多传感器异步采样信息融合估计
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摘要
随着多传感器数据融合技术在军事和民用等领域中的广泛应用，国内外学者对它的研究也在迅速升温然而目前研究较多的是同步数据融合问题，即假设各传感器同步对目标进行测量，并且同步传送数据到融合中心而在实际中经常遇到的却是异步融合问题，如所用的各种传感器具有不同的采样速率，固有延迟和通信延迟，都会产生异步多传感器数据融合问题因此研究多传感器异步采样信息融合技术具有更重要的理论意义和应用价值本文主要对多传感器异步采样信息融合估计的算法进行了研究，包括具有整数倍采样率的多传感器系统的信息融合滤波器的设计，具有有理数倍采样率的多传感器系统的信息融合滤波器的设计，以及具有四种速率的多速率多传感器系统的信息融合滤波器的设计
对具有整数倍采样率的线性离散随机系统，基于已知建立在最细尺度上的状态方程，通过对状态方程和观测方程进行分块，将模型转化为建立在各个尺度上的状态空间模型对于新的具有单采样率的多传感器系统，推导出了任意两个传感器子系统之间的状态滤波误差互协方差阵的计算公式最后基于线性最小方差最优加权融合算法给出了状态融合滤波器
对具有有理数倍采样率的线性离散随机系统，通过模型变换将原来的异步采样系统转化为了具有单采样率的多传感器系统，从而得到局部Kalman滤波器针对多传感器系统，推导了任意两个传感器子系统之间的估计误差互协方差阵最后基于线性最小方差最优加权融合算法给出了状态融合滤波器
对具有多速率的线性离散随机系统，其中涉及到四种速率：状态更新率，观测采样率，估计更新率和估计输出率假定系统模型中的状态更新率与观测采样率各不相同对于单传感器，估计更新率与观测采样率相同，估计输出率为任意的正整数首先通过模型变换将原多速率系统转化为单速率线性离散随机系统，随后给出了局部单传感器的滤波器最后依据分布式加权融合算法，给出了两种加权融合状态滤波器
With the multi-sensor data fusion technology widely used in military and civil-ian fields, it has been received intensive attention by international and domesticresearchers. However, the problem of synchronization data fusion has been gainedmore investigation, which requires that all sensors to measure a target synchronouslyand all measurements data are communicated to the fusion center synchronously.But in practice, we often encountered with the problem of the multi-rate asyn-chronous data fusion. For example, the sensors may have di?erent sampling peri-ods, di?erent inherent delays and di?erent communication delays, which will leadto asynchronous data fusion. So it is more important in theoretical meaning andapplying values to study the multi-rate asynchronous information fusion estimationproblems. In this paper, we study the information fusion estimation algorithms forthe multi-sensor asynchronous sampling systems, including the systems with inte-ger times sampling rates, with rational times sampling rates and with four multiplesampling rates.
For the linear discrete-time stochastic system with integer times sampling rates,based on known state equation modeled in the finest scale, the original system istransformed into a new multi-sensor system based on every scale by augmentationand partition of the state and measurement equations. For the new stochasticsystems with single integer times sampling rate, the cross-covariance matrices offiltering errors between arbitrary two sensors are derived. At last, the multi-sensoroptimal information fusion state filters are presented based on the optimal fusionestimation algorithm in the linear minimum variance sense.
For the linear discrete-time stochastic system with rational times samplingrates, it is formalized into a synchronous sampling system with single samplingrate by the model transformation. Then the local Kalman filter of each sensors isobtained. Meanwhile, the cross-covariance matrices of estimation errors betweenarbitrary sensors are derived. At last, the multi-sensor optimal information fusionstate filters are presented based on the optimal fusion estimation algorithm in thelinear minimum variance sense.
For a multi-rate linear discrete stochastic system, there exist four rates: the state updating rate,the measurement sampling rates, the estimate updating ratesand the estimate output rate. Suppose that the state updating rate is di?erent fromthe measurement sampling rates. For the single sensor the estimate updating ratesare equal to the measurement sampling rates, the estimate output rate is an arbi-trary positive integer. First, through model transform, the multi-rate asynchronoussampling system is formalized into a synchronous sampling system. Then the statefilters of local sensors are given. At last, the multi-sensor optimal information fusionstate filters are presented based on the optimal fusion estimation algorithm in thelinear minimum variance sense.
对具有整数倍采样率的线性离散随机系统，基于已知建立在最细尺度上的状态方程，通过对状态方程和观测方程进行分块，将模型转化为建立在各个尺度上的状态空间模型对于新的具有单采样率的多传感器系统，推导出了任意两个传感器子系统之间的状态滤波误差互协方差阵的计算公式最后基于线性最小方差最优加权融合算法给出了状态融合滤波器
对具有有理数倍采样率的线性离散随机系统，通过模型变换将原来的异步采样系统转化为了具有单采样率的多传感器系统，从而得到局部Kalman滤波器针对多传感器系统，推导了任意两个传感器子系统之间的估计误差互协方差阵最后基于线性最小方差最优加权融合算法给出了状态融合滤波器
对具有多速率的线性离散随机系统，其中涉及到四种速率：状态更新率，观测采样率，估计更新率和估计输出率假定系统模型中的状态更新率与观测采样率各不相同对于单传感器，估计更新率与观测采样率相同，估计输出率为任意的正整数首先通过模型变换将原多速率系统转化为单速率线性离散随机系统，随后给出了局部单传感器的滤波器最后依据分布式加权融合算法，给出了两种加权融合状态滤波器
With the multi-sensor data fusion technology widely used in military and civil-ian fields, it has been received intensive attention by international and domesticresearchers. However, the problem of synchronization data fusion has been gainedmore investigation, which requires that all sensors to measure a target synchronouslyand all measurements data are communicated to the fusion center synchronously.But in practice, we often encountered with the problem of the multi-rate asyn-chronous data fusion. For example, the sensors may have di?erent sampling peri-ods, di?erent inherent delays and di?erent communication delays, which will leadto asynchronous data fusion. So it is more important in theoretical meaning andapplying values to study the multi-rate asynchronous information fusion estimationproblems. In this paper, we study the information fusion estimation algorithms forthe multi-sensor asynchronous sampling systems, including the systems with inte-ger times sampling rates, with rational times sampling rates and with four multiplesampling rates.
For the linear discrete-time stochastic system with integer times sampling rates,based on known state equation modeled in the finest scale, the original system istransformed into a new multi-sensor system based on every scale by augmentationand partition of the state and measurement equations. For the new stochasticsystems with single integer times sampling rate, the cross-covariance matrices offiltering errors between arbitrary two sensors are derived. At last, the multi-sensoroptimal information fusion state filters are presented based on the optimal fusionestimation algorithm in the linear minimum variance sense.
For the linear discrete-time stochastic system with rational times samplingrates, it is formalized into a synchronous sampling system with single samplingrate by the model transformation. Then the local Kalman filter of each sensors isobtained. Meanwhile, the cross-covariance matrices of estimation errors betweenarbitrary sensors are derived. At last, the multi-sensor optimal information fusionstate filters are presented based on the optimal fusion estimation algorithm in thelinear minimum variance sense.
For a multi-rate linear discrete stochastic system, there exist four rates: the state updating rate,the measurement sampling rates, the estimate updating ratesand the estimate output rate. Suppose that the state updating rate is di?erent fromthe measurement sampling rates. For the single sensor the estimate updating ratesare equal to the measurement sampling rates, the estimate output rate is an arbi-trary positive integer. First, through model transform, the multi-rate asynchronoussampling system is formalized into a synchronous sampling system. Then the statefilters of local sensors are given. At last, the multi-sensor optimal information fusionstate filters are presented based on the optimal fusion estimation algorithm in thelinear minimum variance sense.
引文
[1]何友，王国宏，陆大混，彭应宁多传感器信息融合及应用[M]北京：电子工业出版社，2000
[2]文成林，周东华多尺度估计理论及应用[M]北京：清华大学出皈社，2002
[3]W Edward，L JaEles Multisensor data fusion[M]Boston：Artech House，1990
[4]王洁，韩崇昭，李晓榕异步多传感器数据融合[J]控制与决策，2001，16(6)：877—881
[5]郭徽东，章新华多传感器异步数据融合模型分析[J]火力与指挥控制，2003，28(3)：9-11
[6]孙书利，吕楠，白锦花多传感器时滞系统信息融合最优Kalman滤波器[J].控制理论与应用2008，25(3)：501—505
[7]孙书利多模型多传感器信息融合Kalman y-滑器[J]_控制理论与应用2005，22(2)：211—217
[8]E L Waltz，D M Buede Data Fusion and Decision Support fOr Command and Control[J]IEEE Transactions on Systems，Man and Cybernetics，1986，16(16)：865—879
[9]T Kerr Decentralized Filtering and Redundancy Management fOr Multisensor Navigation[J].IEEE Transactions on Aerospace and Electronic Systems，1987，23(1)：83—119
[10]E A Carlson，M P Berarducci Federated Kalman filter Simulation Re—sults[J]Navigation，1994，41(3)：297—321
[11]R Da，C F Lin A New Failure Detection Approach and Its Application to CPS Autonomous Integrity monitoring[J]IEEE Transactions on Aerospace and Electronic Systems，1995，31(1)：499—506
[12]C J Harris Application of Artificial Intelligence to Command and Control Systems[M]Peter Pergrinus LTD，London，1988
[13]N Nabaa，R H Bishop Solution to a multisensor Tracking Problem with Sensor Registration Errors[J]IEEE Transactions on Aerospace and Electronic Systems，1999，35(1)：354—363
[14]R P Simgh，W H Baily Fuzzy Logic Application to Multisensor—Multitarget Correlation[J]_IEEE Transactions on Aerospace and Electronic Systems，1997，33(3)：752—769
[15]D L Hall，J Llinas An Introduction to Multisensor Data Fusion[J]Proceed—ings of the IEEE，1997，85f1)：6-23
[16]Mahler，P S Ronald Statistical Multisource—multitarget In％rmation Fu—sion[M]Artech House，2007
[17]S Sitharama Iyengar，Richard R Brooks Distributed Sensor Networks[M] Chapman and HalI／ORO，2004
[18]S S Blackman Multiple—target Tracking with Radar Application[M]Artech House，INC，1986
[19]J Linas，E Waltz Multisensor Data Fusion[M]Artech House，Norwood，Mas—sachusetts，1990
[20]D L Hall Mathematical Techniques in Multisensor Data Pusion[M]Artec House，Boston，London，l 992
[21]P K Varshney Distributed Detection and Data Fusion[M]New York：Springer—Verlag，1996
[22]A Farina，F A Studer Radar Data Processing[M]Vol I II Research Studies Press LTD，1985
[23]C J Harris Application of Artificial Intelligence to Command and Control Systems[M]Peter Pergrinus LTD，London，1988
[24]A bidi，C onzalez ata Fusion in Robotics and Machine Intelligence[M]Aca- demic Press，INC，1992
[25]彭冬亮，文成林，薛安克多传感器多源信息融合理论及应用[Ml_北京：科学技术出版社，2010
[26]张明路，戈新良，唐志强等多传感器信息融合技术研究现状和发展趋势[J].河北工业大学学报，2003，32(2)：30—35
[27]何衍机动目标跟踪与传感器网络自组织[Dl_杭州：浙江大学，2001
[28]丁锋，姜秋喜，张楠多传感器数据融合发展评述及展望[J].舰船电子对抗，2007，30(3)：52—55
[29]郭雁文，兰艳亭传感器信息融合的结构及其算法[J].太原师范学院学报，2008，7(1)：67—69
[30]何友，王国宏，陆大混多传感器数据融合模型综述[J].清华大学学报，1996，36(9)：14—20
[31]康耀红数据融合理论与应用[Ml_西安：西安电子科技大学出版社，1997
[32]何友，陆大混，彭应宁多传感器数据融合算法综述[J].火力与指挥控制，1996，21(1)：12—21
[33]陈文辉，马铁华多传感器信息融合技术的研究与发展[J].科技情报开发与经济，2006，16(19)：212—213
[34]黄漫国，樊尚春，郑德智，邢维巍多传感器数据融合技术研究进展[J].传感器与微系统，2010，29(3)：5-12
[35]C Y Shen，K T Yu A generalized fuzzy approach for strategic problems：The empiricM study on facility location selection of author’s management consul—tation client as an example[J]Expert Systems with Applications，2009，36(3)：4709—4716
[36]白云飞，曲尔光多传感器信息融合技术及其应用[J].机械管理开发，2008，23(1)：69—70
[37]姜静，姜琳，李华德，等基于遗传算法的模糊神经控制器[J].煤矿机械，2007，28(3)：129—131
[38]A D Tafti，N Sadati Novel adaptive KMman filtering and fuzzy track fusion approach for real time applications[C]Proceedings of the 3rd IEEE Conference on Industrial Electronics and Application．Singapore．2008：120一125
[39]刘素一，张海霞，罗维于基于小波变换和Kalman滤波的多传感器数据融合[J].微计算机信息，2006，22(6一1)：179—181
[40]刘建书，李人厚，常宏基于相关性函数和最小二乘的多传感器数据融合[J].控制与决策，2006，21(6)：714—716
[41]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，2000，6(20)：183—184
[42]S L Sun Multi—sensor Optimal In％rmation Fusion Kalman Filter with Ap—plication[1].Aerospace Science and Technology，2004，8(1)：57—62
[43]孙书利，邓自立多传感器线性最小方差最优信息融合估计准则[J].科学技术与工程，2004，4(5)：334—336
[44]S L Sun．Z L Deng Multi—sensor Optimal In％rmation Fusion Kalman Fil—ter[J].Automatica，2004，40(6)：1017—1023
[45]S L Sun Multi—sensor In％rmation Fusion White Noise Filter Weighted by Scalars based on Kalman Predictor[J]Automatica，2004，40(8)：1447—1453
[46]孙书利，崔平远多传感器标量加权最优信息融合稳态Kalman滤波器[J].控制与决策，2004，19(2)：208—211
[47]S L Sun．Z L Deng Multi—sensor optimal In％rmation Fusion Steady—state Kalman Filter Weighted by Scalars fOr Systems with Colored Measurement Noises[J].Control Theory and Applications，2004，21(4)：365—368
[48]S L Sun Multisensor Optimal In％rmation Fusion Input White Noise Decon—volution Estimators[1].IEEE Transactions on Systems，Man，and Cybernetics，2004，34(4)：1886—1893
[49]孙书利，史雪岩，崔下远多传感器最优信息融合估计Kalman多步预报器及其应用[J].宇航学报，2004，25(20)：241—246
[50]孙书利，崔下远两传感器最优信息融合Kalman滤波器及其在跟踪系统中的应用[J].宇航学报，2003，24(2)：206—209
[51]K H Kim Development of Track to Track Fusion Algorithm[C]Proceeding of the American Control Conference，Maryland，1994：1037—1041
[52] K. C. Chou, A. S. Willsky, A. Benveniste, M. Basseville. Recursive and iterative estimation algorithms for multiresolution stochastic processes [C]. Proceedings of the 28th IEEE Conference on Decision and Control, Fampa, Florida, 1989, 2: 1184-1189.
[53] A. Benveniste, R. Nikoukhah, A. S. Willsky. Multiscale system theory[C]. Proceeding of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, 1990,4: 2484-2487.
[54] M. Basseville, A. Benveniste, K. C. Chou, S. A. Golden, R. Nikoukhah, A. S. Willsky. Modeling and estimation of multiresolution stochastic processes[J]. IEEE Transactions on Information Theory, 1992, 38(2): 766-784.
[55] M. Basseville, A. Benveniste, A. S. Willsky. Multiscale autoregressive process, Parts I: Schur-Levinson Parametrization[J]. IEEE Transactions on Signal Processing, 1992,40(8): 1915-1934.
[56] M. Basseville, A. Benveniste, A. S. Willsky. Multiscale autoregressive process, Parts II: Lattice Structures for Whitening and Modeling[J]. IEEE Transactions on Signal Processing, 1992, 40(8): 1935-1953.
[57] A. Benveniste, R. Nikoukhah, A. S. Willsky. Multiscale system theory [J]. IEEE Trans.on Circuits and Syatems-I: Fundamental Theory and Applications, 1994, 41(1): 2-15.
[58] L. Hong. Multiresolutional filtering using wavelet transform[J]. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(4): 1244-1251.
[59] L. Hong. Multi-resolutional distributed filtering[J]. IEEE Transactions Automatic Control, 1994, 39(4): 853-856.
[60] R. Cristi, M. Tummala. Multirate, multiresolution, recursive Kalman filter [J]. Signal Processing, 2000, 80(9): 1945-1958.
[61]文成林多尺度多速率递归Kalman滤波2001，31(4)：15—18
[62] A. Fabrizio, A. Luciano. Filterbanks design for multisensor data fusion[J]. IEEE Signal Processing Letters, 2000, 7(5): 100-103.
[63] D. Andrisani, C. F. Gau. Estimation Using a Multirate Filter [J]. IEEE Transactions on Automatic Control, 1987, 32(7): 653-656.
[64] D. J. Lee, M. Tomizuka. Multirate optimal state estimation with sensor fu-sion[C]. Proceedings of the American Control Conference, Denver, Colorado, 2003: 2887-2892.
[65] B. S. Chen, C. W. Lin, Y. L. Chen. Optimal signal reconstruction in noisy filter bank systems: multirate Kalman synthesis filtering approach[J]. IEEE Transactions on signal Processing, 1995, 43(11): 2496-2504.
[66] K. C. Chou, A. S. Willsky, A. Benveniste, M. Basseville. Recursive and iterative estimation algorithms for multiresolution stochastic processes [C]. Proceedings of the 28th IEEE Conference on Decision and Control, Fampa, Florida, 1989, 2: 1184-1189.
[67] K. C. Chou, A. S. Willsky, A. Benveniste. Multiscale recursive estimation , data fusion, and regularization[J]. IEEE Transactions on Automatic Control, 1994, 39(3): 464-478.
[68] K. Lo, H. Kimura. Recursive estimation methods for discrete systems[J]. IEEE Transactions on Automatic Control, 2003, 48(11): 2019-2024.
[69]孙红岩基于小波变换的多分辨率多传感器数据融合方法的研究[Dl_清华大学博士后出站报告，1998
[70] L. P. Yan, B. S. Liu, D. H. Zhou. The modeling and estimation of asynchronous multirate multisensor dynamic systems [J]. Aerospace Science and Technology, 2006, 10(1): 63-71.
[71] B. D. O. Anderson, J. B. Moore. Optimal Filtering[M]. Englewood Cliffs, NJ: Prentice-Hall, 1979.
[72]闫丽萍，刘宝生，周东华，文成林一类多速率多传感器系统的状态融合估计算法[J].电子与信息学报，2007，29(2)：443—446
[73] Y. Liang, T. W. Chen, Q. Pan. Multi-rate optimal state estimation[J]. International Journal of Control. 2009, 82(11): 2059-2076.
[2]文成林，周东华多尺度估计理论及应用[M]北京：清华大学出皈社，2002
[3]W Edward，L JaEles Multisensor data fusion[M]Boston：Artech House，1990
[4]王洁，韩崇昭，李晓榕异步多传感器数据融合[J]控制与决策，2001，16(6)：877—881
[5]郭徽东，章新华多传感器异步数据融合模型分析[J]火力与指挥控制，2003，28(3)：9-11
[6]孙书利，吕楠，白锦花多传感器时滞系统信息融合最优Kalman滤波器[J].控制理论与应用2008，25(3)：501—505
[7]孙书利多模型多传感器信息融合Kalman y-滑器[J]_控制理论与应用2005，22(2)：211—217
[8]E L Waltz，D M Buede Data Fusion and Decision Support fOr Command and Control[J]IEEE Transactions on Systems，Man and Cybernetics，1986，16(16)：865—879
[9]T Kerr Decentralized Filtering and Redundancy Management fOr Multisensor Navigation[J].IEEE Transactions on Aerospace and Electronic Systems，1987，23(1)：83—119
[10]E A Carlson，M P Berarducci Federated Kalman filter Simulation Re—sults[J]Navigation，1994，41(3)：297—321
[11]R Da，C F Lin A New Failure Detection Approach and Its Application to CPS Autonomous Integrity monitoring[J]IEEE Transactions on Aerospace and Electronic Systems，1995，31(1)：499—506
[12]C J Harris Application of Artificial Intelligence to Command and Control Systems[M]Peter Pergrinus LTD，London，1988
[13]N Nabaa，R H Bishop Solution to a multisensor Tracking Problem with Sensor Registration Errors[J]IEEE Transactions on Aerospace and Electronic Systems，1999，35(1)：354—363
[14]R P Simgh，W H Baily Fuzzy Logic Application to Multisensor—Multitarget Correlation[J]_IEEE Transactions on Aerospace and Electronic Systems，1997，33(3)：752—769
[15]D L Hall，J Llinas An Introduction to Multisensor Data Fusion[J]Proceed—ings of the IEEE，1997，85f1)：6-23
[16]Mahler，P S Ronald Statistical Multisource—multitarget In％rmation Fu—sion[M]Artech House，2007
[17]S Sitharama Iyengar，Richard R Brooks Distributed Sensor Networks[M] Chapman and HalI／ORO，2004
[18]S S Blackman Multiple—target Tracking with Radar Application[M]Artech House，INC，1986
[19]J Linas，E Waltz Multisensor Data Fusion[M]Artech House，Norwood，Mas—sachusetts，1990
[20]D L Hall Mathematical Techniques in Multisensor Data Pusion[M]Artec House，Boston，London，l 992
[21]P K Varshney Distributed Detection and Data Fusion[M]New York：Springer—Verlag，1996
[22]A Farina，F A Studer Radar Data Processing[M]Vol I II Research Studies Press LTD，1985
[23]C J Harris Application of Artificial Intelligence to Command and Control Systems[M]Peter Pergrinus LTD，London，1988
[24]A bidi，C onzalez ata Fusion in Robotics and Machine Intelligence[M]Aca- demic Press，INC，1992
[25]彭冬亮，文成林，薛安克多传感器多源信息融合理论及应用[Ml_北京：科学技术出版社，2010
[26]张明路，戈新良，唐志强等多传感器信息融合技术研究现状和发展趋势[J].河北工业大学学报，2003，32(2)：30—35
[27]何衍机动目标跟踪与传感器网络自组织[Dl_杭州：浙江大学，2001
[28]丁锋，姜秋喜，张楠多传感器数据融合发展评述及展望[J].舰船电子对抗，2007，30(3)：52—55
[29]郭雁文，兰艳亭传感器信息融合的结构及其算法[J].太原师范学院学报，2008，7(1)：67—69
[30]何友，王国宏，陆大混多传感器数据融合模型综述[J].清华大学学报，1996，36(9)：14—20
[31]康耀红数据融合理论与应用[Ml_西安：西安电子科技大学出版社，1997
[32]何友，陆大混，彭应宁多传感器数据融合算法综述[J].火力与指挥控制，1996，21(1)：12—21
[33]陈文辉，马铁华多传感器信息融合技术的研究与发展[J].科技情报开发与经济，2006，16(19)：212—213
[34]黄漫国，樊尚春，郑德智，邢维巍多传感器数据融合技术研究进展[J].传感器与微系统，2010，29(3)：5-12
[35]C Y Shen，K T Yu A generalized fuzzy approach for strategic problems：The empiricM study on facility location selection of author’s management consul—tation client as an example[J]Expert Systems with Applications，2009，36(3)：4709—4716
[36]白云飞，曲尔光多传感器信息融合技术及其应用[J].机械管理开发，2008，23(1)：69—70
[37]姜静，姜琳，李华德，等基于遗传算法的模糊神经控制器[J].煤矿机械，2007，28(3)：129—131
[38]A D Tafti，N Sadati Novel adaptive KMman filtering and fuzzy track fusion approach for real time applications[C]Proceedings of the 3rd IEEE Conference on Industrial Electronics and Application．Singapore．2008：120一125
[39]刘素一，张海霞，罗维于基于小波变换和Kalman滤波的多传感器数据融合[J].微计算机信息，2006，22(6一1)：179—181
[40]刘建书，李人厚，常宏基于相关性函数和最小二乘的多传感器数据融合[J].控制与决策，2006，21(6)：714—716
[41]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，2000，6(20)：183—184
[42]S L Sun Multi—sensor Optimal In％rmation Fusion Kalman Filter with Ap—plication[1].Aerospace Science and Technology，2004，8(1)：57—62
[43]孙书利，邓自立多传感器线性最小方差最优信息融合估计准则[J].科学技术与工程，2004，4(5)：334—336
[44]S L Sun．Z L Deng Multi—sensor Optimal In％rmation Fusion Kalman Fil—ter[J].Automatica，2004，40(6)：1017—1023
[45]S L Sun Multi—sensor In％rmation Fusion White Noise Filter Weighted by Scalars based on Kalman Predictor[J]Automatica，2004，40(8)：1447—1453
[46]孙书利，崔平远多传感器标量加权最优信息融合稳态Kalman滤波器[J].控制与决策，2004，19(2)：208—211
[47]S L Sun．Z L Deng Multi—sensor optimal In％rmation Fusion Steady—state Kalman Filter Weighted by Scalars fOr Systems with Colored Measurement Noises[J].Control Theory and Applications，2004，21(4)：365—368
[48]S L Sun Multisensor Optimal In％rmation Fusion Input White Noise Decon—volution Estimators[1].IEEE Transactions on Systems，Man，and Cybernetics，2004，34(4)：1886—1893
[49]孙书利，史雪岩，崔下远多传感器最优信息融合估计Kalman多步预报器及其应用[J].宇航学报，2004，25(20)：241—246
[50]孙书利，崔下远两传感器最优信息融合Kalman滤波器及其在跟踪系统中的应用[J].宇航学报，2003，24(2)：206—209
[51]K H Kim Development of Track to Track Fusion Algorithm[C]Proceeding of the American Control Conference，Maryland，1994：1037—1041
[52] K. C. Chou, A. S. Willsky, A. Benveniste, M. Basseville. Recursive and iterative estimation algorithms for multiresolution stochastic processes [C]. Proceedings of the 28th IEEE Conference on Decision and Control, Fampa, Florida, 1989, 2: 1184-1189.
[53] A. Benveniste, R. Nikoukhah, A. S. Willsky. Multiscale system theory[C]. Proceeding of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, 1990,4: 2484-2487.
[54] M. Basseville, A. Benveniste, K. C. Chou, S. A. Golden, R. Nikoukhah, A. S. Willsky. Modeling and estimation of multiresolution stochastic processes[J]. IEEE Transactions on Information Theory, 1992, 38(2): 766-784.
[55] M. Basseville, A. Benveniste, A. S. Willsky. Multiscale autoregressive process, Parts I: Schur-Levinson Parametrization[J]. IEEE Transactions on Signal Processing, 1992,40(8): 1915-1934.
[56] M. Basseville, A. Benveniste, A. S. Willsky. Multiscale autoregressive process, Parts II: Lattice Structures for Whitening and Modeling[J]. IEEE Transactions on Signal Processing, 1992, 40(8): 1935-1953.
[57] A. Benveniste, R. Nikoukhah, A. S. Willsky. Multiscale system theory [J]. IEEE Trans.on Circuits and Syatems-I: Fundamental Theory and Applications, 1994, 41(1): 2-15.
[58] L. Hong. Multiresolutional filtering using wavelet transform[J]. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(4): 1244-1251.
[59] L. Hong. Multi-resolutional distributed filtering[J]. IEEE Transactions Automatic Control, 1994, 39(4): 853-856.
[60] R. Cristi, M. Tummala. Multirate, multiresolution, recursive Kalman filter [J]. Signal Processing, 2000, 80(9): 1945-1958.
[61]文成林多尺度多速率递归Kalman滤波2001，31(4)：15—18
[62] A. Fabrizio, A. Luciano. Filterbanks design for multisensor data fusion[J]. IEEE Signal Processing Letters, 2000, 7(5): 100-103.
[63] D. Andrisani, C. F. Gau. Estimation Using a Multirate Filter [J]. IEEE Transactions on Automatic Control, 1987, 32(7): 653-656.
[64] D. J. Lee, M. Tomizuka. Multirate optimal state estimation with sensor fu-sion[C]. Proceedings of the American Control Conference, Denver, Colorado, 2003: 2887-2892.
[65] B. S. Chen, C. W. Lin, Y. L. Chen. Optimal signal reconstruction in noisy filter bank systems: multirate Kalman synthesis filtering approach[J]. IEEE Transactions on signal Processing, 1995, 43(11): 2496-2504.
[66] K. C. Chou, A. S. Willsky, A. Benveniste, M. Basseville. Recursive and iterative estimation algorithms for multiresolution stochastic processes [C]. Proceedings of the 28th IEEE Conference on Decision and Control, Fampa, Florida, 1989, 2: 1184-1189.
[67] K. C. Chou, A. S. Willsky, A. Benveniste. Multiscale recursive estimation , data fusion, and regularization[J]. IEEE Transactions on Automatic Control, 1994, 39(3): 464-478.
[68] K. Lo, H. Kimura. Recursive estimation methods for discrete systems[J]. IEEE Transactions on Automatic Control, 2003, 48(11): 2019-2024.
[69]孙红岩基于小波变换的多分辨率多传感器数据融合方法的研究[Dl_清华大学博士后出站报告，1998
[70] L. P. Yan, B. S. Liu, D. H. Zhou. The modeling and estimation of asynchronous multirate multisensor dynamic systems [J]. Aerospace Science and Technology, 2006, 10(1): 63-71.
[71] B. D. O. Anderson, J. B. Moore. Optimal Filtering[M]. Englewood Cliffs, NJ: Prentice-Hall, 1979.
[72]闫丽萍，刘宝生，周东华，文成林一类多速率多传感器系统的状态融合估计算法[J].电子与信息学报，2007，29(2)：443—446
[73] Y. Liang, T. W. Chen, Q. Pan. Multi-rate optimal state estimation[J]. International Journal of Control. 2009, 82(11): 2059-2076.