十字形磁梯度张量系统的误差校正

针对十字形磁梯度张量系统中的单磁力仪误差(三轴灵敏度偏差、非正交误差和零点漂移误差)以及磁力仪之间存在的不对正误差,提出了十字形磁梯度张量系统的误差校正方法。首先,建立单磁力仪误差模型,采用基于椭球约束的最小二乘拟合算法对磁力仪的测量数据进行拟合从而得到椭球拟合参数;然后,接着利用Cholesky分解得到单磁力仪误差校正矩阵;最后在单磁力仪误差校正的基础上,利用正交Procrustes方法对不同磁力仪间的测量数据进行拟合从而得到磁力仪间的不对正误差校正矩阵。对提出的方法进行仿真与实测实验验证,实验结果表明:经过校正,磁梯度张量各分量的最大波动量由10 049nT/m降到52nT/m。提出的校正方法可以基本消除十字形磁梯度张量系统的误差,提高测量结果的准确度,且方法操作简单,不需要高精度的三轴无磁转台等设备,具有较高的实用价值。

Error calibration of cross magnetic gradiometer

For the vector magnetometer errors (scale factors,non-orthogonal error,bias) and misalignment error of the cross magnetic gradiometer,an error calibration method was proposed in this paper.Firstly,an error calibration model of the vector magnetometer errors was established,ellipsoid fitting parameters are calculated by the least square algorithm under ellipsoid restriction for fitting the measurement data to an ellipsoid.Then the Cholesky factorization was used to calculate the error calibration matrix of the vector magnetometer errors,and then the misalignment error calibration matrix could be solved by the orthogonal Procrustes method.Finally,simulations and experiments were carried out for verification of the proposed error calibration method.The experiment result shows:after calibration,the maximum fluctuation quantity of all components of the magnetic gradient tensor reduces from 10 049 nT/m to 52 nT/m.The proposed error calibration method can effectively calibrate the cross magnetic gradiometer,and the cross magnetic gradiometer can be calibrated without using high precision tri-axial non-magnetic platform,the proposed method has high value for practical application.