﻿ 基于递推更新卡尔曼滤波的磁偶极子目标跟踪<sup>*</sup>
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Magnetic dipole target tracking based on recursive update Kalman filter
WU Yuanfu, SUN Yue
School of Automation, Chongqing University, Chongqing 400044, China
Received: 2016-08-30; Accepted: 2016-10-28; Published online: 2016-11-29 08:55
Foundation item: National Natural Science Foundation of China (51509252)
Corresponding author. SUN Yue, E-mail:syue06@cqu.edu.cn
Abstract: The magnetic target tracking problem is addressed in this paper by establishing the discrete state-space model on the basis of the equivalent magnetic dipole model in order to formulate the real-time magnetic dipole target tracking problem as filtering estimation problem of state-space model. Then a novel filtering approach with the recursive update process is proposed to address the divergence problem of magnetic target tracking under large prior error condition when using present Kalman-type filters. The one-step measurement update is replaced by recursive update process; hence the large nonlinearized error caused by large prior error is reduced in each recursive step. The proposed algorithm is tested by simulation and real-world magnetic data. Both results validate the superior performance in comparison with present filters in terms of accuracy and convergence, and the capacity to suppress the divergence problem caused by large prior error in magnetic dipole target tracking.
Key words: magnetic dipole     tracking     nonlinear filtering     linearization     Kalman filter

1 磁性目标跟踪的状态空间描述

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2 递推更新卡尔曼滤波

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3 结果与分析

3.1 仿真实验分析

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 图 1 Ψ=π/3时位置和磁矩分量RMSE Fig. 1 RMSE of position and magnetic moment component at Ψ=π/3
 图 2 Ψ=π/8时位置和磁矩分量RMSE Fig. 2 RMSE of position and magnetic moment component at Ψ=π/8
 图 3 Ψ=π/16时位置和磁矩分量RMSE Fig. 3 RMSE of position and magnetic moment component at Ψ=π/16

3.2 实测数据测试

 图 4 车辆转弯通过测量点 Fig. 4 Vehicle making turn at measuring position

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 图 5 降采样后的运动车辆磁场测量数据 Fig. 5 Motion vehicle magnetic data after downsampling process

 图 6 不同初值条件下各算法对实测数据的跟踪处理结果 Fig. 6 Real-world data tracking and processing results by each algorithm under different initializing conditions

 算法 r* 偏离实际初始位置 接近实际初始位置 EKF 9.363×104 9.285×104 UKF 1.179×105 9.635×104 CKF 9.453×105 1.623×107 PUKF 4.722×105 3.725×103 PCKF 1.504×105 2.341×106 RUKF 8.356×104 1.538×103

4 结论

1) RUKF算法具有良好的准确性和强收敛性, 有效抑制了大初始误差导致的滤波发散, 适于处理实际应用中初始条件未知条件下的磁性目标跟踪问题。

2) 若进一步将RUKF算法与多初值假设方法结合, 可大幅减少并行滤波器数量, 相比现有算法更适合工程实现。

3) 对于一般非线性滤波应用, RUKF算法作为通用算法的性能需针对具体问题, 尤其是包含非线性过程模型的情况进行分析和验证。

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#### 文章信息

WU Yuanfu, SUN Yue

Magnetic dipole target tracking based on recursive update Kalman filter

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(9): 1805-1812
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0694