基于椭球曲面拟合的三维磁罗盘误差补偿算法

Three-dimensional magnetic compass error compensation algorithm based on ellipsoid surface fitting

针对现有三维磁罗盘误差补偿速度慢、需专用转台、野外使用不便的问题,提出了一种建立总磁场的不等边椭球曲面数学模型进行误差补偿的方法。首先根据Poisson方程描述的总磁场测量模型,得出一般椭球曲面模型,然后,采用牛顿迭代法对椭球曲面方程线性化,分别使用最小二乘法和总体最小二乘法计算线性化方程,推导椭球曲面拟合的数学公式,计算椭球曲面参数,最后,利用最小二乘法提出并推导参数初值的计算公式,给出了选取数据点的方法。实验结果表明,仅手持磁罗盘在各象限旋转即可实现误差补偿,航向测量精度可达0.8°,补偿精度与传统的转台补偿基本相同,而补偿方式更为灵活,适用于无转台设备的野外环境测量使用。

To solve the problems in existing 3D magnetic compasses（such as,error compensation is slow,special turntable is needed,and field applying is inconvenient）,we put forward a method to establish a scalene ellipsoid surface mathematical model of the general magnetic field to compensate errors.First,we established the ellipsoid surface model according to the general magnetic field model presented by Poisson equation.Then,we linealized the ellipsoid surface equation using Newton iteration method,and used least square method and total least square method respectively to calculate linear equations,derive the mathematical forum of ellipsoid surface fitting and the ellipsoid surface parameters.Finally,we derived the calculation forum of parameters’ initial value by using least square method,and gave the method of selecting data point.The results show that the errors can be compensated only by using a hand to hold a magnetic compass and let it spin in all quadrants.And the heading measurement precision can reach 0.8°.The compensation precision of this method is almost the same as that of traditional turntable compensation methods,but it is more agile and fit for the field use with no turntable equipment.