The three-axis magnetic sensors are mostly calibrated by scalar method such as ellipsoid fitting and so on, but these methods cannot completely determine the 12 parameters of the error model. A two-stage calibration method based on particle swarm optimization (TSC-PSO) is proposed, which makes full use of the amplitude invariance and direction invariance of Earth’s magnetic field vector.,The TSC-PSO designs two-stage fitness function. Stage 1: design a fitness function of the particle swarm by the amplitude invariance of the Earth’s magnetic field to obtain a preliminary error matrix G and the bias error B. Stage 2: further design the fitness function of the particle swarm by the invariance of the Earth’s magnetic field to obtain a rotation matrix R, thereby determining the error matrix uniquely.,The proposed TSC-PSO can completely determine 12 unknown parameters in error model and further decrease the maximum fluctuation error of the Earth’s magnetic field amplitude and the absolute error of heading.,The proposed TSC-PSO provides an effective solution for three-axis magnetic sensor error compensation, which can greatly reduce the price of magnetic sensors and be used in the fields of Earth’s magnetic survey, drilling and Earth’s magnetic integrated navigation.,The proposed TSC-PSO has significantly improved the magnetic field amplitude and heading accuracy and does not require additional heading reference. In addition, the method is insensitive to noise and initialization conditions, has good robustness and can converge to a global optimum.

中文翻译：

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基于粒子群优化的三轴磁传感器误差两步标定方法

三轴磁传感器大多采用椭球拟合等标量方法进行标定，但这些方法不能完全确定误差模型的12个参数。提出了一种基于粒子群优化的两阶段标定方法(TSC-PSO)，充分利用了地球磁场矢量的幅度不变性和方向不变性。TSC-PSO设计了两阶段适应度函数。第一阶段：根据地球磁场的幅值不变性设计粒子群适应度函数，得到初步误差矩阵G和偏置误差B。 第二阶段：进一步根据地球磁场的不变性设计粒子群适应度函数地球磁场得到一个旋转矩阵R，从而唯一确定误差矩阵。，提出的TSC-PSO可以完全确定误差模型中的12个未知参数，进一步降低地球磁场幅度的最大波动误差和航向绝对误差。提出的TSC-PSO为三轴磁传感器提供了有效的解决方案误差补偿，可大大降低磁传感器的价格，可用于地球磁测、钻井和地磁综合导航等领域。,所提出的TSC-PSO显着提高了磁场幅度和航向精度，不需要附加标题参考。此外，该方法对噪声和初始化条件不敏感，鲁棒性好，能收敛到全局最优。