanovskii V B,Myshkis A.Introduction to the theory and application of functional differential equations.Dordrecht:Kluwer Academy,1997.
[2]Richard.I P.Time-delay systems:an overview of some recent advances and open problems.Automatica.2003,39(10):1667-1694.
[3]Bramanian A,Sayed A H.Multi-Objective flter design for uncertain stochastic time-delay systems.IEEE Trans.Automat.Contr..2004,49(1):149-154.
[4]Kahane A C,Mirkin L,Palmor Z J.On the discrete-time H_∞ fixed-lag smoothing.Proc.15th IFAC World Congr.,Barcelona,Spain,2002.
[5]Elsayed A,Grimble M J.A new approach to H_∞ design of optimal digital linear filters.IMA J.Math.Contr.Informat.1989,6(8):233-251.
[6]Sayed A H,Hassibi B,Kailath T.Inertia conditions for the minimization of quadratic forms in indefinite metric spaces.Operator Theory:Advances and Applications,Ⅰ.Gohberg,P.Lancaster,and P.N.Shivakumar,eds.,Birkhauser,Basel.1996,87:309-347.
[7]Kojima A,Ishijima S.H_∞ perfornlance of preview control systems.Automatica.2003,39(4):693-701.
[8]Kojima A,Ishijima S.H_∞ control for preview and delayed strategies.Proc.40th IEEE Conf.Decision and Control,Orlando,FL,2001:991-996.
[9]Pila A W,Shaked U,de Souza C E.H_∞ Filtering for Continuous-Tinle Linear Systems with Delay.IEEE Trans.Automat.Contr..1999,44(7):1412-1418.
[10]Bittanti B,Cuzzola F A.Continuous-time periodic H_∞ filtering via LMI.Eur.J.Contr..2001,7:2-16.
[11]Levy B C,Benveniste A,Nikoukhah R.High-level prinfitives tbr recursive maximum likeli-hood estimation.IEEE Trans.Automat.Contr..1996,41(8):1125-1145.
[12]Anderson B D O,Moore J B.Optimal filtering.Englewood,Cliffs,N.J.:Prentice-Hall,1979.
[13]Hassibi B,Sayed A H,Kailath T.Indefinite-Quadratic Estimation and Control A unified Approach to H_2 and H_∞ Theories.Englewood,Cliffs,N.J.:Prentice-Hall,1999.
[14]Hassibi B,Sayed A H,Kailath T.Linear estimation in Krein spaces-Part Ⅰ:Theory.IEEE Trans.Automat.Contr..1996,41(1):18-33.
[15]Hassibi B,Sayed A H,Kailath T.Linear estimation in Krcin spaces-Part Ⅱ:Applications.IEEE Trans.Automat.Contr..1996,41(1):34-49.
[16]Chen B S,Hung J C.Fixed-order H_2 and H_∞ optimal deconvolution filter designs.IEEE Trans.Signal Processing.2000,80(2):311-33l.
[17]Xu B,Liu Y H.Delay-dependent/delay-independent stability of linear systems with multiple time varying delays.IEBE Trans.Automat.Contr..2003,48:697-701.
[18]de Souda C E,Phlhares R M,Peres P L D.Robust H_∞ filtering design for uncertain linear systenls with nmltiple time varying state delays.IEEE Trans.Signal Processing.2001,49(3):569-576.
[19]Sims C S,Kim H,Jalali A A et al.Prediction,filtering,smoothing and deconvolution in a discrete-time H_∞ setting:a game theory approach.Int.J.Contr..1998,70(6):841-857.
[20]Wang C M.Location estilnation and uncertainty analysis for mobile robots.Proc.1988 Int.Conf.Robotics and Automation,Philadelphia,USA,1988:1230-1235.
[21]Steven D B,Zhao L,Robert M C.Three-dilnensional trajectory estimation from image position and velocity.IEEE Trans.Aerospace and Electronic Systems.2000,36(4):1075-1087.
[22]Healy D M,Hendriks H,Kim P T.Spherical Deconvolution.J.of Multivariate Analysis.1998,67(1):1-22.
[23]Cator E A.Deconvolution with arbitrarily smooth kernels.Statistics and Probability Letters.2001,54(2):205-214.
[24]王好谦.时滞广义系统最优估计:(博士学位论文).哈尔滨:哈尔滨工业大学,2005.
[25]Briggs N,Vinter R.Linear filtering for time-delay systems.IMA J.Math.Contr.and Inf..1989,6(2):167-178.
[26]Xu S,Lain J,Yang C.Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay.Syst.Contr.Lett..2003,43(2):77-84.
[27]Pila W,Shaked U,de Souza C E.H_∞ filtering for continuous-time linear systems with delays.IEEE Trans.Automat.Contr..1999,14(7):1412-1417.
[28]Guan X P,Liu Y,Duan G R.Observer-based robust multi-delays uncertain systems.Proc.3th Asia Control Conf..Shanghai,China,2000:700-704.
[29]Cai Y Z.Robust H_∞ filter design for uncertain linear systems with state delay.Proc.4th World Congr.Intelligent Control and Automation.Shanghai,2002:1726-1730.
[30]Kwakernaak H.Optimal filtering in linear systems with time delays.IEEE Trans.on Au-tomat.Contr..1967,12(2):169-173.
[31]Zhang H S,Zhang D,Xie L H.An innovation approach to H_∞ prediction for continuous-time systems with application to systems with delayed measurements.Automatica.2004,40(7):1253-1261.
[32]Zhang H S,Xie L H,Zhang D et al.A Re-oganized hmovation Approach to Linear Estimation.IEEE Trans.Automat.Contr..2004,49(10):1810-1814.
[33]Basin M V,Martinez Zuniga R.Optimal linear filtering over observations with multiple delays.Int.J.Robust Nonlinear Control.2004,14(8):685-696.
[34]Basin M V,Alcort G M A,Rodriguez Gonzalez J G.Optimal filtering for linear systems with state and observation delays.Int.J.Robust Nonlinear Control.2005,15(17):859-871.
[35]Fridman E,Shaked U.A New H_∞ Filter Design for Linear Time Delay Systems.IEEE Trans.Signal Processing.2001,49(11):2839-2843.
[36]Zhang H S,Xie L H,Soh Y C.A Unified Approach to Linear Estimation for Discrete-Time Systems-Part Ⅰ:H_∞ Estimation.Proc.40th IEEE Conf.Decision Control,Orlando,Florida USA,2001:2917-2922.
[37]Deng Z L,Qi R B.Multi-sensor information fusion suboptimal steady-state Kalman filter.Chinese Science Abstracts.2000,6(2):183-184.
[38]邓自立.最优估计理论及其应用——建模、滤波、信息融合估计.哈尔滨:哈尔滨工业大学出版社,2005.
[39]何友,王国宏,陆大金等.多传感器信息融合及应用.北京:电子工业出版社,2000.
[40]王宇飞,黄显林,胡恒章.GPS/INS/TRN组合导航系统信息融合技术研究.中国惯性技术学报.1999,7(3):30-32.
[41]吴宝林,黄晓瑞,崔平远.信息融合技术及其在组合导航系统中的应用.战术导弹技术.2002,1:39-44.
[42]张崇猛,陈超英,庄良杰等.信息融合理论及其在/INS/TRN/Doppler组合导航系统中的应用.中国惯性技术学报.1999,7(3):1-8.
[43]刘同明,夏明勋,谢洪成.数据融合技术及其应用.北京:国防工业出版社,1998.
[44]Wiener N.Extrapolation interpolation,and smoothing of stationary time series.New York:The Technology Press and Wiley,1950.
[45]Kahnan R E.A new approach to linear filtering and prediction problems.J.of Basic Engi-neering,Trans.ASME-D.1960,82(1):35-45.
[46]Kwong H,Willsky A S.Estimation and filter stability of stochastic delay systems.SIAM J.Contr.and Optimi..1978,16:660-681.
[47]Bagchi A.A martingale approach to state estimation in delay differential systems.J.Math.Anal.and Applics.1976,56:195-210.
[48]Fridman E,Shaked U.A descriptor system approach to H_∞ control of linear time-delay systems.IEEE Trans.Automat.Contr..2002,47(2):253-270.
[49]Briggs M S.Filtering of linear heredity systems with delays in the input:(Ph.D thesis).U.K.:Imperial College,1980.
[50]俞立.鲁棒控制——线性矩阵不等式处理方法.北京:清华大学出版社,2002.
[51]Kailath T,Sayed A H,Hassibi B.Linear Estimation.Englewood,Cliffs,N.J,:Prentice-Hall,1999.
[52]Doyle J C,Glover K,Khargoneckar P P et al.State-space solutions to standard H_∞ and H_∞control problems.IEEE Trans.Automat.Contr..1989,34(8):831-847.
[53]Green M,Glover K,Limerbeer D et al.A J-Spectral factorization approach to H_∞ control.SIAM J.Contr.Optimization.1990,28:1350-1371.
[54]Zhang H S,Xie L H,Soh Y.C.A Unified Approach to Linear Estimation for Discrete-Time Systems-Part Ⅱ:H_∞ Estimation.Proc.40th IEEE Conf.Decision Control,Orlando,Florida USA,2001:2923-2928.
[55]Zhang H S,Xie L H,Zhang D et al.H_∞ fixed-lag smoothing for linear tiine-varying discrete-time systems.Automatica.2005,41(5):839-846.
[56]Zhang H S,Zhang D.Finite horizon H_∞ fixed-lag smoothing for tiine-varying continuous systeins.IEEE Trans.Circuits Syst.Ⅱ.2004,51(9):496-499.
[57]Mendel J M.White-Noise Estimators for Seismic Data Processing in Oil Exploration.IEEE Trans.Automat.Contr..1986,AC-31(1):80-83.
[58]Rousseaux P,Troquet J.Deconvolution of time-varying systems by Kalman filtering:Its application to the active state in the muscle.Signal Processing.1986,10:291-301.
[59] Douglas R K, Speyer J L. An H_∞ Bounded Fault Detection Filter. Proc. American Control Conf., America, 1995: 86-90.
[60] Hanshaw T C, Anderson M J, Hsu C S. An H_∞ Deconvolution Filter Design and Its Appli cation to Ultrasonic Nondestructive Evaluation of Materials. Proc. American Control Conf., America, 1999: 3878-3884.
[61] Chung W C, Speyer J L. A Game Theoretic Fault Detection. IEEE Trans. Automat. Contr.. 1998, 43(2): 143-161.
[62] Yu X G, Hsu C S, Bamberger R H. H_∞ Deconvolution Filter Design and Its Application in Image Restoration. Proc. 35th Conf. Decision and Control, Japan, 1996: 4802-4807.
[63] Dai G Z, Mendel J M. A Straightforward and Unified Approach to the Derivation of Minimum-Variance Deconvolution Algorithms. IEEE Trans. Automat. Contr.. 1977, AC- 22(5): 694-706.
[64] Mendel J M. Lessons in Estimation Theory for Signal Processing, Communications, and Control. Englewood. Cliffs, N.J.: Prentice-Hall, 1995.
[65] Mendel J M. Minmum Variance Deconvolution. IEEE Trans. Geoscience and Romote Sensing. 1981, GE-19(3): 161-171.
[66] Mendel J M. Optimal Seismic Deconvolution: An Estimation-Based Approach. New York: Academic Press, 1983.
[67] Deng Z L, Guo Y. Modern Time Series Analysis and its Application, Modeling, Filtering, Deconvolution, Prediction and Control. Beijing: Knowledge Press, 1989.
[68] Ahlen A, Sternad M. Optimal deconvolution basal on polynominal method. IEEE Trans. Acoust. Speech Sig. Process. 1989, 37: 217-226.
[69] Cuzzola F A, Ferrante A. Explicit formulas for LMI-based H_2 filtering and deconvolution. Automatica. 2001, 37(9): 1443-1449.
[70] Wang L X, Dai G Z, Mendel J. M. One-Pass Minimum-Variance Deconvolution Algorithms. IEEE Trans. Automat, Contr.. 1990, AC-35(3): 326-329.
[71] Ott N, Meder H G. The Kalman Filter as a Prediction Error Filter. Geophysical rospecting. 1972, 20: 549-560.
[72] Hagander P, Wittenmark B. A self-tuning filter for fixed-lag smoothing. IEEE Trans. Theory. 1977, IT-23(3): 377-384.
[73] Deng Z L, Zhang H S, Liu S J et al. Optimal and Self-tuning White Noise Estimators with Applications to Deconvolution and Filtering Problems. Automatica. 1996, 32(2): 199-216.
[74] Kim H, Jalali A. A, Sims C S et al. Prediction, filtering, smoothing and white noise in a discrete H_∞ setting: a game theory approach. Int. J. Contr.. 1998, 70(6): 841-857.
[75] Zhang H S, Xie L H. Son Y C. H_∞ Deconvolution Filtering, Prediction, and Smoothing: A Krein Space Poloynominal Approach. IEEE Trans. Automat. Contr.. 2000, 48(3): 888-892.
[76] Rho H, Hsu C S. A Game Theory Approach to H_∞ Deconvolution Filter Design. Proc. American Control Conf., America, 1999: 2891-2895.
[77] Xie L H, Wang S, Du C L eta al. H_∞ deconvolution of periodic channels. IEEE Trans. Sig. Proc.. 2000. 80: 2365-2378.
[78]Grimble M J.H_∞ inferential filtering,prediction and smoothing problems.IEEE Trans.Signal Processing.1997,60:289-304.
[79]Grimble M J.H_∞ optimal multichannel linear deconvohltion filters,predictors and smoothers.Int.J.Contr..1996,63(3):519-533.
[80]Grimble M J.Robust filter design for uncertain systems defined by both hard and soft bounds.IEEE Trans.Signal Processing.1996,44(5):1063-1071.
[81]Wang S,Xie L H,Zhang C S.Mixed H_2/H_∞ deconvolution of uncertain periodic FIR chan-nels.IEEE Trans.Signal Processing.2001,81:2089-2103.
[82]Moir T J,Vishwanath T G,Campbell D R.Real-time self:tuning deconvolution filter and smoother.Int.J.Contr..1987,45:969-985.
[83]Shaked U,Theodor Y.A frequency domain approach to the problems of H_∞-minimum error state estimation and white noise.IEEE Trans.Signal Processing.1992,40(12):3001-3011.
[84]Kalman R E,Buoy R S.New Results in Linear Filtering and Prediction Theory Transactions of the ASME-J.Basic Engineering.1961,83:95-107.
[85]Kucera V.Discrete Linear Control,the Polynomial Approach.Chichester:Wiley,1979.
[86]Grimble M J.Polynomial Approach to Optimal Linear Filtering and Prediction.Int.,J.Contr..1985,41(6):1545-1564.
[87]Zhang H S,Liu X J,Chai T Y.A new method tbr optimal deconvolution.IEEE Trans.Signal Processing.1997,45(10):2596-2599.
[88]邓自立.现代时间序列分析——建模、滤波、去卷、预报和控制.北京:知识出版社,1989.
[89]邓自立.自校正滤波理论及其应用——现代时间序列分析方法.哈尔滨:哈尔滨工业大学出版社,2003.
[90]邓自立,许燕.基于Kalman滤波的白噪声理论.自动化学报.2003,29(1):23-31.
[91]邓自立,许燕.基于Kalman滤波的通用的和统一的白噪声估计方法.控制理论与应用.2004.21(4):501-506.
[92]Zavarei M M,Jamshidi M.Time Delay Systems:Analysis,Optimization and Applications.Amsterdan,The Netherlands:North-Holland,1987.
[93]Goodwin G C,Sin K S.Adaptive filtering,prediction and control.In.:Prentice-Hall,1984.
[94]Meditch J S.Stochastic Optimal Linear Estimation and Control.New York:McGraw-Hill,1969.
[95]Bolzern P,Colaneri P,Nicolao G D.On Discrete-Time H_∞ Fixed-Lag Smoothing.IEEE Trans.Signal Processing.2004,52(1):132-141.
[96]Chisel L,Mosca E.Polynomial equations for the linear MMSE state estimation.IEEE Trans.Automat.Contr..1992,AC-37(5):623-626.
[97]Kucera V.New results in state estimation and regulation.Automatica.1981,17(9):745-748.
[98]Pridman E,Shaked U.New Bounded Real Lelnma Representations for Time-Delay Systems and Their Applications.IEEE Trans.Automat.Contr..2001,46(12):1973-1979.
[99]胡剑波,苏宏业,褚健.不确定时滞系统的二次稳定无记忆变结构控制.系统工程理论与实践.2001,15(5):13-23.
[100]姜偕富,费树岷,冯纯伯.线性时滞系统依赖于时滞的H_∞控制.自动化学报.2001,27(1):108-114.
[101]关新平,张群亮.不确定离散时滞系统的鲁棒H_∞滤波与仿真.系统仿真学报.2002,14(8):1078-1080.
[102]张群亮,关新平.不确定关联时时滞系统的鲁棒H_∞滤波.控制理论与应用.2004,21(2):267-270.
[103]郭雷,冯纯伯.一类不确定系统的鲁棒H_∞控制器设计.中国科学E辑.1998,28(1):56-62.
[104]郭雷,忻欣,冯纯伯.基于LMI的一类混合H_2/H_∞控制器问题的降阶控制器设计——离散情形.自动化学报.1998,24(3):355-358.
[105]徐胜远,陈雪如,杨成梧.一类离散广义系统的H_∞控制.控制理论与应用.2000,17(5):739-741
[106]Kaszkurewicz E,Bhaya A.Discrete-time state estimation with two counters and measure-ment delay.Proc.35th IEEE Conf.Decision and Control,Kobe,Japan,1996:1472-1476.
[107]Chenavier F,Crowley J L.Position estimation for a mobile robot using vision and odometry.Proc.1992 IEEE Int.Conf.Robotics and Automation,Nice,Prance,1992:2588-2593.
[108]Hsiao F H,Pan S T.Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems.J.of Dynam.Syst.,Measur.,and Contr..1996,118(4):803-808.
[109]Andersen G L,Christensen A C,Ravn O.Augmented models for improving vision control of a mobile robot.Proc.3rd IEEE Conf.Control Applications,Glasgow,UK,1994:53-58.
[110]Murata S,Hirose T.Onboard locating system using real-time image processing for a self-navigating vehicle.IEEE Trans.Industrial Electronics.1993,40(11):145-154.
[111]Larsen T D,Andersen N A,Ravn O et al.Incorporation of Time Delayed Measurements in a Discrete-time Kalman Filter.Proc.37th IEEE Conf.Decision and Control,Tainpa,Florida America,1998:3972-3977.
[112]Klein L A.Sensor and Data Fusion Concepts and Applications.SPIE Press,1999.
[113]邓自立,刘玉梅.一种统一的Kalman估值器.信息与控制.1999,28(4):249-254.
[114]Zames G.Feedback and optimal sensitivity:Model reference transforinations,multiplicative seminorms,and approximate inverses.IEEE Trans.Automat.Contr..1981,26:301-320.
[115]Li H,Fu M.A linear matrix in equality approach to robust H_∞ filtering.IEEE Trans.Signal Processing.1997,45:2338-2350.
[116]Grimble M J.Minmax design of optimal linear filters.MTNS Conf.,Phoenix,Arizona,1987.
[117]Grimble M J.H_∞ design of optimal linear filters.MTNS Conf.,Phoenix,Arizona,1987:533-540.
[118]Theodor Y,Shaked U.Robust discrete-time minimum-variance filtering.IEEE Trans.Au-tomat.Contr..1994,39(9):1944-1948.
[119]Colaneri P,Maroni M,Shaked U.H_∞ prediction and smoothing for discerte-time systems:A J-sepctral factorization approach.Proc.37th IEEE Conf.Decision and Control,Tampa,Florida,1998:2836-2842.
[120]Colaneri P,Ferrante A.A J-spectral factorization approach for H_∞ estimation problem in discrete time.IEEE Trans.Automat..Contr..2002,47(12):2108-2113.
[121]Mirkin L.Continuous-time fixed-lag smoothing in an H_∞ setting.Proc.40th IEEE Conf.Decision and Control,Orlando,FL,2001:3512-3517.
[122]Yaesh I,Shaked U.Game Theory Approach to Optimal Linear State Estimation and Its Relation to the Minimum H_∞-norm Estimation.IEEE Trans.Automat.Contr..1992,37(6):828-831.
[123]Grimble M J.H_∞ fixed-lag smoothing filter for scalar systems.IEEE Trans.Signal Process-ing.1991,39(9):1955-1963.
[124]Barbosa K.A,de Souza C E,Trofino A.Robust filtering for uncertain linear systems with state-dependent noise.Proc.42th IEEE Conf.Decision and Control,Maul,Hawaii USA,2003:880-885.
[125]范训礼,谢振华,张勇.离散系统LMI滤波技术.飞行力学.1999:17(4),55-60.
[126]Zhang H S,Zhang D,Xie L H.H_∞ Fixed-lag smoothing and prediction for linear continuous-time systems.Proc.American Control Conf.,Denver,2003:4201-4206.
[127]Blondel V D.Open Problem in Mathematics Systems and Control Theory.London,UK:Spinger-Verlag,1999.
[128]Tadmor G,Mirkin L.H_∞ control and estimation with preview-part Ⅰ:Matrix ARE solutions in continuous time.IEEE Trans.Automat.Contr..2005,50(1):19-28.
[129]Tadmor G,Mirkin L.H_∞ control and estimation with preview -part Ⅱ:Matrix ARE solu-tions in discrete time.IEEE Trans.Automat.Contr..200,5,50(1):29-40.
[130]Deng Z L.Self-tuning white noise estimators with application to seismic data deconvolution.Acta Automatica Sinica.1986,12:155-161.
[131]Dabis H S,Moir T J.A unitied approach to optimal estimation using diophantine equations.Int.J.Contr..1993,57:577-598.
[132]Zhang H S,Xie L H,Soh Y C.Optimal and self-tuning deconvolution in time domain.IEEE Trans.Signal Process.1999,47(8):2253-2261.
[133]Van Trees H L.Detection,Estimation and Modulation Theory,Part Ⅰ.New York:John Wiley,1968.
[134]邱天爽,李婷,毕英伟等.随机过程——滤波、估计与检测.北京:电子工业出版社,2005。
[135]徐宁寿.随机信号估计与系统控制,北京:北京工业大学出版社,2001。
[136]Kalman R E and Bucy R C.New results in linear filtering and prediction theory.Trans.ASME,J.Basic Eng.1961,83:95-107.
[137]鲍齐克S M著,凌云旦译.数字滤波和卡尔曼滤波,科学出版社,1984.
[138]史忠科.最优估计的计算方法.科学出版社.2001.
[139]付梦印,邓志红,张继伟.Kalman滤波理论及其在导航系统中的应用.科学出版社.2003.
[140]Mirkin L.On the H_∞ fixed-lag smoothing:How to exploit the information preview.Auto-matica.2003,39(8):1495-1504.
[141]Bolzern P,Colaneri P,Nicolao G D.H_∞ smoothing in discrete-time:a direct approach.Proc.41th IEEE Conf.Decision and Control,Las Vegas,2002:4233-4238.
[142]Tadmor G.The standard H_∞ problem in systems with a single input delay.IEEE Trans.Automat.Contr..2002,45(3):382-397.
[143]Uchida K,Ikeda K,Azuma T et al.Finite-dimensional characterizations of H_∞ control for linear systems with delays in input and output.Int.J.Robust and Nonlinear Control.2003,special issue.
[144]Duan G,Wang H.Multi-model switching control and its application to BTT missile design.Acta Aeronautica Et Astronautica Sinica2005,26(2):144-147.
[145]Hanshaw T C,Anderson M J,Hsu C S.An Hoo deconvolution filter and its application to ultrasonic nondestructive evaluation of materials.ISA Trans..1999,38(4):2891-2895.
[146]Petersen I R,McFarlane D C.Optimal guaranteed cost filtering for uncertain discrete-time linear systems.Int.J.Robust Nonlinear Control.1996,6:267-280.
[147]Geromel J C.Optimal Linear Filtering under Parameter Uncertainty.IEEE Trans.Signal Processing.1999,47:168-175.
[148]Geromel J C,Bernussou J,Garcia Get al.H_2 and H_∞ robust filtering for discrete-time linear systems.SIAM J.Contr.Optim..2000,38(5):1353-1368.
[149]Xie L H,Sob Y C,de Souza C E.Robust Kalman filtering for uncertain discrete-time systems.IEEE Trans.Automat.Contr..1994,39(6):1310-1321.
[150]Fu M,de Souza C E,Luo Z.Finite-Horizon Robust Kalman Filter Design.IEEE Trans.Signal Processing.2001,49(9):2103-2112.
[151]Mahmoud M,Al-Muthairi N,Bingulac S.Robust Kalman filtering for continuous time-lag systems.Syst.Contr.Lett..1999,38(5):309-319.
[152]Shaked U,Xie L H,Soh Y.C.New approaches to robust minimum variance filter design.IEEE Trans.Signal Processing.2001,49:2620-2629.
[153]Zhang W H,Chen B S,Tseng C S.Robust H_∞ Filtering for Nonlinear Stochastic Systems.IEEE Trans.Signal Processing.2005,53(2):589-598.
[154]Zhu X,Soh Y C,Xie L H.Design and analysis of discrete-time robust Kalman filters.Automatica.2002,38(6):1069-1077.
[155]张维海.随机不确定系统的鲁棒H_∞滤波.控制理论与应用.2003,20(5):741-745.
[156]Petersen I R,McFarlane D C.Optimal guaranteed cost control and filtering for uncertain linear systems.IEEE Trans.Automat.Contr..1994,39:1971-1977.
[157]Bolzern P,Colaneri P,de Nicolao G.Finite escape and convergence properties of guaranteed-cost robust filters.Automatica.1997,33(1):31-47.
[158]Shaked U,de Souza C E.Robust Minimum Variance Filtering.IEEE Trans.Signal Process-ing.2002,43(11):2474-2483.
[159]Carlson N A.Federated square root filter for decentralized parallel process.IEEE Trans.Aerospace and Electronic Systems.1990,26(2):517-525.
[160]Sasiadek J Z.Sensor Fusion.Annual Review In Control.2002,26(2):203-228.
[161]Herrera F,and Herrera-Viedma E.Aggregation operators for linguistic weighted informa-tion.IEEE Trans.Syst.,Man,and Cybernetic-Part A:Syst.and Humans.1997,27(5):646-656.
[162]Sun S L.Multi-sensor weighted fusion suboptimal filtering for systems with multiple time delayed measurements.Proc.6th World Congress on Intelligent Control and Automation.Jun.21-23,2006,Dalian China,pp.1617-1620.
[163]Sun S L,and Cui P.Multi-sensor optimal information fusion steady-state Kalman filter weighted by scalars.Control and Decision.2004,19(2):208-211.
[164]Sun S L.Multi-sensor information fusion white noise weighted by scalars based on Kalman predictor.Automatica.2004,40(8):1447-1453.
[165]韩崇昭,朱洪艳.多传感器信息融合与自动化.自动化学报.2002,28(suppl):117-124.
[166]Wang H X,Su X C,Lu X,Cao M Y.An Improved Algorithm of the Hand-Eye Vision Positioning System Based on the Constant Rotation Matrix,Proc.6th World Congress on Intelligent Control and Automation,Dalian,China,June 21-23,2006:9222-9226.
[167]Nejatali A,and Ciric I R.Novel image fusion methodology using fuzzy set theory.Optical Engineering.1998,37(2):485-491.
[168]Guo H.Researches and advances in multi-sensor information fusion technology.Science Foundation in China.2005,19(1):17-21.
[169]Deng Z L,and Wu X.Fast algorithms for multisensor centralized measurement fusion Kalman filter.Science Technology and Engineer.2005,5(20):1469-1472.
[170]He Y,Wang G,Lu D,and Peng Y.Multisensor information fusion with applications.Beijing:Publishing House of Electronics Industry,2000.
[171]Hashmipour H R,Roy S and Laub A J.Decentralized structures for parallel Kalman filtering.IEEE Trans.Automat.Contr..1988,33(1):88-93.
[172]Sun S L.Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother.Automatica.2005,41(10):2153-2159.
[173]Sun S L and Deng Z L.Multi-sensor optimal information fusion Kalman filter.Automatica.2004,40(6):1017-1023.
[2]Richard.I P.Time-delay systems:an overview of some recent advances and open problems.Automatica.2003,39(10):1667-1694.
[3]Bramanian A,Sayed A H.Multi-Objective flter design for uncertain stochastic time-delay systems.IEEE Trans.Automat.Contr..2004,49(1):149-154.
[4]Kahane A C,Mirkin L,Palmor Z J.On the discrete-time H_∞ fixed-lag smoothing.Proc.15th IFAC World Congr.,Barcelona,Spain,2002.
[5]Elsayed A,Grimble M J.A new approach to H_∞ design of optimal digital linear filters.IMA J.Math.Contr.Informat.1989,6(8):233-251.
[6]Sayed A H,Hassibi B,Kailath T.Inertia conditions for the minimization of quadratic forms in indefinite metric spaces.Operator Theory:Advances and Applications,Ⅰ.Gohberg,P.Lancaster,and P.N.Shivakumar,eds.,Birkhauser,Basel.1996,87:309-347.
[7]Kojima A,Ishijima S.H_∞ perfornlance of preview control systems.Automatica.2003,39(4):693-701.
[8]Kojima A,Ishijima S.H_∞ control for preview and delayed strategies.Proc.40th IEEE Conf.Decision and Control,Orlando,FL,2001:991-996.
[9]Pila A W,Shaked U,de Souza C E.H_∞ Filtering for Continuous-Tinle Linear Systems with Delay.IEEE Trans.Automat.Contr..1999,44(7):1412-1418.
[10]Bittanti B,Cuzzola F A.Continuous-time periodic H_∞ filtering via LMI.Eur.J.Contr..2001,7:2-16.
[11]Levy B C,Benveniste A,Nikoukhah R.High-level prinfitives tbr recursive maximum likeli-hood estimation.IEEE Trans.Automat.Contr..1996,41(8):1125-1145.
[12]Anderson B D O,Moore J B.Optimal filtering.Englewood,Cliffs,N.J.:Prentice-Hall,1979.
[13]Hassibi B,Sayed A H,Kailath T.Indefinite-Quadratic Estimation and Control A unified Approach to H_2 and H_∞ Theories.Englewood,Cliffs,N.J.:Prentice-Hall,1999.
[14]Hassibi B,Sayed A H,Kailath T.Linear estimation in Krein spaces-Part Ⅰ:Theory.IEEE Trans.Automat.Contr..1996,41(1):18-33.
[15]Hassibi B,Sayed A H,Kailath T.Linear estimation in Krcin spaces-Part Ⅱ:Applications.IEEE Trans.Automat.Contr..1996,41(1):34-49.
[16]Chen B S,Hung J C.Fixed-order H_2 and H_∞ optimal deconvolution filter designs.IEEE Trans.Signal Processing.2000,80(2):311-33l.
[17]Xu B,Liu Y H.Delay-dependent/delay-independent stability of linear systems with multiple time varying delays.IEBE Trans.Automat.Contr..2003,48:697-701.
[18]de Souda C E,Phlhares R M,Peres P L D.Robust H_∞ filtering design for uncertain linear systenls with nmltiple time varying state delays.IEEE Trans.Signal Processing.2001,49(3):569-576.
[19]Sims C S,Kim H,Jalali A A et al.Prediction,filtering,smoothing and deconvolution in a discrete-time H_∞ setting:a game theory approach.Int.J.Contr..1998,70(6):841-857.
[20]Wang C M.Location estilnation and uncertainty analysis for mobile robots.Proc.1988 Int.Conf.Robotics and Automation,Philadelphia,USA,1988:1230-1235.
[21]Steven D B,Zhao L,Robert M C.Three-dilnensional trajectory estimation from image position and velocity.IEEE Trans.Aerospace and Electronic Systems.2000,36(4):1075-1087.
[22]Healy D M,Hendriks H,Kim P T.Spherical Deconvolution.J.of Multivariate Analysis.1998,67(1):1-22.
[23]Cator E A.Deconvolution with arbitrarily smooth kernels.Statistics and Probability Letters.2001,54(2):205-214.
[24]王好谦.时滞广义系统最优估计:(博士学位论文).哈尔滨:哈尔滨工业大学,2005.
[25]Briggs N,Vinter R.Linear filtering for time-delay systems.IMA J.Math.Contr.and Inf..1989,6(2):167-178.
[26]Xu S,Lain J,Yang C.Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay.Syst.Contr.Lett..2003,43(2):77-84.
[27]Pila W,Shaked U,de Souza C E.H_∞ filtering for continuous-time linear systems with delays.IEEE Trans.Automat.Contr..1999,14(7):1412-1417.
[28]Guan X P,Liu Y,Duan G R.Observer-based robust multi-delays uncertain systems.Proc.3th Asia Control Conf..Shanghai,China,2000:700-704.
[29]Cai Y Z.Robust H_∞ filter design for uncertain linear systems with state delay.Proc.4th World Congr.Intelligent Control and Automation.Shanghai,2002:1726-1730.
[30]Kwakernaak H.Optimal filtering in linear systems with time delays.IEEE Trans.on Au-tomat.Contr..1967,12(2):169-173.
[31]Zhang H S,Zhang D,Xie L H.An innovation approach to H_∞ prediction for continuous-time systems with application to systems with delayed measurements.Automatica.2004,40(7):1253-1261.
[32]Zhang H S,Xie L H,Zhang D et al.A Re-oganized hmovation Approach to Linear Estimation.IEEE Trans.Automat.Contr..2004,49(10):1810-1814.
[33]Basin M V,Martinez Zuniga R.Optimal linear filtering over observations with multiple delays.Int.J.Robust Nonlinear Control.2004,14(8):685-696.
[34]Basin M V,Alcort G M A,Rodriguez Gonzalez J G.Optimal filtering for linear systems with state and observation delays.Int.J.Robust Nonlinear Control.2005,15(17):859-871.
[35]Fridman E,Shaked U.A New H_∞ Filter Design for Linear Time Delay Systems.IEEE Trans.Signal Processing.2001,49(11):2839-2843.
[36]Zhang H S,Xie L H,Soh Y C.A Unified Approach to Linear Estimation for Discrete-Time Systems-Part Ⅰ:H_∞ Estimation.Proc.40th IEEE Conf.Decision Control,Orlando,Florida USA,2001:2917-2922.
[37]Deng Z L,Qi R B.Multi-sensor information fusion suboptimal steady-state Kalman filter.Chinese Science Abstracts.2000,6(2):183-184.
[38]邓自立.最优估计理论及其应用——建模、滤波、信息融合估计.哈尔滨:哈尔滨工业大学出版社,2005.
[39]何友,王国宏,陆大金等.多传感器信息融合及应用.北京:电子工业出版社,2000.
[40]王宇飞,黄显林,胡恒章.GPS/INS/TRN组合导航系统信息融合技术研究.中国惯性技术学报.1999,7(3):30-32.
[41]吴宝林,黄晓瑞,崔平远.信息融合技术及其在组合导航系统中的应用.战术导弹技术.2002,1:39-44.
[42]张崇猛,陈超英,庄良杰等.信息融合理论及其在/INS/TRN/Doppler组合导航系统中的应用.中国惯性技术学报.1999,7(3):1-8.
[43]刘同明,夏明勋,谢洪成.数据融合技术及其应用.北京:国防工业出版社,1998.
[44]Wiener N.Extrapolation interpolation,and smoothing of stationary time series.New York:The Technology Press and Wiley,1950.
[45]Kahnan R E.A new approach to linear filtering and prediction problems.J.of Basic Engi-neering,Trans.ASME-D.1960,82(1):35-45.
[46]Kwong H,Willsky A S.Estimation and filter stability of stochastic delay systems.SIAM J.Contr.and Optimi..1978,16:660-681.
[47]Bagchi A.A martingale approach to state estimation in delay differential systems.J.Math.Anal.and Applics.1976,56:195-210.
[48]Fridman E,Shaked U.A descriptor system approach to H_∞ control of linear time-delay systems.IEEE Trans.Automat.Contr..2002,47(2):253-270.
[49]Briggs M S.Filtering of linear heredity systems with delays in the input:(Ph.D thesis).U.K.:Imperial College,1980.
[50]俞立.鲁棒控制——线性矩阵不等式处理方法.北京:清华大学出版社,2002.
[51]Kailath T,Sayed A H,Hassibi B.Linear Estimation.Englewood,Cliffs,N.J,:Prentice-Hall,1999.
[52]Doyle J C,Glover K,Khargoneckar P P et al.State-space solutions to standard H_∞ and H_∞control problems.IEEE Trans.Automat.Contr..1989,34(8):831-847.
[53]Green M,Glover K,Limerbeer D et al.A J-Spectral factorization approach to H_∞ control.SIAM J.Contr.Optimization.1990,28:1350-1371.
[54]Zhang H S,Xie L H,Soh Y.C.A Unified Approach to Linear Estimation for Discrete-Time Systems-Part Ⅱ:H_∞ Estimation.Proc.40th IEEE Conf.Decision Control,Orlando,Florida USA,2001:2923-2928.
[55]Zhang H S,Xie L H,Zhang D et al.H_∞ fixed-lag smoothing for linear tiine-varying discrete-time systems.Automatica.2005,41(5):839-846.
[56]Zhang H S,Zhang D.Finite horizon H_∞ fixed-lag smoothing for tiine-varying continuous systeins.IEEE Trans.Circuits Syst.Ⅱ.2004,51(9):496-499.
[57]Mendel J M.White-Noise Estimators for Seismic Data Processing in Oil Exploration.IEEE Trans.Automat.Contr..1986,AC-31(1):80-83.
[58]Rousseaux P,Troquet J.Deconvolution of time-varying systems by Kalman filtering:Its application to the active state in the muscle.Signal Processing.1986,10:291-301.
[59] Douglas R K, Speyer J L. An H_∞ Bounded Fault Detection Filter. Proc. American Control Conf., America, 1995: 86-90.
[60] Hanshaw T C, Anderson M J, Hsu C S. An H_∞ Deconvolution Filter Design and Its Appli cation to Ultrasonic Nondestructive Evaluation of Materials. Proc. American Control Conf., America, 1999: 3878-3884.
[61] Chung W C, Speyer J L. A Game Theoretic Fault Detection. IEEE Trans. Automat. Contr.. 1998, 43(2): 143-161.
[62] Yu X G, Hsu C S, Bamberger R H. H_∞ Deconvolution Filter Design and Its Application in Image Restoration. Proc. 35th Conf. Decision and Control, Japan, 1996: 4802-4807.
[63] Dai G Z, Mendel J M. A Straightforward and Unified Approach to the Derivation of Minimum-Variance Deconvolution Algorithms. IEEE Trans. Automat. Contr.. 1977, AC- 22(5): 694-706.
[64] Mendel J M. Lessons in Estimation Theory for Signal Processing, Communications, and Control. Englewood. Cliffs, N.J.: Prentice-Hall, 1995.
[65] Mendel J M. Minmum Variance Deconvolution. IEEE Trans. Geoscience and Romote Sensing. 1981, GE-19(3): 161-171.
[66] Mendel J M. Optimal Seismic Deconvolution: An Estimation-Based Approach. New York: Academic Press, 1983.
[67] Deng Z L, Guo Y. Modern Time Series Analysis and its Application, Modeling, Filtering, Deconvolution, Prediction and Control. Beijing: Knowledge Press, 1989.
[68] Ahlen A, Sternad M. Optimal deconvolution basal on polynominal method. IEEE Trans. Acoust. Speech Sig. Process. 1989, 37: 217-226.
[69] Cuzzola F A, Ferrante A. Explicit formulas for LMI-based H_2 filtering and deconvolution. Automatica. 2001, 37(9): 1443-1449.
[70] Wang L X, Dai G Z, Mendel J. M. One-Pass Minimum-Variance Deconvolution Algorithms. IEEE Trans. Automat, Contr.. 1990, AC-35(3): 326-329.
[71] Ott N, Meder H G. The Kalman Filter as a Prediction Error Filter. Geophysical rospecting. 1972, 20: 549-560.
[72] Hagander P, Wittenmark B. A self-tuning filter for fixed-lag smoothing. IEEE Trans. Theory. 1977, IT-23(3): 377-384.
[73] Deng Z L, Zhang H S, Liu S J et al. Optimal and Self-tuning White Noise Estimators with Applications to Deconvolution and Filtering Problems. Automatica. 1996, 32(2): 199-216.
[74] Kim H, Jalali A. A, Sims C S et al. Prediction, filtering, smoothing and white noise in a discrete H_∞ setting: a game theory approach. Int. J. Contr.. 1998, 70(6): 841-857.
[75] Zhang H S, Xie L H. Son Y C. H_∞ Deconvolution Filtering, Prediction, and Smoothing: A Krein Space Poloynominal Approach. IEEE Trans. Automat. Contr.. 2000, 48(3): 888-892.
[76] Rho H, Hsu C S. A Game Theory Approach to H_∞ Deconvolution Filter Design. Proc. American Control Conf., America, 1999: 2891-2895.
[77] Xie L H, Wang S, Du C L eta al. H_∞ deconvolution of periodic channels. IEEE Trans. Sig. Proc.. 2000. 80: 2365-2378.
[78]Grimble M J.H_∞ inferential filtering,prediction and smoothing problems.IEEE Trans.Signal Processing.1997,60:289-304.
[79]Grimble M J.H_∞ optimal multichannel linear deconvohltion filters,predictors and smoothers.Int.J.Contr..1996,63(3):519-533.
[80]Grimble M J.Robust filter design for uncertain systems defined by both hard and soft bounds.IEEE Trans.Signal Processing.1996,44(5):1063-1071.
[81]Wang S,Xie L H,Zhang C S.Mixed H_2/H_∞ deconvolution of uncertain periodic FIR chan-nels.IEEE Trans.Signal Processing.2001,81:2089-2103.
[82]Moir T J,Vishwanath T G,Campbell D R.Real-time self:tuning deconvolution filter and smoother.Int.J.Contr..1987,45:969-985.
[83]Shaked U,Theodor Y.A frequency domain approach to the problems of H_∞-minimum error state estimation and white noise.IEEE Trans.Signal Processing.1992,40(12):3001-3011.
[84]Kalman R E,Buoy R S.New Results in Linear Filtering and Prediction Theory Transactions of the ASME-J.Basic Engineering.1961,83:95-107.
[85]Kucera V.Discrete Linear Control,the Polynomial Approach.Chichester:Wiley,1979.
[86]Grimble M J.Polynomial Approach to Optimal Linear Filtering and Prediction.Int.,J.Contr..1985,41(6):1545-1564.
[87]Zhang H S,Liu X J,Chai T Y.A new method tbr optimal deconvolution.IEEE Trans.Signal Processing.1997,45(10):2596-2599.
[88]邓自立.现代时间序列分析——建模、滤波、去卷、预报和控制.北京:知识出版社,1989.
[89]邓自立.自校正滤波理论及其应用——现代时间序列分析方法.哈尔滨:哈尔滨工业大学出版社,2003.
[90]邓自立,许燕.基于Kalman滤波的白噪声理论.自动化学报.2003,29(1):23-31.
[91]邓自立,许燕.基于Kalman滤波的通用的和统一的白噪声估计方法.控制理论与应用.2004.21(4):501-506.
[92]Zavarei M M,Jamshidi M.Time Delay Systems:Analysis,Optimization and Applications.Amsterdan,The Netherlands:North-Holland,1987.
[93]Goodwin G C,Sin K S.Adaptive filtering,prediction and control.In.:Prentice-Hall,1984.
[94]Meditch J S.Stochastic Optimal Linear Estimation and Control.New York:McGraw-Hill,1969.
[95]Bolzern P,Colaneri P,Nicolao G D.On Discrete-Time H_∞ Fixed-Lag Smoothing.IEEE Trans.Signal Processing.2004,52(1):132-141.
[96]Chisel L,Mosca E.Polynomial equations for the linear MMSE state estimation.IEEE Trans.Automat.Contr..1992,AC-37(5):623-626.
[97]Kucera V.New results in state estimation and regulation.Automatica.1981,17(9):745-748.
[98]Pridman E,Shaked U.New Bounded Real Lelnma Representations for Time-Delay Systems and Their Applications.IEEE Trans.Automat.Contr..2001,46(12):1973-1979.
[99]胡剑波,苏宏业,褚健.不确定时滞系统的二次稳定无记忆变结构控制.系统工程理论与实践.2001,15(5):13-23.
[100]姜偕富,费树岷,冯纯伯.线性时滞系统依赖于时滞的H_∞控制.自动化学报.2001,27(1):108-114.
[101]关新平,张群亮.不确定离散时滞系统的鲁棒H_∞滤波与仿真.系统仿真学报.2002,14(8):1078-1080.
[102]张群亮,关新平.不确定关联时时滞系统的鲁棒H_∞滤波.控制理论与应用.2004,21(2):267-270.
[103]郭雷,冯纯伯.一类不确定系统的鲁棒H_∞控制器设计.中国科学E辑.1998,28(1):56-62.
[104]郭雷,忻欣,冯纯伯.基于LMI的一类混合H_2/H_∞控制器问题的降阶控制器设计——离散情形.自动化学报.1998,24(3):355-358.
[105]徐胜远,陈雪如,杨成梧.一类离散广义系统的H_∞控制.控制理论与应用.2000,17(5):739-741
[106]Kaszkurewicz E,Bhaya A.Discrete-time state estimation with two counters and measure-ment delay.Proc.35th IEEE Conf.Decision and Control,Kobe,Japan,1996:1472-1476.
[107]Chenavier F,Crowley J L.Position estimation for a mobile robot using vision and odometry.Proc.1992 IEEE Int.Conf.Robotics and Automation,Nice,Prance,1992:2588-2593.
[108]Hsiao F H,Pan S T.Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems.J.of Dynam.Syst.,Measur.,and Contr..1996,118(4):803-808.
[109]Andersen G L,Christensen A C,Ravn O.Augmented models for improving vision control of a mobile robot.Proc.3rd IEEE Conf.Control Applications,Glasgow,UK,1994:53-58.
[110]Murata S,Hirose T.Onboard locating system using real-time image processing for a self-navigating vehicle.IEEE Trans.Industrial Electronics.1993,40(11):145-154.
[111]Larsen T D,Andersen N A,Ravn O et al.Incorporation of Time Delayed Measurements in a Discrete-time Kalman Filter.Proc.37th IEEE Conf.Decision and Control,Tainpa,Florida America,1998:3972-3977.
[112]Klein L A.Sensor and Data Fusion Concepts and Applications.SPIE Press,1999.
[113]邓自立,刘玉梅.一种统一的Kalman估值器.信息与控制.1999,28(4):249-254.
[114]Zames G.Feedback and optimal sensitivity:Model reference transforinations,multiplicative seminorms,and approximate inverses.IEEE Trans.Automat.Contr..1981,26:301-320.
[115]Li H,Fu M.A linear matrix in equality approach to robust H_∞ filtering.IEEE Trans.Signal Processing.1997,45:2338-2350.
[116]Grimble M J.Minmax design of optimal linear filters.MTNS Conf.,Phoenix,Arizona,1987.
[117]Grimble M J.H_∞ design of optimal linear filters.MTNS Conf.,Phoenix,Arizona,1987:533-540.
[118]Theodor Y,Shaked U.Robust discrete-time minimum-variance filtering.IEEE Trans.Au-tomat.Contr..1994,39(9):1944-1948.
[119]Colaneri P,Maroni M,Shaked U.H_∞ prediction and smoothing for discerte-time systems:A J-sepctral factorization approach.Proc.37th IEEE Conf.Decision and Control,Tampa,Florida,1998:2836-2842.
[120]Colaneri P,Ferrante A.A J-spectral factorization approach for H_∞ estimation problem in discrete time.IEEE Trans.Automat..Contr..2002,47(12):2108-2113.
[121]Mirkin L.Continuous-time fixed-lag smoothing in an H_∞ setting.Proc.40th IEEE Conf.Decision and Control,Orlando,FL,2001:3512-3517.
[122]Yaesh I,Shaked U.Game Theory Approach to Optimal Linear State Estimation and Its Relation to the Minimum H_∞-norm Estimation.IEEE Trans.Automat.Contr..1992,37(6):828-831.
[123]Grimble M J.H_∞ fixed-lag smoothing filter for scalar systems.IEEE Trans.Signal Process-ing.1991,39(9):1955-1963.
[124]Barbosa K.A,de Souza C E,Trofino A.Robust filtering for uncertain linear systems with state-dependent noise.Proc.42th IEEE Conf.Decision and Control,Maul,Hawaii USA,2003:880-885.
[125]范训礼,谢振华,张勇.离散系统LMI滤波技术.飞行力学.1999:17(4),55-60.
[126]Zhang H S,Zhang D,Xie L H.H_∞ Fixed-lag smoothing and prediction for linear continuous-time systems.Proc.American Control Conf.,Denver,2003:4201-4206.
[127]Blondel V D.Open Problem in Mathematics Systems and Control Theory.London,UK:Spinger-Verlag,1999.
[128]Tadmor G,Mirkin L.H_∞ control and estimation with preview-part Ⅰ:Matrix ARE solutions in continuous time.IEEE Trans.Automat.Contr..2005,50(1):19-28.
[129]Tadmor G,Mirkin L.H_∞ control and estimation with preview -part Ⅱ:Matrix ARE solu-tions in discrete time.IEEE Trans.Automat.Contr..200,5,50(1):29-40.
[130]Deng Z L.Self-tuning white noise estimators with application to seismic data deconvolution.Acta Automatica Sinica.1986,12:155-161.
[131]Dabis H S,Moir T J.A unitied approach to optimal estimation using diophantine equations.Int.J.Contr..1993,57:577-598.
[132]Zhang H S,Xie L H,Soh Y C.Optimal and self-tuning deconvolution in time domain.IEEE Trans.Signal Process.1999,47(8):2253-2261.
[133]Van Trees H L.Detection,Estimation and Modulation Theory,Part Ⅰ.New York:John Wiley,1968.
[134]邱天爽,李婷,毕英伟等.随机过程——滤波、估计与检测.北京:电子工业出版社,2005。
[135]徐宁寿.随机信号估计与系统控制,北京:北京工业大学出版社,2001。
[136]Kalman R E and Bucy R C.New results in linear filtering and prediction theory.Trans.ASME,J.Basic Eng.1961,83:95-107.
[137]鲍齐克S M著,凌云旦译.数字滤波和卡尔曼滤波,科学出版社,1984.
[138]史忠科.最优估计的计算方法.科学出版社.2001.
[139]付梦印,邓志红,张继伟.Kalman滤波理论及其在导航系统中的应用.科学出版社.2003.
[140]Mirkin L.On the H_∞ fixed-lag smoothing:How to exploit the information preview.Auto-matica.2003,39(8):1495-1504.
[141]Bolzern P,Colaneri P,Nicolao G D.H_∞ smoothing in discrete-time:a direct approach.Proc.41th IEEE Conf.Decision and Control,Las Vegas,2002:4233-4238.
[142]Tadmor G.The standard H_∞ problem in systems with a single input delay.IEEE Trans.Automat.Contr..2002,45(3):382-397.
[143]Uchida K,Ikeda K,Azuma T et al.Finite-dimensional characterizations of H_∞ control for linear systems with delays in input and output.Int.J.Robust and Nonlinear Control.2003,special issue.
[144]Duan G,Wang H.Multi-model switching control and its application to BTT missile design.Acta Aeronautica Et Astronautica Sinica2005,26(2):144-147.
[145]Hanshaw T C,Anderson M J,Hsu C S.An Hoo deconvolution filter and its application to ultrasonic nondestructive evaluation of materials.ISA Trans..1999,38(4):2891-2895.
[146]Petersen I R,McFarlane D C.Optimal guaranteed cost filtering for uncertain discrete-time linear systems.Int.J.Robust Nonlinear Control.1996,6:267-280.
[147]Geromel J C.Optimal Linear Filtering under Parameter Uncertainty.IEEE Trans.Signal Processing.1999,47:168-175.
[148]Geromel J C,Bernussou J,Garcia Get al.H_2 and H_∞ robust filtering for discrete-time linear systems.SIAM J.Contr.Optim..2000,38(5):1353-1368.
[149]Xie L H,Sob Y C,de Souza C E.Robust Kalman filtering for uncertain discrete-time systems.IEEE Trans.Automat.Contr..1994,39(6):1310-1321.
[150]Fu M,de Souza C E,Luo Z.Finite-Horizon Robust Kalman Filter Design.IEEE Trans.Signal Processing.2001,49(9):2103-2112.
[151]Mahmoud M,Al-Muthairi N,Bingulac S.Robust Kalman filtering for continuous time-lag systems.Syst.Contr.Lett..1999,38(5):309-319.
[152]Shaked U,Xie L H,Soh Y.C.New approaches to robust minimum variance filter design.IEEE Trans.Signal Processing.2001,49:2620-2629.
[153]Zhang W H,Chen B S,Tseng C S.Robust H_∞ Filtering for Nonlinear Stochastic Systems.IEEE Trans.Signal Processing.2005,53(2):589-598.
[154]Zhu X,Soh Y C,Xie L H.Design and analysis of discrete-time robust Kalman filters.Automatica.2002,38(6):1069-1077.
[155]张维海.随机不确定系统的鲁棒H_∞滤波.控制理论与应用.2003,20(5):741-745.
[156]Petersen I R,McFarlane D C.Optimal guaranteed cost control and filtering for uncertain linear systems.IEEE Trans.Automat.Contr..1994,39:1971-1977.
[157]Bolzern P,Colaneri P,de Nicolao G.Finite escape and convergence properties of guaranteed-cost robust filters.Automatica.1997,33(1):31-47.
[158]Shaked U,de Souza C E.Robust Minimum Variance Filtering.IEEE Trans.Signal Process-ing.2002,43(11):2474-2483.
[159]Carlson N A.Federated square root filter for decentralized parallel process.IEEE Trans.Aerospace and Electronic Systems.1990,26(2):517-525.
[160]Sasiadek J Z.Sensor Fusion.Annual Review In Control.2002,26(2):203-228.
[161]Herrera F,and Herrera-Viedma E.Aggregation operators for linguistic weighted informa-tion.IEEE Trans.Syst.,Man,and Cybernetic-Part A:Syst.and Humans.1997,27(5):646-656.
[162]Sun S L.Multi-sensor weighted fusion suboptimal filtering for systems with multiple time delayed measurements.Proc.6th World Congress on Intelligent Control and Automation.Jun.21-23,2006,Dalian China,pp.1617-1620.
[163]Sun S L,and Cui P.Multi-sensor optimal information fusion steady-state Kalman filter weighted by scalars.Control and Decision.2004,19(2):208-211.
[164]Sun S L.Multi-sensor information fusion white noise weighted by scalars based on Kalman predictor.Automatica.2004,40(8):1447-1453.
[165]韩崇昭,朱洪艳.多传感器信息融合与自动化.自动化学报.2002,28(suppl):117-124.
[166]Wang H X,Su X C,Lu X,Cao M Y.An Improved Algorithm of the Hand-Eye Vision Positioning System Based on the Constant Rotation Matrix,Proc.6th World Congress on Intelligent Control and Automation,Dalian,China,June 21-23,2006:9222-9226.
[167]Nejatali A,and Ciric I R.Novel image fusion methodology using fuzzy set theory.Optical Engineering.1998,37(2):485-491.
[168]Guo H.Researches and advances in multi-sensor information fusion technology.Science Foundation in China.2005,19(1):17-21.
[169]Deng Z L,and Wu X.Fast algorithms for multisensor centralized measurement fusion Kalman filter.Science Technology and Engineer.2005,5(20):1469-1472.
[170]He Y,Wang G,Lu D,and Peng Y.Multisensor information fusion with applications.Beijing:Publishing House of Electronics Industry,2000.
[171]Hashmipour H R,Roy S and Laub A J.Decentralized structures for parallel Kalman filtering.IEEE Trans.Automat.Contr..1988,33(1):88-93.
[172]Sun S L.Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother.Automatica.2005,41(10):2153-2159.
[173]Sun S L and Deng Z L.Multi-sensor optimal information fusion Kalman filter.Automatica.2004,40(6):1017-1023.