Research on Improved Divided Difference Particle Filter under Non-stationary Non-Gaussian Noise Background

doi:10.3969/j.issn.1000-1093.2014.07.015

Abstract

Abstract: An improved divided difference particle filter (IDDPF) is proposed to improve the low accuracy of state estimation and divergent tend problem which may be caused by divided difference particle filter (DDPF) in the condition of the non-stationary non-Gaussian measurement noise (NSNGN). The IDDPF algorithm adopts Gaussian mixture density function to approximately estimate the measurement noise, instead of the Gaussian density function usually adopted in DDPF. The noise parameters are estimated by maximizing the log likelihood function of the measurement noise model. The model is then used to calculate the particle weight, which avoids the particle degeneracy problem. The IDDPF algorithm is tested by establishing bearing-only tracking of underwater target under the glint measurement noise background. The results of 50 Monte-Carlo simulation experiments show that the IDDPF algorithm has the advantages of fast tracking response, high estimated precision and robustness, etc. under NSNGN background.

Key words: control science and technology, non-stationary non-Gaussian noise, divided difference particle filter, Gaussian mixture density function, underwater target bearing-only tracking

CLC Number:

TB566

WANG Hong-jian，XU Jin-long，LI Juan，ZHANG Ai-hua. Research on Improved Divided Difference Particle Filter under Non-stationary Non-Gaussian Noise Background[J]. Acta Armamentarii, 2014, 35(7): 1032-1039.

References

［1］ Daum F. Nonlinear filters: beyond the Kalman filter［J］. IEEE AES Systems Magazine, 2005, 20(8): 57-69.
［2］ Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with applications to tracking and navigation［M］. New York:Wiley & Sons, 2001:157-163.
［3］周东华,席裕庚,张钟俊. 一种带多重次优渐消因子的扩展卡尔曼滤波器［J］. 自动化学报, 1991, 17(6):689-696.
ZHOU Dong-hua, XI Yu-geng, ZHANG Zhong-jun. A suboptimal multiple fading extended Kalman filter［J］. Acta Automatica Sinca, 1991, 17(6):689-696.(in Chinese)
［4］ Gelb A. Applied optimal estimation［M］. Cambridge:the MIT Press, 1974:567-590.
［5］ Julier S J, Uhlmann J K, Durrant W H. A new approach for filtering nonlinearing systems［C］∥Proceedings of the American Control Conference. Seattle, WA:IEEE,1995: 1628-1632.
［6］ Norgaard M, Poulsen N K, Ravn O. New development in state estimation for nonlinear systems［J］. Automatica, 2000, 36(11): 1627-1638.
［7］王晓旭, 赵琳, 夏全喜. 噪声相关条件下Unscented卡尔曼滤波器设计［J］. 控制理论与应用, 2010, 27(10):1362-1369.
WANG Xiao-xu, ZHAO Lin, XIA Quan-xi. Design of umscented Kalman filter with correlative noises［J］. Control Theory & Applications, 2010, 27(10):1362-1369.(in Chinese)
［8］王晓旭, 赵琳, 潘泉. 基于最小均方根误差估计的噪声相关UKF设计［J］. 控制与决策, 2010, 25(9): 1393-1398.
WANG Xiao-xu, ZHAO Lin, PAN Quan. Design of UKF with correlative noises based on minimum mean square error estimation［J］. Control and Decision, 2010, 25(9): 1393-1398.(in Chinese)
［9］王晓旭, 梁彦, 潘泉. 带有色量测噪声的非线性系统Unscented 卡尔曼滤波器［J］. 自动化学报, 2012, 38(6): 986-998.
WANG Xiao-xu, LIANG Yan, PAN Quan. Unscented Kalman filter for nonlinear systems with colored measurement noise［J］. Acta Automatica Sinca, 2012, 38(6):986-998.(in Chinese)
［10］范炜, 李勇. Sigma点卡尔曼滤波方法精度分析［C］∥2009 Chinese Control and Decision Conference, 2009: 2883-2888.
FAN Wei, LI Yong. Accuracy analysis of sigma-point Kalman filters［C］∥2009 Chinese Control and Decision Conference. Guilin: IEEE, 2009: 2883-2888. (in Chinese)
［11］ Lefebvre T, Bruyninckx H, Schutter J. Kalman filter for nonli-near systems: a comparison of performance［J］. International Journal of Control, 2004, 77(7): 639-653.
［12］ Duník J, Simandl M, Straka O, et al. Performance analysis of derivative-free filters［C］∥Proceedings of the 44th IEEE Conference on Decision and Control. Seville: IEEE, 2005: 1941-1946.
［13］ Lee D J. Nonlinear Bayesian filtering with applications to estimation and navigation［D］. Texas:Texas A&M University, 2005.
［14］ Shi Y, Chongzhao H, Liang Y. Improved divided difference filter based on Newton-Raphson method for target tracking［C］∥12th International Conference on Information Fusion. Seattle, WA:IEEE, 2009: 2068-2074.
［15］ Wang C Y, Zhang j, Mu J. Maximum likelihood-based iterated divided difference filter for nonlinear systems from discrete noisy measurement［J］. Sensors, 2012, 12(7): 8912-8929.
［16］ Subrahmanya N, Shin Y C. Adaptive divided difference filtering for simultaneous state and parameter estimation［J］. Automatica, 2009, 45(7): 1686-1693.
［17］ Miele A. Optimal trajectories and guidance trajectories for aircraft flight through wing shears［C］∥ Proceeding of 29th IEEE Conference on Decision and Control. Phoenix: IEEE, 1990: 737-743.
［18］ Gondon N, Salmonod D. Novel approach to non-linear and non-Gaussian Bayesian state estimation［C］∥Proceedings of Institute Electric Engineering. Michigan: IEEE,1993,140(2): 107-113.
［19］朱志宇. 粒子滤波算法及其应用［M］. 北京：科学出版社, 2010:123-135.
ZHU Zhi-yu. Particle filter and applications［M］. Beijing:Science Press, 2010:123-135. (in Chinese)
［20］石勇, 韩崇昭. 二阶中心差分粒子滤波算法［J］. 西安交通大学学报, 2008, 42(4): 409-413.
SHI Yong, HAN Chong-zhao. Particle filter using second-order central difference［J］. Journal of Xi'an Jiaotong University, 2008, 42(4): 409-413. (in Chinese)
［21］熊剑, 刘建业, 赖际舟. 基于二阶差值滤波的粒子滤波改进算法研究［J］. 控制与决策, 2009, 24(6): 907-910.
XIONG Jian, LIU Jian-ye, LAI Ji-zhou. Improved particle filter-ing algorithm based on 2-order interpolation filtering［J］. Control and Decision, 2009, 24(6): 907-910. (in Chinese)
［22］朱明清, 王智灵, 陈宗海. 基于改进Bhattacharyya系数的粒子滤波视觉跟踪算法［J］. 控制与决策, 2012, 27(10): 1579-1583.
ZHU Ming-qing, WANG Zhi-ling, CHEN Zong-hai. Modified Bhattacharyya coefficient for particle filter visual tracking［J］. Control and Decision, 2012, 27(10):1579-1583. (in Chinese)
［23］夏楠, 邱天爽, 李景春. 一种卡尔曼滤波与粒子滤波相结合的非线性滤波算法［J］. 电子学报, 2013, 41(1): 148-152.
XIA Nan, QIU Tian-shuang, LI Jing-chun. A nonlinear filtering algorithm combining the Kalman filter and the particle filter［J］. Acta Electronica Sinica, 2013, 41(1): 148-152. (in Chinese)
［24］熊剑, 刘建业, 赖际舟. 基于结构分解的GPS/INS组合导航粒子滤波技术［J］. 控制与决策, 2012, 27(6): 957-960.
XIONG Jian, LIU Jian-ye, LAI Ji-zhou. GPS/INS integrated navigation particle filter based on structural decomposition［J］. Control and Decision, 2012, 27(6): 957-960. (in Chinese)
［25］王欣, 赵连义, 薛龙. 基于主成分分析的粒子滤波器目标跟踪算法［J］. 吉林大学学报：理学版, 2012, 50(6): 1156-1162.
WANG Xin, ZHAO Lian-yi, XUE Long. Particle filter algorithm based on principal component analysis［J］. Journal of Jilin University: Science Edition, 2012: 50(6): 1156-1162. (in Chinese)
［26］陈志敏, 薄煜明, 吴盘龙. 基于自适应粒子群优化的新型粒子滤波在目标跟踪中的应用［J］. 控制与决策, 2013, 28(2): 193-200.
CHEN Zhi-min, BO Yu-ming, WU Pan-long. Novel particle filter algorithm based on adaptive particle swarm optimization and its application to radar target tracking［J］. Control and Decision, 2013, 28(2):193-200. (in Chinese)
［27］ Lichtenauer J, Reinders M, Hendriks E. Influence of the observation likelihood function on particle filtering performance in tracking applications［C］∥Proceedings of 6th IEEE International Conference on Automatic Face and Gesture Recognition. Netherlands: IEEE, 2004: 767-772.
［28］ Mukherjee A, Sebgupta A. Parameter estimation of a signal along with non-stationary non-Gaussian noise［C］∥ the 33rd Annual Conference of the IEEE Industrial Electronica Society. Taipei:IEEE,2007: 2429-2433.
［29］盛骤, 谢式千, 潘承毅. 概率论与数理统计［M］. 北京：高等教育出版社, 2001:157-163.
SHENG Zhou, XIE Shi-qian, PAN Cheng-yi. Probability theory and mathematical statistics［M］. Beijing:Higher Education Press, 2001:157-163. (in Chinese)
［30］ Hewer G A, Martin R D. Robust preprocessing for Kalman filter of glint noise［J］. IEEE Transactions on Aerospace and Electronic Systems, 1987, 23(1):120-128.
［31］李建武. 非高斯噪声下基于EM改进算法的多用户检测研究［D］. 郑州：河南工业大学, 2011:53-60.
LI Jian-wu. The research of multiuser detection based on EM accelerate algorithms under non-Gauss noise［D］. Zhengzhou: Henan University of Technology, 2011:53-60. (in Chinese)

[1]	LI Dian-qi， DUAN Yong. Implementation of Active Disturbance Rejection Control of Robot by Tracking Differentiator [J]. Acta Armamentarii, 2016, 37(9): 1721-1729.
[2]	MENG Ke-zi, ZHOU Di. H_∞ Guidance Law Accounting for Dynamics of Missile Autopilot [J]. Acta Armamentarii, 2016, 37(7): 1194-1202.
[3]	WANG Jie， XIONG Zhi， XING Li， DAI Yi-jie, HUA Bing, LIU Jian-ye. Online Calibration of IMU errors of Inertial Navigation System Based on Innovation-based Adaptive Filtering [J]. Acta Armamentarii, 2016, 37(7): 1203-1213.
[4]	ZHANG Fu-bin, MA Peng, WANG Zhi-hui. SINS/DVL Integrated Navigation Algorithm Based on Transversal Coordinate Frame in Polar Region [J]. Acta Armamentarii, 2016, 37(7): 1229-1235.
[5]	YU Xiao-ting， YU Feng， HE Zhen， XIONG Zhi， WANG Zhen-yu. Virtual Sliding Mode Control-based Attitude Estimation for Non-cooperative Spacecraft [J]. Acta Armamentarii, 2016, 37(7): 1282-1290.
[6]	DUAN Mei-jun, ZHOU Di. A Guidance Law with Finite Time under Control Variable Constraint [J]. Acta Armamentarii, 2016, 37(6): 1030-1037.
[7]	JIN Ying-lian, REN Jie, FENG Wei-bo, LI Jian-jun, WANG Bin-rui. Gait Analysis of an Inchworm-like Robot Climbing on Curved Surface and CPG-based Planning [J]. Acta Armamentarii, 2016, 37(6): 1104-1110.
[8]	CHEN Chen， MA Guang-fu， SUN Yan-chao， LI Chuan-jiang. Recursive Sliding Mode Control for Hypersonic Vehicle Based on Nonlinear Disturbance Observer [J]. Acta Armamentarii, 2016, 37(5): 840-850.
[9]	FENG Ka-li， LI An， QIN Fang-jun， LI Feng. Temperature Error Compensation Method Based on Adaptive Neuro Fuzzy Inference for Fiber-optic Gyro [J]. Acta Armamentarii, 2016, 37(4): 641-647.
[10]	ZHANG Chun-yan, SONG Jian-mei, HOU Bo, ZHANG Min-qiang. Cooperative Guidance Law with Impact Angle and Impact Time Constraints for Networked Missiles [J]. Acta Armamentarii, 2016, 37(3): 431-438.
[11]	DONG Zao-peng， WAN Lei， SUN Yu-shan， LIU Tao， LI Yue-ming， ZHANG Guo-cheng. Trajectory Tracking Control of an Underactuated Unmanned Marine Vehicle Based on Asymmetric Model [J]. Acta Armamentarii, 2016, 37(3): 471-481.
[12]	DU Ming-fang, WANG Jun-zheng, LI Duo-yang, HE Yu-dong. Ground Robot Multi-scale Road Perception Based on Semantic Tree MRF Model [J]. Acta Armamentarii, 2016, 37(3): 512-517.
[13]	LIU Ming-yong, ZHU Li, DONG Hai-xia. Research on Gyroscope Array Based on Kalman Filter [J]. Acta Armamentarii, 2016, 37(2): 272-278.
[14]	ZHAO Hui, XIONG Zhi, SHI Li-juan, YU Feng, LIN Ai-jun. A SINS/STAR Integrated Navigation Method Based on Online Estimation of Gyroscope Error in Inertial Coordinate [J]. Acta Armamentarii, 2016, 37(12): 2259-2267.
[15]	WANG Bin-rui, REN Jie, XU Hai-dong, BAO Chun-lei. Detection and Identification of Axial and Radial Impacts on Pneumatic Muscle [J]. Acta Armamentarii, 2016, 37(10): 1896-1901.