Two-Point Positioning Method with Magnetic Gradient Tensor Invariant Constraints
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摘要: 文中针对单点磁梯度张量定位方法受地磁场估计误差影响较大, 同时多点磁梯度张量定位方法容易陷入局部最优解等问题, 提出一种两点磁梯度张量定位方法。该方法在单点磁梯度张量定位算法的基础上, 采用两点磁梯度张量测量数据, 叠加张量几何不变量的约束条件, 构建关于目标位置坐标的非线性目标函数, 采用基于自然选择的粒子群算法对目标位置坐标进行求解。仿真实验表明, 文中提出的方法受地磁场估计误差影响较小, 且能实现对全局最优解的搜索, 定位精度较高。仿真分析不同系统基线长度和磁力仪灵敏度条件下文中方法对磁性目标的定位效果可知, 当系统的基线长度越大, 磁力仪的灵敏度越高, 磁性目标定位误差越小。Abstract: Single-point magnetic gradient tensor positioning methods are greatly affected by geomagnetic field estimation errors, and multi-point magnetic gradient tensor positioning methods are easy to get trapped in local optima. To address these issues, a two-point magnetic gradient tensor positioning method was proposed. Based on the single-point magnetic gradient tensor positioning algorithm, this method used two-point magnetic gradient tensor measurement data and superimposed the constraints of tensor geometric invariants to construct a nonlinear objective function about the target position coordinates, and it used the natural selection-based particle swarm optimization(NSPSO) algorithm to solve the target position coordinates. Simulation experiments demonstrate that the proposed method is less affected by geomagnetic field estimation errors and can search for global optima. It exhibits high localization accuracy. The simulation analysis considers the positioning performance of the proposed method for magnetic targets under different system baseline lengths and magnetometer sensitivities. The results indicate that as the system baseline length and the magnetometer sensitivity improve, the positioning error for magnetic targets decreases.
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图 2 搭载十字形磁梯度张量系统的UUV运动示意图
Figure 2. Motion of UUV equipped with a cross magnetic gradient tensor system
图 4 不同磁力仪灵敏度下文中方法定位误差
Figure 4. Positioning error of the proposed method under different magnetometer sensitivities
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