磁偶极子跟踪的渐进贝叶斯滤波方法

张宏欣; 周穗华; 张伽伟

doi:10.16383/j.aas.2017.c160052

磁偶极子跟踪的渐进贝叶斯滤波方法

doi: 10.16383/j.aas.2017.c160052

1.
海军工程大学兵器工程系武汉 430033

基金项目:

国家自然科学基金 51509252

详细信息

作者简介:
张宏欣海军工程大学兵器工程系博士研究生. 2010年获得西安理工大学信息与控制系学士学位.主要研究方向为非线性估计和滤波, 及其目标跟踪应用. E-mail:mylifeforthebattle@hotmail.com

张伽伟海军工程大学兵器工程系讲师. 2013年获得海军工程大学博士学位.主要研究方向为军用目标信息处理, 舰船物理场. E-mail: gaweizhang@163.com

通讯作者:
周穗华海军工程大学兵器工程系教授. 1990年获得海军工程学院博士学位.主要研究方向为军用目标信息处理, 武器系统总体设计. E-mail: zzs_rice@163.com

计量
- 文章访问数: 3152
- HTML全文浏览量: 280
- PDF下载量: 615
- 被引次数: 0
出版历程
- 收稿日期: 2016-01-19
- 录用日期: 2016-07-20
- 刊出日期: 2017-05-01

A Progressive Bayesian Filtering Approach to Magnetic

1.
Department of Weaponry Engineering, Naval University of Engineering, Wuhan 430033

Funds:

National Natural Science Foundation of China 51509252

More Information

Author Bio:
Ph.D. candidate in the Department of Weaponry Engineering, Naval University of Engineering. He received his bachelor degree from Xi'an University of Technology in 2010. His research interest covers nonlinear estimation and filtering, especially their applications on target tracking

Lecturer in the Department of Weaponry Engineering, Naval University of Engineering. He received his Ph.D. degree from Naval Institute of Engineering in 2013. His research interest covers military target signal processing, physical field of vessel

Corresponding author: ZHOU Sui-Hua rofessor in the Department of Weaponry Engineering, Naval University of Engineering. He received his Ph.D. degree from Naval Institute of Engineering in 1990. His research interest covers military target signal processing and integrated design of weapon system. Corresponding author of this paper

摘要

摘要: 提出一种新的非线性滤波器应用于磁偶极子目标跟踪问题.建立了跟踪问题的状态空间模型, 在此基础上, 从高斯矩近似误差的角度分析了现有卡尔曼滤波更新在磁偶极子跟踪中的问题.对此, 将贝叶斯更新过程等效为求解连续时间上的渐进贝叶斯问题, 在线性高斯条件下推导了其解析解, 表明渐进贝叶斯更新可等效为定常系统的Kalman-Bucy滤波器; 进一步采用一阶Taylor展开得到非线性近似解表达式, 导出一种渐进贝叶斯滤波器, 从理论上分析了与现有方法的异同.仿真与实测磁目标跟踪试验结果表明, 渐进贝叶斯滤波器具有良好的精度和收敛性, 能够有效抑制磁目标跟踪中由于大初始误差导致的性能下降和滤波发散, 且计算效率与扩展卡尔曼滤波器相当, 适于实际应用.
- 磁偶极子 /
- 跟踪 /
- 状态--空间模型 /
- 非线性滤波
Abstract: A nonlinear filter is proposed for magnetic dipole tracking. A state-space model of magnetic dipole target is established. The difficulty of ordinary Kalman type measurement update is analyzed in a perspective of the error existing in typical Gaussian moment approximation strategies. In this regard, the traditional Bayesian update in discrete-time is reformulated to a continuous progressive Bayesian problem, and the analytical solution is derived under linear Gaussian condition. It is shown that the linear Gaussian progressive Bayesian update is naturally interpreted as a Kalman-Bucy filter for non-stochastic constant estimation. Further, the first-order approximation using Taylor series expansion is applied to a derived nonlinear progress Bayesian filter (PBF), and theoretical comparison with the existing method is presented. Simulation and real-world magnetic dipole tracking experiments are performed to demonstrate the effectiveness of PBF. Both results suggest that our filter not only effectively suppresses the performance degeneration and filter divergence caused by large initialization error, but also has straightforward implementation resembling that of extended Kalman filter, which is suitable for practical magnetic dipole tracking application.
- Magnetic dipole /
- tracking /
- state-space model /
- nonlinear

HTML全文

图 1 不同初始误差条件下先验观测矩近似结果

Fig. 1 Prior moment approximation under different initial error covariance

下载: 全尺寸图片幻灯片

图 2 位置分量与磁矩分量估计RMSE(ψ=π/3)

Fig. 2 RMSE of position and magnetic moment estimation(ψ=π/3)

下载: 全尺寸图片幻灯片

图 3 位置分量与磁矩分量估计RMSE(ψ=π/8)

Fig. 3 RMSE of position and magnetic moment estimation(ψ=π/8)

下载: 全尺寸图片幻灯片

图 4 位置分量与磁矩分量估计RMSE(ψ=π/16)

Fig. 4 RMSE of position and magnetic moment estimation(ψ=π/16)

下载: 全尺寸图片幻灯片

图 5 总均方误差vs.渐进(迭代)次数

Fig. 5 TRMSE vs. progressive (recursive) steps

下载: 全尺寸图片幻灯片

图 6 各算法执行时间随渐进(迭代)次数增长

Fig. 6 quad Running time vs. progressive (recursive) steps

下载: 全尺寸图片幻灯片

图 7 PBF随ϵ变化的总均方误差

Fig. 7 TRMSE of PBF vs. variation of ϵ

下载: 全尺寸图片幻灯片

图 8 三轴磁强计

Fig. 8 Magnetometer

下载: 全尺寸图片幻灯片

图 9 磁体目标

Fig. 9 Magnet target

下载: 全尺寸图片幻灯片

图 10 参考坐标系

Fig. 10 Reference coordinate

下载: 全尺寸图片幻灯片

图 11 参考轨迹

Fig. 11 Reference trajectory

下载: 全尺寸图片幻灯片

图 12 实测跟踪试验结果

Fig. 12 Experimental results of target tracking

下载: 全尺寸图片幻灯片

表 1 仿真场景参数

Table 1 Parameter of simulation scenario

参数(单位)	量值
r₀(m)	[-150, -150, 50]^T
v₀(m/s)	[8, 8, 0.6]^T
M0(A·m²)	10^6·[6.0, -9.0, 9.0]^T
V(m³)	10³
o_{1, 2}(m)	[-60, ±6, 10]^T
T_N, T_s(s)	60, 0.5

下载: 导出CSV

表 2 滤波初始条件

Table 2 Filter initialization

参数	初值(${{{\mathit{\boldsymbol{\hat{x}}}}}_{0}}$)	初始均方误差(P₀)
${{{\mathit{\boldsymbol{\hat{r}}}}}_{0}}$	R(ψ_n)·[-160, -160, { 40}]^T	${{I}_{3\times 3}}{{{\mathit{\boldsymbol{\tilde{r}}}}}_{0}}{{I}_{3\times 3}}{{{\mathit{\boldsymbol{\tilde{r}}}}}_{0}}$
${{{\mathit{\boldsymbol{\hat{v}}}}}_{0}}$	[5, 5, 0.2]^T	diag{2², 2², 2²}
${{{\mathit{\boldsymbol{\hat{M}}}}}_{0}}$	[0, 0, 0]^T	diag{10¹³, 10¹³, 10¹³}
${\hat{V}}$	0	2·10³

下载: 导出CSV

表 3 归一化后验残差平方和

Table 3 Normalized posterior residual square

	r^*
	试验1	试验2
RU-EKF	1.913×10⁵	7.908×10⁵
RU-CKF	2.286×10⁵	1.363×10⁶
PEKF	1.891×10⁵	2.142×10⁵
PUKF	2.076×10⁵	8.071×10⁷
PCKF	2.188×10⁶	2.424×10⁹
PBF	1.746×10⁵	1.703×10⁵

下载: 导出CSV

参考文献(28)

[1]	McAulay A. Computerized model demonstrating magnetic submarine localization. IEEE Transactions on Aerospace and Electronic Systems, 1977, AES-13(3): 246-254 doi: 10.1109/TAES.1977.308392
[2]	McFee J E, Das Y, Ellingson R O. Locating and identifying compact ferrous objects. IEEE Transactions on Geoscience and Remote Sensing, 1990, 28(2): 182-193 doi: 10.1109/36.46697
[3]	Pham D M, Aziz S M. A real-time localization system for an endoscopic capsule using magnetic sensors. Sensors, 2014, 14(11): 20910-20929 doi: 10.3390/s141120910
[4]	Birsan M. Recursive Bayesian method for magnetic dipole tracking with a tensor gradiometer. IEEE Transactions on Magnetics, 2011, 47(2): 409-415 doi: 10.1109/TMAG.2010.2091964
[5]	Wahlström N. Target Tracking Using Maxwell0s Equations. [Master dissertation], Linköping University, Sweden, 2010
[6]	宋宇, 孙富春, 李庆玲.移动机器人的改进无迹粒子滤波蒙特卡罗定位算法.自动化学报, 2010, 36(6): 851-857 http://www.aas.net.cn/CN/abstract/abstract13665.shtml Song Yu, Sun Fu-Chun, Li Qing-Ling. Mobile robot Monte Carlo localization based on improved unscented particle filter. Acta Automatica Sinica, 2010, 36(6): 851-857 http://www.aas.net.cn/CN/abstract/abstract13665.shtml
[7]	Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269 doi: 10.1109/TAC.2009.2019800
[8]	Wahlström N, Gustafsson F. Magnetometer modeling and validation for tracking metallic targets. IEEE Transactions on Signal Processing, 2014, 62(3): 545-556 doi: 10.1109/TSP.2013.2274639
[9]	Andrews A P. Method of Estimating Location and Orientation of Magnetic Dipoles Using Extended Kalman Filtering and Schweppe Likelihood Ratio Detection, U. S. Patent 5381095, January 1995.
[10]	姚振宁, 刘大明, 刘道胜, 朱兴乐.基于不敏粒子滤波的水中非合作磁性目标实时磁定位方法.物理学报, 2014, 63(22): 309-314 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201422042.htm Yao Zhen-Ning, Liu Da-Ming, Liu Sheng-Dao, Zhu XingLe. A real-time magnetic localization method of underwater non-cooperative magnetic targets based on unscented particle filter. Acta Physica Sinica, 2014, 63(22): 309-314 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201422042.htm
[11]	Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with Applications to Tracking and Navigation. New York: John Wiley & Sons, 2001.
[12]	Zhang K. A new GPS/RFID integration algorithm based on iterated reduced sigma point Kalman filter for vehicle navigation. In: Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation. Seattle, USA: The Institute of Navigation, 2009. 1604-1611
[13]	Zhan R H, Wan J W. Iterated unscented Kalman filter for passive target tracking. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(3): 1155-1163 doi: 10.1109/TAES.2007.4383605
[14]	Zanetti R. Adaptable recursive update filter. Journal of Guidance, Control, & Dynamics, 2015, 38(7): 1295-1300
[15]	Huang Y L, Zhang Y G, Li N, Zhao L. Design of sigma-point Kalman filter with recursive updated measurement. Circuits, Systems, & Signal Processing, 2016, 35(5): 1767-1782
[16]	Huang Y L, Zhang Y G, Li N, Zhao L. Gaussian approximate filter with progressive measurement update. In: Proceedings of the 54th Annual Conference on Decision and Control. Osaka, Japan: IEEE, 2015. 4344-4349
[17]	Daum F, Huang J. Nonlinear filters with particle flow induced by log-homotopy. In: Proceedings of the 2009 SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII. Orlando, Florida, USA: SPIE, 2009. DOI: 10.1117/12.814241
[18]	Daum F, Huang J, Noushin A. Coulomb0s law particle flow for nonlinear filters. In: Proceedings of the 2011 SPIE 8137, Signal and Data Processing of Small Targets. San Diego, USA: SPIE, 2011. DOI: 10.1117/12.887514
[19]	Charalampidis D, Jilkov V P, Wu J D. Implementation and performance of FPGA-accelerated particle flow filter. In: Proceedings of SPIE 9596, Signal and Data Processing of Small Targets. San Diego, California, United States: SPIE, 2015. DOI: 10.1117/12.2179546
[20]	Yang T, Laugesen R S, Mehta P G, Meyn S P. Multivariable feedback particle filter. Automatica, 2016, 71: 10-23 doi: 10.1016/j.automatica.2016.04.019
[21]	彭孝东, 张铁民, 李继宇, 陈瑜.基于传感器校正与融合的农用小型无人机姿态估计算法.自动化学报, 2015, 41(4): 854-860 http://www.aas.net.cn/CN/abstract/abstract18659.shtml Peng Xiao-Dong, Zhang Tie-Min, Li Ji-Yu, Chen Yu. Attitude estimation algorithm of agricultural small-UAV based on sensors fusion and calibration. Acta Automatica Sinica, 2015, 41(4): 854-860 http://www.aas.net.cn/CN/abstract/abstract18659.shtml
[22]	Gustafsson F, Hendeby G. Some relations between extended and unscented Kalman filters. IEEE Transactions on Signal Processing, 2012, 60(2): 545-555 doi: 10.1109/TSP.2011.2172431
[23]	Perea L, How J, Breger L, Elosegui P. Nonlinearity in sensor fusion: divergence issues in EKF, modified truncated SOF, and UKF. In: Proceedings of the 2007 AIAA Guidance, Navigation and Control Conference and Exhibit. South Carolina, USA: AIAA, 2007. DOI: 10.2514/6.2007-6514
[24]	Morelande M R, García-Fernáandez A F. Analysis of Kalman filter approximations for nonlinear measurements. IEEE Transactions on Signal Processing, 2013, 61(22): 5477-5484 doi: 10.1109/TSP.2013.2279367
[25]	Jazwinski A H. Stochastic Processes and Filtering Theory. New York: Academic Press, 1970.
[26]	李杰, 陈建兵.随机动力系统中的概率密度演化方程及其研究进展.力学进展, 2010, 40(2): 170-188 doi: 10.6052/1000-0992-2010-2-J2009-105 Li Jie, Chen Jian-Bing. Advances in the research on probability density evolution equations of stochastic dynamical systems. Advances in Mechanics, 2010, 40(2): 170-188 doi: 10.6052/1000-0992-2010-2-J2009-105
[27]	Simon D. Optimal State Estimation. New York: John Wiley & Sons, 2006. 234
[28]	Berntorp K. Feedback Particle Filter: Application and Evaluation, Technical Report TR2015-074, Mitsubishi Electric Research Laboratories, USA, 2015.