School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China.
School of Electrical and Information Engineering, The University of Sydney, Camperdown, NSW 2006, Australia.
Sensors (Basel). 2018 Sep 29;18(10):3284. doi: 10.3390/s18103284.
The geomagnetic field is as fundamental a constituent of passive navigation as Earth's gravity. In cases where no other external attitude reference is available, for the direct heading angle estimation by a typical magnetic compass, a two-step optimized correction algorithm is proposed to correct the model coefficients caused by hard and soft iron nearby. Specifically, in Step 1, a Levenberg-Marquardt (L-M) fitting estimator with an ellipsoid constraint is applied to solve the hard magnetic coefficients. In Step 2, a Lagrange multiplier estimator is used to deal with the soft magnetic iron circumstance. The essential attribute of "the two-step" lies in its eliminating the coupling effects of hard and soft magnetic fields, and their mutual interferences on the pure geomagnetic field. Under the conditions of non-deterministic magnetic interference sources with noise, the numerical simulation by referring to International Geomagnetic Reference Field (IGRF), and the laboratory tests based upon the turntable experiments with Honeywell HMR3000 compass (Honeywell, Morristown, NJ, USA) conducted, the experimental results indicate that, in the presence of the variation of multi-magnetic interferences, the RMSE (Root Mean Square Error) value of the estimated total magnetic flux density by the proposed two-step estimator falls to 0.125 μT from its initial 2.503 μT, and the mean values of the heading angle error estimates are less than 1°. The proposed solution therefore, exhibits ideal convergent properties, fairly meeting the accuracy requirements of non-tactical level navigation applications.
地磁场是被动导航的基本组成部分，就像地球重力一样。在没有其他外部姿态参考的情况下，对于典型的磁罗盘进行直接航向角估计，提出了一种两步优化校正算法，以校正由于附近硬铁和软铁引起的模型系数。具体来说，在步骤 1 中，应用具有椭球约束的 Levenberg-Marquardt（L-M）拟合估计器来求解硬磁系数。在步骤 2 中，使用拉格朗日乘子估计器来处理软磁铁情况。“两步”的本质属性在于消除硬磁和软磁场的耦合效应，以及它们对纯地磁场的相互干扰。在存在具有噪声的不确定磁场干扰源的情况下，通过参考国际地磁参考场（IGRF）进行数值模拟，并基于 Honeywell HMR3000 罗盘（Honeywell，Morristown，NJ，USA）的转台实验进行实验室测试，实验结果表明，在多磁干扰变化的情况下，所提出的两步估计器估计的总磁通密度的均方根误差（RMSE）值从初始的 2.503 μT 降至 0.125 μT，航向角误差估计的平均值小于 1°。因此，所提出的解决方案表现出理想的收敛特性，完全满足非战术级导航应用的精度要求。
