基于递推最小二乘的三轴磁强计在线自校正方法
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摘要
针对现有三轴磁强计误差校正方法存在计算量大、依赖外界参考信息、不能在线校正等问题,提出一种基于递推最小二乘的误差在线自校正方法。根据Poisson方程对磁场测量模型的描述,导出磁场矢量误差校正模型;基于椭球假设理论,建立校正模型与椭球曲面方程系数之间的关系;推导了基于递推最小二乘的椭球方程系数在线辨识的实现过程,进而求得误差校正参数。实验结果表明:提出的方法能有效校正软磁和硬磁效应引起的数据畸变;采样点磁场强度最大波动幅度由67. 112 8μT降低至14. 064 8μT,误差标准差由15. 828 7μT降低至6. 345 1μT,适用于无外部参考基准下三轴磁强计的误差自动校正。
To solve the problems existing in three-axis magnetometer error correction method as such amount of computation is large,reliance on outside reference information is excessive,and online calibration is unrealizable,an online self-calibration method based on recursive least square is proposed. According to description by the Poisson equation on measurement model,magnetic field vector error correction model is derived. Rrelationship between calibration model and coefficients of ellipsoid surface equation is established based on theory of ellipsoid hypothesis. Realization process of on-line identification of coefficients of ellipsoid equation is derived based on recursive least squares,and then obtain error correction parameters. The results show that this method can correct effectively data distortion caused by soft and hard magnetic effects. And the maximum fluctuation range of magnetic field intensity of sampling points is reduced from 67. 112 8 μT to 14. 064 8 μT,and the error standard deviation is reduced from 15. 828 7 μT to 6. 345 1 μT,which indicate that the proposed method is suitable for error selfcalibration of three-axis magnetometer without external reference Benchmark.
To solve the problems existing in three-axis magnetometer error correction method as such amount of computation is large,reliance on outside reference information is excessive,and online calibration is unrealizable,an online self-calibration method based on recursive least square is proposed. According to description by the Poisson equation on measurement model,magnetic field vector error correction model is derived. Rrelationship between calibration model and coefficients of ellipsoid surface equation is established based on theory of ellipsoid hypothesis. Realization process of on-line identification of coefficients of ellipsoid equation is derived based on recursive least squares,and then obtain error correction parameters. The results show that this method can correct effectively data distortion caused by soft and hard magnetic effects. And the maximum fluctuation range of magnetic field intensity of sampling points is reduced from 67. 112 8 μT to 14. 064 8 μT,and the error standard deviation is reduced from 15. 828 7 μT to 6. 345 1 μT,which indicate that the proposed method is suitable for error selfcalibration of three-axis magnetometer without external reference Benchmark.
引文
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[11]吴浩文,杜刚,叶萍,等.基于椭圆假设的磁罗盘航向测量算法研究[J].计算机仿真,2010,27(2):352-355.
[12]张宏欣,周穗华,张伽伟.三轴磁强计实时自校正算法[J].电子学报,2017,45(7):1750-1757.
[13]李智,李翔.基于椭球假设的三轴电子罗盘罗差补偿研究[J].仪器仪表学报,2011,32(10):2210-2215.
[14]刘艳霞,李希胜,窦晓霞.基于椭球假设的三轴磁强计标定算法改进[J].计算机测量与控制,2013,21(6):1590-1593.
[15] Basterretxeairibar I,Sotés I,Uriarte J I. Towards an improvement of magnetic compass accuracy and adjustment[J]. Journal of Navigation,2016,69(6):1325-1340.
[16] Wahlstr9m N,Gustafsson F. Magnetometer modeling and validation for tracking metallic targets[J]. IEEE Transactions on Signal Processing,2014,62(3):545-556.
[2]刘宇,陈俊杰,吴林志,等.微航姿仪的磁力计标定算法及误差补偿研究[J].压电与声光,2017,39(3):392-396.
[3]徐东甫,白越,宫勋,等.多旋翼无人机在变控制量下的三轴磁罗盘校正[J].光学精密工程,2016,24(8):1940-1947.
[4]郭鹏飞,任章,邱海韬,等.一种十二位置不对北的磁罗盘标定方法[J].中国惯性技术学报,2007,15(5):598-601.
[5]范崧伟,卞鸿巍.小型多旋翼无人机三轴电子罗盘设计与误差分析校准[J].舰船电子工程,2013,33(7):113-116.
[6]杨新勇,黄圣国.智能磁航向传感器的研制及误差补偿算法分析[J].北京航空航天大学学报,2004,30(3):244-248.
[7]管斌,高扬,王成宾,等.基于递推最小二乘的在线罗差校正方法[J].中国惯性技术学报,2012,20(1):69-73.
[8]高可,林新华,储志伟,等.无磁转台的电子罗盘误差分离标定方法[J].传感器与微系统,2017,36(2):21-24.
[9]刘诗斌.无人机磁航向测量的自动罗差补偿研究[J].航空学报,2007,28(2):411-414.
[10] Moulin M,Goudon J C,Marsy J M,et al. Process for compensating the magnetic disturbances in the determination of a magnetic heading,and devices for carrying out this process:US,US4414753[P]. 1983—06—01.
[11]吴浩文,杜刚,叶萍,等.基于椭圆假设的磁罗盘航向测量算法研究[J].计算机仿真,2010,27(2):352-355.
[12]张宏欣,周穗华,张伽伟.三轴磁强计实时自校正算法[J].电子学报,2017,45(7):1750-1757.
[13]李智,李翔.基于椭球假设的三轴电子罗盘罗差补偿研究[J].仪器仪表学报,2011,32(10):2210-2215.
[14]刘艳霞,李希胜,窦晓霞.基于椭球假设的三轴磁强计标定算法改进[J].计算机测量与控制,2013,21(6):1590-1593.
[15] Basterretxeairibar I,Sotés I,Uriarte J I. Towards an improvement of magnetic compass accuracy and adjustment[J]. Journal of Navigation,2016,69(6):1325-1340.
[16] Wahlstr9m N,Gustafsson F. Magnetometer modeling and validation for tracking metallic targets[J]. IEEE Transactions on Signal Processing,2014,62(3):545-556.