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

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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

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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

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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)

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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)

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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)

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图 5 总均方误差vs.渐进(迭代)次数

Fig. 5 TRMSE vs. progressive (recursive) steps

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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

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图 7 PBF随ϵ变化的总均方误差

Fig. 7 TRMSE of PBF vs. variation of ϵ

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图 8 三轴磁强计

Fig. 8 Magnetometer

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图 9 磁体目标

Fig. 9 Magnet target

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图 10 参考坐标系

Fig. 10 Reference coordinate

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图 11 参考轨迹

Fig. 11 Reference trajectory

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图 12 实测跟踪试验结果

Fig. 12 Experimental results of target tracking

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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

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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

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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

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