Abstract：Research on target tracking with glint noise is important to improve detection performance of sensor, in which the glint noise’s unknown distribution and non-stationary property puzzle researchers for a long time. In order to solve this problem, the tracking theoretical framework of variational Bayesian parameter learning with glint noise is firstly introduced. Then, a novel algorithm called Variational Bayesian-Interacting Multiple Model (VB-IMM) is proposed to estimate the system states as well as the unknown glint noise’s distribution. The proposed algorithm designs a bank of tracking filters in parallel with different measurement noise. Moreover, the algorithm utilizes variational Bayesian method to learn distribution parameters of the glint noise online and feed these parameters back to the tracking filters to revise the filters. In order to validate the performance of this algorithm, comparative experiments are carried out from two aspects of tracking accuracy and computational complexity. Simulation results verify good performance of tracking error and low computational complexity of the proposed algorithm.
SKOLNIK M. Radar Handbook(Third Edition)[M]. U.S., McGraw Hill Press, 2008: 377-368.
[2]
HEWER G A, MARTIN R D, and ZEH J. Robust preprocessing for Kalman filtering of glint noise[J]. IEEE Tranactions on Aerospace and Electronic Systems, 1987, 23(1): 120-128. doi: 10.1109/TAES.1987.313340.
[3]
WU Wengrong. Target racking with glint noise[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(1): 174-185. doi: 10.1109/7.249123.
[4]
DAEIPOUR E and BAR-SHALOM Y. IMM tracking of maneuvering targets in the presence of glint[J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(3): 996-1003. doi: 10.1109/7.705913.
LU Cheng, LI Wei, LI Xiangping, et al. Research on target tracking in angular glint noise condition based on improved EKPF algorithm[J]. Tactical Missile Technology, 2017, (2): 81-85. doi: 10.16358/j.issn.1009-1300.2017.02.14.
ZHANG Xueying, CAI Zongping, and WEI Hao. Target tracking based on cubature particle filter algorithm in glint noise environment[J]. Science Technology and Engineering, 2016, (29): 271-274. doi: 10.3969/j.issn.1671-1815.2016.29. 047.
[7]
LI Hongwei and WANG Jun. Particle filter for manoeuvring target tracking via passive radar measurements with glint noise[J]. IET Radar, Sonar and Navigation, 2012, 6(3): 180-189. doi: 10.1049/iet-rsn.2011.0075.
[8]
KIM J, TANDALE M, MENON P K, et al. Particle filter for ballistic target tracking with glint noise[J]. Journal of Guidance Control and Dynamics, 2010, 33(6): 1918-1921. doi: 10.2514/1.51000.
[9]
BILIK I and 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.
[10]
WANG Hongjian and LI Cun. An improved Gaussian mixture CKF algorithm under non-Gaussian observation noise[J]. Discrete Dynamics in Nature and Society, 2016(12): 1-10. doi: 10.1155/2016/1082837.
WANG Lei, CHENG Xianghong, and LI Shuangxi. Gaussian sum high order Unscented Kalman filtering algorithm[J]. Acta Electronica Sinica, 2017, 45(2): 424-430. 10.3969/j.issn. 0372-2112.2017.02.022.
HUANG Binke, WANG Gang, and WANG Wenbing. General proof of observation distance independence of the far-zone angular glint of radar targets[J]. Systems Engineering and Electronics, 2007, 29(4): 505-508. doi: 10.3321/j.issn:1001- 506X.2007.04.002.
[14]
BISHOP C M. Pattern Recognition and Machine Learning [M]. New York, Springer, 2006: 423-517.
[15]
TZIKAS D G, LIKAS C L, and GALATSANOS N P. The variational approximation for bayesian inference[J]. IEEE Signal Processing Magazine, 2008, 25(6): 131-146. doi: 10.1109/MSP.2008.929620.
[16]
BLEI D M, KUCUKELBIR A, and MCAULIFFE J D. Variational inference: A review for statisticians[J]. Journal of The American Statistical Association, 2017, 112(518): 859-877. doi: 10.1080/01621459.2017.1285773.
[17]
ZHU Hao, LEUNG H, and HE Zhongshi. State estimation in unknown non-Gaussian measurement noise using variational bayesian technique[J]. IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(49): 2601-2614. doi: 10.1109/ TAES.2013.6621839.
[18]
SARKKA S and 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.
SHEN Chen, Xu Dingjie, SHEN Feng, et al. Generalized noises adaptive kalman filtering based on variational inference[J]. Systems Engineering and Electronics, 2014, 36(8): 1466-1472. doi: 10.3969/j.issn.1001-506X.2014.08.03.
[20]
HUANG Yulong, ZHANG Yonggang, WU Zhemin, et al. A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices[J]. IEEE Transactions on Automatic Control, 2018, 63(2): 594-601. doi: 10.1109/TAC.2017.2730480.
[21]
ARDESHIRI T,ÖZKAN E, ORGUNER U, et al. Approximate bayesian smoothing with unknown process and measurement noise covariances[J]. IEEE Signal Processing Letters, 2015, 22(12): 2450-2454. doi: 10.1109/LSP.2015. 2490543.
[22]
MA Tianli, WANG Xinmin, XIE Rong, et al. Variational bayesian cubature kalman filter for bearing-only tracking in glint noise environment[C]. IEEE Chinese Guidance, Navigation and Control Conference, Nanjing, China, 2016: 232-237.
[23]
MIAO Zhiyong, LÜ Yunlong, XU Dingjie, et al. Analysis of a variational Bayesian adaptive cubature Kalman filter tracking loop for high dynamic conditions[J]. Gps Solutions, 2017, 21(1): 111-122. doi: 10.1007/s10291-015-0510-0.
[24]
DONG Peng, JING Zhongliang, LEUNG H, et al. Variational bayesian adaptive Cubature information filter based on Wishart distribution[J]. IEEE Transactions on Automatic Control, 2017, 62(11): 6051-6057. doi: 10.1109/TAC.2017. 2704442.
[25]
BORDEN B H and MUMFORD M L. A statistical glint/radar cross section target model[J]. IEEE Transactions on Aerospace and Electronic Systems, 1983, 19(5): 781-785. doi: 10.1109/TAES.1983.309383.
[26]
ARASARATNAM I and HAYKIN S. Cubature Kalman filters[J]. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269. doi: 10.1109/TAC.2009.2019800.
[27]
AGAMENNONI G, NIETO J I, and NEBOT E M. Approximate inference in state-space models with heavy- tailed noise[J]. IEEE Transactions on Signal Processing, 2012, 60(10): 5024-5037. doi: 10.1109/TSP.2012.2208106.
[28]
LI Tiancheng, BOLIC M, and DJURIC P. Resampling methods for particle filtering: Classification implementation and strategies[J]. IEEE Signal Processing Magazine, 2015, 32(3): 70-86. doi: 10.1109/MSP.2014.2330626.
