含未知参数的自校正融合Kalman滤波器及其收敛性

陶贵丽; 邓自立

doi:10.3724/SP.J.1004.2012.00109

含未知参数的自校正融合Kalman滤波器及其收敛性

doi: 10.3724/SP.J.1004.2012.00109

陶贵丽^1,2,
邓自立^1, ,

1.
黑龙江大学自动化系哈尔滨 150080;
2.
黑龙江科技学院计算机与信息工程学院哈尔滨 150027

详细信息

通讯作者:
邓自立黑龙江大学自动化系教授. 主要研究方向为最优和自校正滤波,状态估计,多传感器信息融合和信号处理. 本文通信作者. E-mail: dzl@hlju.edu.cn

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出版历程
- 收稿日期: 2010-11-17
- 修回日期: 2011-09-07
- 刊出日期: 2012-01-20

Self-tuning Fusion Kalman Filter with Unknown Parameters and Its Convergence

TAO Gui-Li^1,2,
DENG Zi-Li^{1
, ,}

1.
Department of Automation, Heilongjiang University, Harbin 150080;
2.
Computer and Information Engineering College, Heilongjiang Institute of Science and Technology, Harbin 150027

摘要

摘要: 对于带未知模型参数和噪声方差的多传感器系统,基于分量按标量加权最优融合准则,提出了自校正解耦融合Kalman滤波器,并应用动态误差系统分析(Dynamic error system analysis,DESA)方法证明了它的收敛性.作为在信号处理中的应用,对带有色和白色观测噪声的多传感器多维自回归(Autoregressive,AR)信号,分别提出了AR信号模型参数估计的多维和多重偏差补偿递推最小二乘(Bias compensated recursive least-squares,BCRLS)算法,证明了两种算法的等价性,并且用DESA方法证明了它们的收敛性.在此基础上提出了AR信号的自校正融合Kalman滤波器,它具有渐近最优性.仿真例子说明了其有效性.
- 多传感器信息融合 /
- 自校正融合 /
- 偏差补偿最小二乘法 /
- 收敛性 /
- 动态误差系统分析方法 /
- Kalman滤波器
Abstract: For the multisensor systems with unknown model parameters and noise variances, a self-tuning decoupled fused Kalman filter is presented based on the optimal fusion rule weighted by scalars for components. Its convergence is proved by using the dynamic error system analysis (DESA) method. As an application to signal processing, the multidimensional and multiple bias compensated recursive least-squares (BCRLS) algorithms for estimating the AR parameters are presented for the multisensor multidimensional autoregressive (AR) signal with white and colored measurement noises. The equivalence between the two BCRLS algorithms is proved. The convergence of the two BCRLS algorithms is proved by DESA method. Further more, a self-tuning fused Kalman filter for the AR signal is presented, which has asymptotic optimality. A simulation example shows the effectiveness.
- Multisensor information fusion /
- self-tuning fusion /
- bias compensated least-squares (BCRLS) method /
- convergence /
- dynamic error system analysis (DESA) method /
- Kalman filter

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参考文献(1)

[1]

Liggins M E,Hall D L,Llinas J. Handbook of Multisensor Data Fusion:Theory and Practice (Second Edition). Boca Raton:CRC Press,2009[2] Li X R,Zhu Y M,Wang J,Han C Z. Optimal linear estimation fusion I:unified fusion rules. IEEE Transactions on Information Theory,2003,49(9):2192-2208[3] Song E B,Zhu Y M,Zhou J,You Z S. Optimal Kalman filtering fusion with cross-correlated sensor noises. Automatica,2007,43(8):1450-1456[4] Sun S L,Deng Z L. Multi-sensor optimal information fusion Kalman filter. Automatica,2004,40(6):1017-1023[5] Deng Z L,Gao Y,Mao L,Li Y,Hao G. New approach to information fusion steady-state Kalman filtering. Automatica,2005,41(10):1695-1707[6] Hagander P,Wittenmark B. A self-tuning filter for fixed-lag smoothing. IEEE Transactions on Information Theory,1977,23(3):377-384[7] Moir T,Grimble M J. Optimal self-tuning filtering,prediction,and smoothing for discrete multivariable processes. IEEE Transactions on Automatic Control,1984,29(2):128-137[8] Deng Z L,Zhang H S,Liu S J,Zhou L. Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems. Automatica,1996,32(2):199-216[9] Deng Zi-Li. Self-tuning Filtering Theory with Applications. Harbin:Harbin Institute of Technology Press,2003(邓自立. 自校正滤波理论及其应用. 哈尔滨:哈尔滨工业大学出版社,2003)[10] Wang Jian-Wen,Shui Hai-Tao,Li Xun,Zhang Hui,Ma Hong-Xu. Robust Kalman filter design for unknown noise covariance. Control Theory and Application,2011,28(5):693-697(王建文,税海涛,李迅,张辉,马宏绪. 噪声统计特性未知时的鲁棒卡尔曼滤波算法设计. 控制理论与应用,2011,28(5):693-697)[11] Julier S J,Uhlmann J K. A non-divergent estimation algorithm in the presence of unknown correlations. In:Proceedings of the American Control Conference. Albuquerque,USA:IEEE,1997. 2369-2373[12] Wu D Z,Zhou J,Qu X M. A robust estimation fusion with unknown cross-covariance in distribution systems. In:Proceedings of the 48th IEEE Conference on Decision and Control Jointly with the 28th Chinese Control Conference. Shanghai,China:IEEE,2009. 7603-7607[13] Deng Z Li,Gao Y,Li C B,Hao G. Self-tuning decoupled information fusion Wiener state component filters and their convergence. Automatica,2008,44(3):685-695[14] Deng Z L,Li C B. Self-tuning information fusion Kalman predictor weighted by diagonal matrices and its convergence analysis. Acta Automatica Sinica,2007,33(2):156-163[15] Sun S L. Optimal and self-tuning information fusion Kalman multi-step predictor. IEEE Transactions on Aerospace and Electronic Systems,2007,43(2):418-427[16] Ran C J,Deng Z L. Self-tuning weighted measurement fusion Kalman filter and its convergence. Journal of Control Theory and Applications,2010,8(4):435-440[17] Gao Y,Jia W J,Sun X J,Deng Z L. Self-tuning multisensor weighted measurement fusion Kalman filter. IEEE Transactions on Aerospace and Electronic Systems,2009,45(1):179-191[18] Gao Y,Ran C J,Sun X J,Deng Z L. Optimal and self-tuning weighted measurement fusion Kalman filters and their asymptotic global optimality. International Journal of Adaptive Control and Signal Processing,2010,24(11):982-1004[19] Ran C J,Tao G L,Liu J F,Deng Z L. Self-tuning decoupled fusion Kalman predictor and its convergence analysis. IEEE Sensors Journal,2009,9(12):2024-2032[20] Tao G L,Deng Z L. Convergence of self-tuning Riccati equation for systems with unknown parameters and noise variances. In:Proceedings of the 8th World Congress on Intelligent Control and Automation. Jinan,China:IEEE,2010. 5732-5736[21] Ljung L. System Identification:Theory for the User (Second Edition). New Jersey:Prentice Hall,1999[22] Kailath T,Sayed A H,Hassibi B. Linear Estimation. New Jersey:Prentice Hall,2000[23] Ran C J,Deng Z L. Information fusion multi-stage identification method for multisensor multi-channel ARMA models. In:Proceedings of the International Conference on Mechatronics and Automation. Beijing,China:IEEE,2011. 2216-2221[24] Kamen E W,Su J K. Introduction to Optimal Estimation. London:Springer,1999[25] Deng Zi-Li. Information Fusion Filter Theory with Applications. Harbin:Harbin Institute of Technology Press,2007(邓自立. 信息融合滤波理论及其应用. 哈尔滨:哈尔滨工业大学出版社,2007)[26] Chen H F,Zhao W X. Identification of both coefficients and orders of ARMAX system. In:Proceedings of the 48th IEEE Conference on Decision and Control Joint with the 28th Chinese Control Conference. Shanghai,China:IEEE,2009. 7250-7255[27] Chui C K,Chen G. Kalman Filtering:with Real-Time Applications (Fourth Edition). Berlin:Springer-Verlag,1999[28] Gibson J D,Koo B,Gray S D. Filtering of colored noise for speech enhancement and coding. IEEE Transactions on Signal Processing,1991,39(8):1732-1742[29] Moir T J,Campbel D R,Dabis H S. A polynomial approach to optimal and adaptive filtering with application to speech. IEEE Transactions on Signal Processing,1991,39(5):1221-1224[30] Box G E P,Jenkins G M,Reinsel G C. Time Series Analysis:Forecasting and Control (Third Edition). New Jersey:Prentice Hall,1994[31] Deng Zi-Li,Xu Hui-Qin,Zhang Ming-Bo. Multivariable bias compensated recursive least-squares algorithm and its convergence. Science Technology and Engineering,2010,10(2):360-365(邓自立,徐慧勤,张明波. 多变量偏差补偿递推最小二乘法及其收敛性. 科学技术与工程,2010,10(2):360-365)

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