平面十字磁梯度张量系统的两步线性校正

磁梯度张量系统的测量精度受限于磁传感器的零漂、灵敏度差异和三轴非正交性等系统误差以及各传感器轴系间的非对准误差。构建了平面十字磁梯度张量系统的误差参数线性模型,提出了两步线性校正法。利用两个非线性变量转换构建单磁传感器系统误差的线性方程组,对误差参数进行最小二乘估计,将传感器实际输出校正为各自理想正交输出;利用旋转矩阵构建各传感器理想正交轴间非对准误差的线性方程组并求出最小二乘解,将各传感器输出校正到参考平台框架正交坐标系上。两步校正过程均无数学简化。仿真与实验表明,相比忽略二阶及以上高阶小量的常规线性校正,提出的张量系统两步线性校正法更为精确,误差参数仿真估计准确率高于93%,实测校正后总场强度均方根误差小于13 n T,张量分量均方根误差小于90 n T/m。

Two step linear calibration of planar cross magnetic gradient tensor system

The measurement accuracy of magnetic gradient tensor system is limited by the system errors such as zero drift, sensitivity difference and the three axis non orthogonality of the magnetic sensor, as well as the misalignment errors among the axis systems of different sensors. In this paper, an error parameter linear model of the planar cross magnetic gradient tensor system is constructed, and a two step linear calibration method is proposed. Firstly, the linear equation set of single magnetic sensor system error is constructed by using two nonlinear variable conversions, and the error parameters are estimated by least squares method. The actual output of the sensor is calibrated to its ideal orthogonal output. Secondly, the linear equation set of the misalignment errors among the ideal orthogonal axes of the sensors is constructed by using the rotation matrices and the least square solution is obtained. The outputs of sensors are calibrated to the orthogonal coordinate system in reference platform frame. Both processes have no any mathematical simplification. Simulations and experiments show that the proposed two step linear calibration method of the tensor system is more accurate compared with the conventional linear calibration method neglecting the second or higher order small quantities. The simulated estimation accuracy of the error parameters is better than 93%, the root mean square error of the actually tested total field intensity is less than 13 nT and the root mean square error of the tensor components is less than 90 nT/m in the experiments after calibration.