
浏览全部资源
扫码关注微信
1. 北京理工大学 宇航学院, 北京 100081
2. 中国兵器工业导航与控制技术研究所, 北京 100089
3. 北京理工大学 设计与艺术学院, 北京 100081
Received:23 January 2022,
Published Online:19 July 2023,
Published:31 May 2023
移动端阅览
Can LIU, Hui WANG, Defu LIN, et al. Bearings-Only Target Tracking Algorithm with Non-Gaussian Heavy-Tailed Distributed Noise[J]. Acta Armamentarii, 2023, 44(5): 1469-1481.
Can LIU, Hui WANG, Defu LIN, et al. Bearings-Only Target Tracking Algorithm with Non-Gaussian Heavy-Tailed Distributed Noise[J]. Acta Armamentarii, 2023, 44(5): 1469-1481. DOI: 10.12382/bgxb.2022.0058.
纯方位目标跟踪是目标跟踪研究中的热点问题
针对目标跟踪方程中的非高斯重尾分布噪声问题
提出了一种针对非高斯重尾分布噪声的卡尔曼滤波算法。该方法通过建立基于存在异常值的高斯分布的层次高斯模型来近似未知的非高斯重尾分布系统过程噪声和测量噪声
并使用变分贝叶斯推断来学习混合概率
解决混合概率不确定带来的滤波性能下降的问题
从而提高滤波的鲁棒性。同时针对纯方位目标跟踪模型的非线性
结合修正增益卡尔曼滤波来降低量测方程非线性的影响。数值仿真结果表明
相对于EKF、UKF和变分贝叶斯卡尔曼滤波PEKF-VB、VBEKF
新算法VBMGEKF估计精度分别提高了69.31%、58.08%、127.84%和9.36%
具备更好的鲁棒性与精度。
The bearings-only target tracking is a classic problem in the reserach on target tracking. Focusing on the problem of non-Gaussian heavy-tailed distributed noise in the model of target tracking
this paper proposes a new Kalman filter algorithm. Firstly
the hierarchical Gaussian model is established to approximate the unknown process noise and measurement noise of the non-Gaussian heavy-tailed distributed system. Next
the variational Bayesian inference is used to learn Mixture Probability to solve the problem of the filter’s performance degradation caused by the uncertainty of Mixture Probability
so as to improve the robustness of the filter. At the same time
for the nonlinearity of the bearings-only target tracking model
Modified Gain Kalman filter is used to reduce the influence of nonlinearity on the observation equation. The numerical simulations have verified that the proposed filter has better estimation accuracy and robustness than EKF
UKF and the variational Bayesian Kalman filters PEKF-Vb and VBEKF. The estimation accuracy of the proposed algorithm VBMGEKF is improved by 69.31%
58.08%
127.84% and 9.36%.
李康 , 丁国如 , 李京华 , 等 . 无源定位技术发展动态及其应用分析 [J ] . 航空兵器 , 2021 , 28 ( 2 ): 104 - 112 .
LI K , DING G R , LI J H , et al. Development and application analysis of passive localization [J ] . Aero Weaponry , 2021 , 28 ( 2 ): 104 - 112 . (in Chinese)
占荣辉 , 张军 , 欧建平 , 等 . 非线性滤波理论与目标跟踪应用 [M ] . 北京 : 国防工业出版社 , 2013 : 45 - 46 .
ZHAN R H , ZHANG J , OU J P , et al. Nonlinear filtering theory with target tracking application [M ] . Beijing : National Defense Industry Press , 2013 : 45 - 46 . (in Chinese)
EINICKEG A , WHITE L B . Robust extended Kalman filtering [J ] . IEEE Transactions on Signal Processing , 1999 , 47 ( 9 ): 2596 - 2599 . DOI: 10.1109/78.782219 http://doi.org/10.1109/78.782219 http://ieeexplore.ieee.org/document/782219/ http://ieeexplore.ieee.org/document/782219/
AIDALA V , HAMMEL S . Utilization of modified polar coordinates for bearings-only tracking [J ] . IEEE Transactions on Automatic Control , 1983 , 28 ( 3 ): 283 - 294 . DOI: 10.1109/TAC.1983.1103230 http://doi.org/10.1109/TAC.1983.1103230 http://ieeexplore.ieee.org/document/1103230/ http://ieeexplore.ieee.org/document/1103230/
JAWAHAR A , RAO S K . Modified polar extended Kalman filter (MPEKF) for bearings-only target tracking [J ] . Indian Journal of Science and Technology , 2016 , 9 ( 26 ): 1 - 5 .
LERRO D , BAR-SHALOM Y . Bias compensation for improved recursive bearings-only target state estimation [C ] ∥Proceedings of 1995 American Control Conference. MN, US:AACC , 1995 : 648 - 652 .
WANG W P , LIAO S , XING T W . The unscented Kalman filter for state estimation of 3-Dimension bearing-only tracking [C ] ∥Proceedings of 2009 International Conference on Information Engineering and Computer Science. Wuhan, China:IEEE , 2009 : 1 - 5 .
ARASARATNAM I , HAYKIN S . Cubature Kalman filters [J ] . IEEE Transactions on Automatic Control , 2009 , 54 ( 6 ): 1254 - 1269 . DOI: 10.1109/TAC.2009.2019800 http://doi.org/10.1109/TAC.2009.2019800 http://ieeexplore.ieee.org/document/4982682/ http://ieeexplore.ieee.org/document/4982682/
陈林秀 , 郝明瑞 , 赵佳佳 . 混合噪声条件下的目标被动定位算法 [J ] . 兵工学报 , 2021 , 42 ( 9 ): 1923 - 1930 . DOI: 10.3969/j.issn.1000-1093.2021.09.013 http://doi.org/10.3969/j.issn.1000-1093.2021.09.013 为提高被动传感器观测噪声为含时变有色噪声、跳变噪声的混合噪声时容积卡尔曼滤波(CKF)算法的滤波精度和稳定性,提出一种自适应容积卡尔曼滤波(ACKF)算法。在ACKF算法中,在基本CKF算法基础上,采用观测重构、待定系数去相关方法,推导得到有色噪声条件下的容积卡尔曼滤波算法。针对时变有色噪声和跳变噪声导致滤波精度受损的问题,引入噪声方差在线修正及有害观测剔除的思想,进行了ACKF算法设计。仿真结果表明,与基本CKF算法相比,ACKF算法在x轴、y轴、z轴3个方向得到的被动定位精度分别提升了24.75%、32.57%和28.48%,具有更高的滤波稳定性和精度。
CHEN L X , HAO M R , ZHAO J J . Passive target positioning algorithm for mixed noise [J ] . Acta Armamentarii , 2021 , 42 ( 9 ): 1923 - 1930 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.09.013 http://doi.org/10.3969/j.issn.1000-1093.2021.09.013 An adaptive cubature Kalman filter(ACKF) algorithm is proposed to improve the filtering accuracy and stability of the cubature Kalman filter(CKF) algorithm when the passive sensor measurement noise is a mixed noise containing time-varying colored noise and jumping noise. Based on the basic CKF algorithm, the measurement reconstruction and undetermined coefficient decorrelation methods are used to derive the cubature Kalman filter algorithm with colored measurement noise (CKF-CMN). For the impaired filtering accuracy caused by time-varying colored noise and jumping noise, the idea of online correction of noise variance and removal of harmful measurement is introduced, and the ACKF algorithm is designed. The simulated results show that, compared with the basic CKF algorithm, the passive positioning accuracies of ACKF algorithm on x, y, and z axes are increased by 24.75%, 32.57% and 28.48%, respectively. The ACKF algorithm has higher filtering stability and accuracy.
DAUM F . Nonlinear filters: beyond the Kalman filter [J ] . IEEE Aerospace and Electronic Systems Magazine , 2005 , 20 ( 8 ): 57 - 69 . DOI: 10.1109/MAES.2005.1499276 http://doi.org/10.1109/MAES.2005.1499276 http://ieeexplore.ieee.org/document/1499276/ http://ieeexplore.ieee.org/document/1499276/
CHANG D C , FANG M W . Bearing-only maneuver-ing mobile tracking with nonlinear filtering algorithms in wireless sensor networks [J ] . IEEE Systems Journal , 2014 , 8 ( 1 ): 160 - 170 . DOI: 10.1109/JSYST.4267003 http://doi.org/10.1109/JSYST.4267003 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4267003 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4267003
HONG S H , SHI Z G , CHEN K S . Novel roughening algorithm and hardware architecture for bearings-only tracking using particle filter [J ] . Journal of Electromagnetic Waves & Applications , 2008 , 22 ( 2/3 ): 411 - 422 .
MILLER A , MILLER B . Tracking of the UAV trajectory on the basis of bearing-only observations [C ] ∥Proceedings of the 53rd IEEE Conference on Decision and Control. Los Angeles, CA, US:IEEE , 2014 : 4178 - 4184 .
NGUYEN N H , DOGANÇAY K . Improved pseudolinear Kalman filter algorithms for bearings-only target tracking [J ] . IEEE Transactions on Signal Processing , 2017 , 5 ( 23 ): 6119 - 6134 .
ROTH M , ÖZKAN E , GUSTAFSSON F . A Student’s t filter for heavy tailed process and measurement noise [C ] ∥ Proceedings of the 2013th IEEE International Conference on Acoustics, Speech and Signal Processing. Vancouver, BC, Canada:IEEE , 2013 : 5770 - 5774 .
HUANG Y L , ZHANG Y G , LI N , et al. A robust Gaussian approximate filter for nonlinear systems with heavy tailed measurement noises [C ] ∥Proceedings of the 2016th IEEE International Conference on Acoustics, Speech and Signal Processing. Shanghai, China:IEEE , 2016 : 4209 - 4213 .
CONTE A , MAIO A D , FARINA A , et al. Design and analysis of a knowledge-based radar detector [C ] ∥Proceedings of 2005 IEEE International Radar Conference. Arlington, VA , US : IEEE , 2005 : 387 - 392 .
BILIK I , TABRIKIAN J . Maneuvering target tracking in the presence of glint using the nonlinear Gaussian mixture Kalman filter [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2010 , 46 ( 1 ): 246 - 262 . DOI: 10.1109/TAES.2010.5417160 http://doi.org/10.1109/TAES.2010.5417160 http://ieeexplore.ieee.org/document/5417160/ http://ieeexplore.ieee.org/document/5417160/
JAMES LOXAM , TOM DRUMMOND . Student’s t mixture filter for robust, real-time visual tracking [C ] ∥Proceedings of the 10th European Conference on Computer Vision:Part III Springer-Verlag. Marseille, France:ECCV , 2008 : 372 - 385 .
TING J , THEODOROU E , SCHAAL S . Learning an outlier robust Kalman filter [C ] ∥Proceedings of the 18th European Conference on Machine Learning.Warsaw, Poland:ECML/PKDD , 2007 : 748 - 756 .
ZHU H , HENRY LEUNG , HE Z S . A variational Bayesian approach to robust sensor fusion based on Student’s t distribution [J ] . Information Sciences , 2013 , 221 ( 1 ): 201 - 214 . DOI: 10.1016/j.ins.2012.09.017 http://doi.org/10.1016/j.ins.2012.09.017 https://linkinghub.elsevier.com/retrieve/pii/S002002551200610X https://linkinghub.elsevier.com/retrieve/pii/S002002551200610X
HUANG Y L , ZHANG Y G , LI N , et al. A robust Gaussian approximate fixed-interval smoother for nonlinear systems with heavy-tailed process and measurement noises [J ] . IEEE Signal Processing Letters , 2016 , 23 ( 4 ): 468 - 472 . DOI: 10.1109/LSP.2016.2533543 http://doi.org/10.1109/LSP.2016.2533543 http://ieeexplore.ieee.org/document/7416166/ http://ieeexplore.ieee.org/document/7416166/
HU Y M , WANG X Z , LAN H , et al. An iterative nonlinear filter using variational Bayesian optimization [J ] . Sensors (Basel) , 2018 , 18 ( 12 ): 4222 - 4235 . DOI: 10.3390/s18124222 http://doi.org/10.3390/s18124222 http://www.mdpi.com/1424-8220/18/12/4222 http://www.mdpi.com/1424-8220/18/12/4222 We propose an iterative nonlinear estimator based on the technique of variational Bayesian optimization. The posterior distribution of the underlying system state is approximated by a solvable variational distribution approached iteratively using evidence lower bound optimization subject to a minimal weighted Kullback-Leibler divergence, where a penalty factor is considered to adjust the step size of the iteration. Based on linearization, the iterative nonlinear filter is derived in a closed-form. The performance of the proposed algorithm is compared with several nonlinear filters in the literature using simulated target tracking examples.
闫文旭 , 兰华 , 王增福 , 等 . 基于变分贝叶斯的星载雷达非线性滤波 [J ] . 航空学报 , 2020 , 41 ( 增刊2 ): 220 - 228 .
YAN W X , LAN H , WANG Z F , et al. Nonlinear filtering for spaceborne radars based on variational Bayes [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( S2 ): 220 - 228 . (in Chinese)
HUANG Y L , ZHANG Y G , LI N , et al. A novel robust student’s t-based Kalman filter [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2017 , 53 ( 3 ): 1545 - 1554 . DOI: 10.1109/TAES.2017.2651684 http://doi.org/10.1109/TAES.2017.2651684 http://ieeexplore.ieee.org/document/7814285/ http://ieeexplore.ieee.org/document/7814285/
O’HAGAN A J J . Forster Kendall’s advanced theory of statistics: Bayesian inference [M ] . London , UK : Ar-nold , 2004 , 2B .
SARKKA S , NUMMENMAA A . Recursive noise adaptive Kalman filtering by variational Bayesian approximations [J ] . IEEE Transactions on Automatic Control , 2009 , 54 ( 3 ): 596 - 600 . DOI: 10.1109/TAC.2008.2008348 http://doi.org/10.1109/TAC.2008.2008348 http://ieeexplore.ieee.org/document/4796261/ http://ieeexplore.ieee.org/document/4796261/
BISHOP C M . Pattern recognition and machine learning [M ] . New York,NY, US:Springer , 2006 .
SONG TEAK L , JASON S . A stochastic a nalysis of a modified gain extended kalman filter with applications to estimation with bearings only measurements [J ] . IEEE Transactions on Automatic Control , 1985 , 30 ( 10 ): 940 - 949 . DOI: 10.1109/TAC.1985.1103821 http://doi.org/10.1109/TAC.1985.1103821 http://ieeexplore.ieee.org/document/1103821/ http://ieeexplore.ieee.org/document/1103821/
ZHANG Y G , JIA G L , LI N , et al. A novel adaptive Kalman filter with colored measurement noise [J ] . IEEE Access , 2018 , 63 ( 3 ): 74569 - 74578 .
马宝宏 , 林强 . MGEKF可修正增益矩阵的研究 [J ] . 航天电子对抗 , 2010 , 26 ( 3 ): 22 - 26 .
MA B H , LIN Q . Research of the MGEKF modified gain matrix [J ] . Aerospace Electronic Warfare , 2010 , 26 ( 3 ): 22 - 26 . (in Chinese)
0
Views
223
下载量
0
CNKI被引量
Publicity Resources
Related Articles
Related Author
Related Institution
京公网安备11010802024360号