逆协方差交叉融合鲁棒Kalman滤波器
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摘要
分布式状态估计系统通过将多个传感器状态融合以得到更精确的融合结果,当传感器之间的协方差未知时,常采用保守估计的策略,但结果精确度较差。为了在传感器之间互协方差未知时得到更精确的融合结果,引入了逆协方差交叉算法,将其与局部稳态Kalman滤波器相结合,提出逆协方差交叉融合鲁棒Kalman滤波器。它克服了协方差交叉融合(CI)算法保守的缺点,证明了ICI的精度高于CI的精度,并基于协方差椭圆给出ICI、CI和局部传感器精度的几何解释。通过两传感器系统的蒙特卡洛仿真例子表明,其实际精度相比于CI融合鲁棒稳态Kalman滤波器更接近于带已知互协方差的最优融合器的精度。
Aimed at the problems that in distributed state estimation systems, the fusion methods are often employed to systematically combine multiple estimates of the state into a single, more accurate estimate, and if the correlation structure is unknown, conservative strategies are typically pursued with less accurate, an inverse covariance intersection fusion robust steady-state Kalman filter is proposed to gain more accurate estimate. As a major advantage of the novel approach, the fusion results prove to be more accurate than those provided by the well-known covariance intersection method. The geometric interpretation of the accuracy relations is given based on the covariance ellipses. A Monte-Carlo simulation example for a two-sensor system shows that its actual accuracy is close to that of the optimal Kalman fuser with known cross-covariance.
Aimed at the problems that in distributed state estimation systems, the fusion methods are often employed to systematically combine multiple estimates of the state into a single, more accurate estimate, and if the correlation structure is unknown, conservative strategies are typically pursued with less accurate, an inverse covariance intersection fusion robust steady-state Kalman filter is proposed to gain more accurate estimate. As a major advantage of the novel approach, the fusion results prove to be more accurate than those provided by the well-known covariance intersection method. The geometric interpretation of the accuracy relations is given based on the covariance ellipses. A Monte-Carlo simulation example for a two-sensor system shows that its actual accuracy is close to that of the optimal Kalman fuser with known cross-covariance.
引文
[1] JULIER S J,UHLMANN J K.General Decentralized Data Fusion with Covariance Intersection[M]//Handbook of Multisensor Data Fusion:Theory and Practice,2nd Edition.Boca Raton,FL:CRC Press,2009:319-3423.
[2] HAJIYEV C,SOKEN H E.Robust Adaptive Kalman-Filter for Estimation of UAV Dynamics in the Presence of Sensor/Actuator Faults[J].Aerospace Science and Technology,2013,28(1):376-3834.
[3] MENEC S L,SHIN H S,MARKHAM K,et al.Cooperative Allocation and Guidance for Air Defence Application[J].Control Engineering Practice,2014,32:236-244.
[4] JULIER S J,UHLMANN J K.Non-Divergent Estimation Algorithm in the Presence of Unknown Correlations[C]//Proc of 1997 IEEE American Control Conf.Albuquerque:IEEE,1997:2369-2373.
[5] UHLMANN J K.General Data Fusion for Estimateswith Unknown Cross Covariances[C]//Proc of the SPIE Aerosence Conference.[S.l.]:SPIE,1996:536-547.
[6] JULIER S,UHLMANN J K.General Decentralized Data Fusion with Covariance Intersection[M]//Hand-Book of Multisensory Data Fusion,Theory and Practice,2nd Edition.New York:Taylor & Francis Group,CRC Press,2009:319-342.
[7] CHEN L,ARAMBEL P O,MEHRA R K.Estimation under Unknown Correlation:Covariance Intersection Revisited[J].IEEE Trans on Automatic Control,2002,47(11):1879-1882.
[8] UHLMANN J K.Covariance Consistency Methods for Faulttolerant Distributed Data Fusion[J].Information Fusion.2003,4(3):201-215.
[9] JULIER S J,UHLMANN J K.Using Covariance Intersection for SLAM[J].Robotics & Autonomous Systems,2007,55(1):3-20.
[10] QI W J,ZHANG P,NIE G H,et al.Robust Weighted Fusion Kalman Predictors with Uncertain Noise Variances[J].Digital Signal Processing,2014,30:37-54.
[11] QI W J,ZHANG P,DENG Z L.Robust Weighted Fusion Timevarying Kalman Smoothers for Multisensor System with Uncertain Noise Variances[J].Information Sciences,2014,282:15-37.
[12] QI W J,ZHANG P,DENG Z L.Weighted Fusion Robust Steadystate Kalman Filter for Multisensor System with Uncertain Noise Variances[J].Journal of Applied Mathematics,2014,2014:369252.
[13] SIJS J,LAZAR M.State Fusion with Unknown Correlation:Ellipsoidal Intersection[J].Automatica,2012,48(8):1874-1878.
[14] NOACK B,SIJS J.Marc ReinhardtDecentralized Data Fusion with Inverse Covariance Intersection[J].Automatica,2017,79:35-41.
[15] 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,2007:305-318.DENG Z L.Information Fusion Filtering Theory with Applications[M].Harbin:Harbin Institute of Technology Press,2007:305-318.(in Chinese)
[16] 张鹏,齐文娟,邓自立.协方差交叉融合鲁棒 Kalman滤波器[J].控制与决策,2012,27(6):904-908.ZHANG P,QI W J,DENG Z L.Covariance Intersection Fusion Robust Steady-State Kalman Filter[J].Control and Decision,2012,27(6):904-908.(in Chinese)
[17] BAR-SHALOM Y,CAMPO L.The Effect of the Common Noise on the Two-Sensor Fused-Track Covariance[J].IEEE Trans on Aerospace and Electronic Systems,1986,22(6):803-805.
[18] 袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,2003:69-74.YUAN Y X,SUN W Y.Optimization Theory and Methods[M].Beijing:Science Press,2003:69-74.(in Chinese)
[19] 黄珏,颜冰,陈浩文.基于分离协方差交叉的全局反馈航迹融合[J].华中科技大学学报(自然科学版),2016,44(1):52-55.HUANG J,YAN B,CHEN H W.Track-to-Track Fusion with Global Feedback Based on Split Covariance Intersection[J].Huazgong Univ.of Sci.&Tech:Natutal Science Edition,2016,44(1):52-55.(in Chinese)
[20] CHEN L,ARAMBEL P O,MEHRA R K.Estimation under Unknown Correlation:Covariance Intersection Revisited[J].IEEE Trans on Automatic Control,2002,47(11):1879-1882.
[21] 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,2006:338-361.HAN C Z,ZHU H Y,DUAN Z S.Multi-Source Information Fusion[M].Beijing:Tsinghua University Press,2006:338-361.(in Chinese)
[2] HAJIYEV C,SOKEN H E.Robust Adaptive Kalman-Filter for Estimation of UAV Dynamics in the Presence of Sensor/Actuator Faults[J].Aerospace Science and Technology,2013,28(1):376-3834.
[3] MENEC S L,SHIN H S,MARKHAM K,et al.Cooperative Allocation and Guidance for Air Defence Application[J].Control Engineering Practice,2014,32:236-244.
[4] JULIER S J,UHLMANN J K.Non-Divergent Estimation Algorithm in the Presence of Unknown Correlations[C]//Proc of 1997 IEEE American Control Conf.Albuquerque:IEEE,1997:2369-2373.
[5] UHLMANN J K.General Data Fusion for Estimateswith Unknown Cross Covariances[C]//Proc of the SPIE Aerosence Conference.[S.l.]:SPIE,1996:536-547.
[6] JULIER S,UHLMANN J K.General Decentralized Data Fusion with Covariance Intersection[M]//Hand-Book of Multisensory Data Fusion,Theory and Practice,2nd Edition.New York:Taylor & Francis Group,CRC Press,2009:319-342.
[7] CHEN L,ARAMBEL P O,MEHRA R K.Estimation under Unknown Correlation:Covariance Intersection Revisited[J].IEEE Trans on Automatic Control,2002,47(11):1879-1882.
[8] UHLMANN J K.Covariance Consistency Methods for Faulttolerant Distributed Data Fusion[J].Information Fusion.2003,4(3):201-215.
[9] JULIER S J,UHLMANN J K.Using Covariance Intersection for SLAM[J].Robotics & Autonomous Systems,2007,55(1):3-20.
[10] QI W J,ZHANG P,NIE G H,et al.Robust Weighted Fusion Kalman Predictors with Uncertain Noise Variances[J].Digital Signal Processing,2014,30:37-54.
[11] QI W J,ZHANG P,DENG Z L.Robust Weighted Fusion Timevarying Kalman Smoothers for Multisensor System with Uncertain Noise Variances[J].Information Sciences,2014,282:15-37.
[12] QI W J,ZHANG P,DENG Z L.Weighted Fusion Robust Steadystate Kalman Filter for Multisensor System with Uncertain Noise Variances[J].Journal of Applied Mathematics,2014,2014:369252.
[13] SIJS J,LAZAR M.State Fusion with Unknown Correlation:Ellipsoidal Intersection[J].Automatica,2012,48(8):1874-1878.
[14] NOACK B,SIJS J.Marc ReinhardtDecentralized Data Fusion with Inverse Covariance Intersection[J].Automatica,2017,79:35-41.
[15] 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,2007:305-318.DENG Z L.Information Fusion Filtering Theory with Applications[M].Harbin:Harbin Institute of Technology Press,2007:305-318.(in Chinese)
[16] 张鹏,齐文娟,邓自立.协方差交叉融合鲁棒 Kalman滤波器[J].控制与决策,2012,27(6):904-908.ZHANG P,QI W J,DENG Z L.Covariance Intersection Fusion Robust Steady-State Kalman Filter[J].Control and Decision,2012,27(6):904-908.(in Chinese)
[17] BAR-SHALOM Y,CAMPO L.The Effect of the Common Noise on the Two-Sensor Fused-Track Covariance[J].IEEE Trans on Aerospace and Electronic Systems,1986,22(6):803-805.
[18] 袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,2003:69-74.YUAN Y X,SUN W Y.Optimization Theory and Methods[M].Beijing:Science Press,2003:69-74.(in Chinese)
[19] 黄珏,颜冰,陈浩文.基于分离协方差交叉的全局反馈航迹融合[J].华中科技大学学报(自然科学版),2016,44(1):52-55.HUANG J,YAN B,CHEN H W.Track-to-Track Fusion with Global Feedback Based on Split Covariance Intersection[J].Huazgong Univ.of Sci.&Tech:Natutal Science Edition,2016,44(1):52-55.(in Chinese)
[20] CHEN L,ARAMBEL P O,MEHRA R K.Estimation under Unknown Correlation:Covariance Intersection Revisited[J].IEEE Trans on Automatic Control,2002,47(11):1879-1882.
[21] 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,2006:338-361.HAN C Z,ZHU H Y,DUAN Z S.Multi-Source Information Fusion[M].Beijing:Tsinghua University Press,2006:338-361.(in Chinese)