﻿ 导航定位中地磁测量误差补偿技术研究
 舰船科学技术  2019, Vol. 41 Issue (6): 125-128 PDF

Research on geomagnetic measurement error compensation in navigation and localization
YANG Yun-tao
Xiamen University Tan Kah Kee College, Zhangzhou 363105, China
Abstract: High-precision geomagnetic measurement is the key technology in geomagnetic matching localization, which needs real-time measurement of geomagnetic field data to provide a basis for matching localization algorithm. The interference magnetic field composed of steel members on navigation carrier is the main source of geomagnetic measurement error. Based on the analysis of the geomagnetic measurement error compensation model, this paper proposes to eliminate the measurement error by using the twelve-constant coefficient compensation algorithm in view of the interference magnetic field composed of various steel components on the carrier. By using the experimental data, the effect of error compensation is compared and analyzed, and the solution is put forward, which effectively improves the precision of geomagnetic survey.
Key words: navigation and localization     geomagnetic measurement     error compensation
0 引　言[1]

1 误差补偿算法

 图 1 地磁测量示意图 Fig. 1 Geomagnetic measurement diagram
 ${F_{mx}} \!=\! {F_x} \!+\! {F_{ix}} \!+\! {F_{cx}};{F_{my}} \!=\! {F_y} \!+\! {F_{iy}} \!+\! {F_{cy}};{F_{mz}} \!=\!\! {F_z} \!+\! {F_{iz}} \!+\! {F_{cz}}\text{。}$

 ${F_{ix}} = (3\mu M/8 {\text{π}} {r^3})\sin 2\alpha \cos \beta \text{，}$ (1)
 ${F_{iv}} = (3\mu M/8 {\text{π}} {r^3})\sin 2\alpha \sin \beta \text{，}$ (2)
 ${F_{iz}} = (\mu M/2 {\text{π}} {r^3})(1 - 1.5{\sin ^2}\alpha )\text。$ (3)

 $\begin{split} &\left[ {\begin{array}{*{20}{l}} {{F_{mx}} - {F_{cx}}}\\ {{F_{my}} - {F_{cy}}}\\ {{F_{mz}} - {F_{cz}}} \end{array}} \right] =\\ &\scriptsize\left[ {\begin{array}{*{20}{c}} {\frac{{\mu {\lambda _x}}}{{2 {\text{π}} {r^3}}}(1 - \frac{3}{2}{{\sin }^2}{\alpha _x}) + 1}&{ - \frac{{3\mu {\lambda _y}}}{{8 {\text{π}} {r^3}}}\sin 2{\alpha _y}\sin {\beta _y}}&{\frac{{3\mu {\lambda _z}}}{{8 {\text{π}} {r^3}}}\sin 2{\alpha _z}\cos {\beta _z}}\\ {\frac{{3\mu {\lambda _x}}}{{8 {\text{π}} {r^3}}}\sin 2{\alpha _x}\sin {\beta _x}}&{\frac{{\mu {\lambda _y}}}{{2 {\text{π}} {r^3}}}(1 - \frac{3}{2}{{\sin }^2}{\alpha _y}) + 1}&{\frac{{3\mu {\lambda _z}}}{{8 {\text{π}} {r^3}}}\sin 2{\alpha _z}\sin {\beta _z}}\\ { - \frac{{3\mu {\lambda _x}}}{{8 {\text{π}} {r^3}}}2\sin {\alpha _x}\cos {\beta _x}}&{ - \frac{{3\mu {\lambda _y}}}{{8 {\text{π}} {r^3}}}\sin 2{\alpha _y}\cos {\beta _y}}&{\frac{{\mu {\lambda _z}}}{{2 {\text{π}} {r^3}}}(1 - \frac{3}{2}{{\sin }^2}{\alpha _z}) + 1} \end{array}} \right] \times \!\!\!\!\! \\ & \left[ {\begin{array}{*{20}{l}} {{F_{x'''}}}\\ {{F_{y'''}}}\\ {{F_{z'''}}} \end{array}} \right]\text{。} \end{split}$ (4)

 $\left[ \begin{array}{l} {F_{mx}} - {F_{cx}}\\ {F_{my}} - {F_{cy}}\\ {F_{mz}} - {F_{cz}} \end{array} \right] = \left[ {\begin{array}{*{20}{c}} {{k_{11}}}&{{k_{12}}}&{{k_{13}}}\\ {{k_{21}}}&{{k_{22}}}&{{k_{23}}}\\ {{k_{31}}}&{{k_{32}}}&{{k_{33}}} \end{array}} \right]\left[ \begin{array}{l} {F_{x'''}}\\ {F_{y'''}}\\ {F_{z'''}} \end{array} \right]\text{。}$ (5)

2 实验

 图 2 地磁测量误差补偿平台 Fig. 2 Magnetic measurement error compensation platform

3 误差补偿精度对比

 ${f_1} = (\Delta {F_a}/\Delta {F_f}) \times 100\%\text{。}$ (6)

 ${f_2} = (\Delta {F_a}/F)\times100\% {f_1} = (\Delta {F_a}/\Delta {F_f})\times100\%\text{，}$ (7)

4 结　语

12常系数法地磁测量误差补偿算法对于导航载体强、弱磁场的干扰均有较高的补偿精度。载体干扰磁场较强时，要优于载体磁场较弱时的地磁测量误差补偿率，在实际应用中，传感器尽量安装在距离钢铁构件较远的位置。

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