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全最小二乘法在姿态参数测量中的应用研究

         

摘要

In accordance with the measuring system established by 3-axes GMR magnetic sensor for attitude of flight body, the mathematical relationship between geomagnetic field and attitude angle is derived, and the factors affecting the measurement accuracy are analysed. Through comparing the corrected results for parameters of magnetic sensor by using absolute least squares method and relative least squares method, it is found that because the conventional least squares method only considers the single factor, larger fluctuation and error exist in the three-component of magnetic filed and the total magnetic field value. In order to solve this problem, overall correction is conducted to the parameters of magnetic sensor by adopting the total least squares method. The experiments on non-magnetic turntable prove that this method improves the measurement accuracy of magnetic field and attitude angle.%针对由三轴GMR磁传感器构建的飞行体姿态测量系统,推导出地磁场与姿态角间的数学关系,分析了影响测量精度的因素。通过对比绝对最小二乘法和相对最小二乘法对磁传感器参数的修正结果,发现由于常规最小二乘法只考虑单一因素,导致由测量数据求出的磁场三分量和总磁场值仍存在较大的波动和误差。为解决这一问题,采用全最小二乘法对磁传感器参数进行整体修正。经无磁转台试验表明,该方法极大地提高了磁场和姿态角的测量精度。

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