Calibration of three-axis fluxgate magnetometers with nonlinear least square method

The accuracy of three-axis magnetometers is limited by different scales, bias of each axis and nonorthogonality between axes, which is usually lower than that of scalar magnetometers. In this paper, the nonlinear least square method is proposed to calibrate three-axis magnetometers. The validity of this method was proved by simulation, in which the estimated parameters of the error model are close to prearranged parameters. In experiment, a three-axis fluxgate magnetometer (DM-050), a two dimensional nonmagnetic rotation equipment and a proton magnetometer (GSM-19T) were used. The scalar value of magnetic field was obtained by proton magnetometer and considered to be the true value. The calibration performance of unscented Kalman filter (UKF), two-step algorithm and nonlinear least square were compared. Experimental results show that the error average and standard deviation of nonlinear least square are the least among the three methods. After calibration, the average of scalar error is reduced from −76.2 nT to −0.00093 nT and the standard deviation is reduced from 10.832 nT to 4.298 nT. The results suggest an effective way for the calibration of three-axis fluxgate magnetometers.     

Integrated calibration and magnetic disturbance compensation of three-axis magnetometers

Technological limitations in sensor manufacturing and unwanted magnetic fields will corrupt the measurements of three-axis magnetometers. An experiment with four different magnetic disturbance situations is designed, and the influence of hard-iron and soft-iron material is analyzed. The calibration method with magnetic disturbance parameters is proposed for calibration and magnetic disturbance compensation of three axis magnetometers. It is not necessary to compute pseudo-linear parameters, thus the integrated parameters are computed directly by solving nonlinear equations. To employ this method, a nonmagnetic rotation equipment, a CZM-3 proton magnetometer, a DM-050 three-axis magnetometer, two magnets and two steel tubes are used. Calibration performance is discussed in the four situations. Compared with several traditional calibration methods, experiment results show that the proposed method has better integrated compensation performance in all situations, and error is reduced by several orders of magnitude. After compensation, RMS error is reduced from 10797.962 nT to 15.309 nT when the big magnet and steel tube are deployed. It suggests an useful method for calibration and magnetic disturbance compensation of three-axis magnetometers.     

基于无迹卡尔曼滤波和设备的三轴磁强计校正

采用无迹卡尔曼滤波(unscented Kalman filter,UKF)磁强计模型参数估计方法,提出对三轴磁强计的总量及分量误差进行校正。采用高精度质子磁力仪提供磁场基准值,借助无磁转台实现磁强计全方位转动,对一款DM-050三轴磁强计进行了参数估计,并将参数估计值运用到总量和分量校正。仿真结果表明,参数估计值与磁强计实际参数值一致。校正后,磁强计总量误差从427.9 nT减少到2.06 nT;X、Y、Z轴分量误差分别减少到1.84 nT、1.96 nT、1.72 nT。而且证明了UKF对磁强计模型参数估计的重复性良好,并研究了噪声幅度大小对UKF的性能影响程度。实验结果表明,磁强计误差从114.94 nT减少到14.47 nT,表明该方法能有效提高磁强计测量精度。     

单光束 SERF 磁强计三轴磁场解耦磁补偿校准方法

针对单光束SERF原子磁强计磁补偿过程中的三轴磁场耦合问题,提出了一种对磁强计三轴顺序补偿值进行反向校准的方法,用于减小三轴补偿过程中产生的耦合磁场。首先,构建了三轴磁场耦合数学模型,即一个3×3的耦合系数矩阵,来描述三轴之间的磁场耦合关系,并对实验室磁强计样机进行了三轴耦合系数测试。然后,提出了一种应用三轴耦合系数对三轴顺序补偿值进行反向校准的方法;最后,对比了校准前后的磁补偿效果。实验表明,经三轴顺序补偿反向校准后,磁强计的响应线宽平均变窄2～10 Hz,灵敏度提高3～5 fTHz^1/2,验证了该方法的有效性,为进一步优化磁补偿技术奠定了基础。     

基于阻尼粒子群优化的地磁场测量误差补偿

针对三轴磁力仪在磁场测量过程中的磁干扰问题,提出了基于阻尼粒子群优化算法的磁测误差补偿方法。建立了磁力仪误差和载体磁干扰的一体化误差补偿模型,分别采用阻尼粒子群算法和Two-step方法对非线性观测模型进行参数估计。以质子磁力仪数据作为真值,借助无磁转台充分连续采样,实验结果显示,阻尼粒子群算法对于磁场测量误差具有良好的抑制作用。补偿后,由阻尼粒子群算法和Two-step方法得到的均方根误差分别由1 025.7降至60.304 4、581 n T。结果表明,阻尼粒子群算法取得了更好的补偿效果,补偿精度提高了至少一个数量级,为磁场测量误差提供了一种非常有效的补偿方法。     

无人机磁惯导系统中航向校正的双内积算法

针对无人机磁惯导系统中广泛采用的三轴磁强计,建立航向角误差模型,分析出航向角的非对准误差等效为常值误差加半圆罗差,提出了一种基于双内积的航向误差校正方法,即利用地磁场矢量与自身内积得到的模值为定值以及地磁矢量与重力矢量二者的内积为常数原理进行航向角解算补偿。该方法能克服基于矢量模值不变校正方法无法补偿非对准误差的缺陷,可实现三轴磁强计的完全校正。数值仿真及实验结果显示,该方法校正效果优于标量校正法、点积不变法以及两步法,能有效降低磁场矢量的模值误差和无人机航向角误差,且对磁惯导系统中的传感器噪声有较好的鲁棒性。     

航姿参考系统三轴磁强计校正的点积不变法

为改善航姿参考系统中三轴磁强计校正精度,提出了一种基于泊松模型以及矢量点积不变性的校正方法。该方法利用地磁场矢量与一辅助矢量的点积为常数,无需本地地磁场精确数据,能完全确定泊松模型中的12个补偿系数,并能同时实现三轴磁强计的坐标系对准。针对辅助矢量的不同选择对该方法校正结果的影响,在电子罗盘上进行了实验验证及讨论。实验结果表明,该方法可使电子罗盘航向误差均方值减小到0.1°。     

基于自适应差分进化算法的三轴光电跟踪策略

为解决传统两轴光电跟踪系统的跟踪盲区问题,实现空间目标的全方位跟踪,提出一种存在冗余自由度的三轴光电跟踪系统。在详细分析三轴光电跟踪系统运动学特性的基础上,运用四元数方法建立三轴光电跟踪系统运动学模型,并提出一种基于自适应差分进化算法的三轴全方位光电跟踪策略。通过对系统运动学模型进行分析,得到三轴转动角度之间的关系,从而将求取三轴转角增量组合的三变量优化问题简化为单变量优化问题,并将自适应差分进化算法应用于求取三轴角增量的最优组合当中。仿真和试验结果证明,此三轴光电跟踪策略避免以往三轴跟踪系统在跟踪过程中进行两轴切换的不连续性,可以真正实现系统的三轴联动全方位连续跟踪运动;同时,与现有的其他跟踪策略相比较,该三轴跟踪策略能够以更小的三轴转动角度实现目标的跟踪定位;因而提高了系统的快速性和跟踪性能,具有良好的工程应用价值。     

考虑横向灵敏度的三轴加速度传感器标定方法研究

横向灵敏度是单轴加速度传感器的重要指标之一,它直接影响到三轴加速度传感器的标定模型与测量精度.本论文以三轴MEMS加速度传感器为研究对象,在传统的标定模型中引入了导致测量耦合的横向灵敏度误差,建立了一种新的三轴加速度传感器标定模型,该模型将传感器的横向灵敏度以对称矩阵的形式引入现有的标定公式,构建了包含零位偏差、标度因...     

Linear calibration method of magnetic gradient tensor system

Based on the detailed analysis of systematic errors, mathematical model of error parameters is constructed and linear calibration method is proposed for magnetic gradient tensor system. Firstly, nonlinear mathematical model of error parameters for single vector magnetometer is constructed based on scalar calibration, and least square solution is deduced by two nonlinear conversions without any mathematical simplification. Then outputs of four tri-axial magnetometers are calibrated to sensor’s orthogonal coordinate respectively. Secondly, a least square estimation is proposed for the misalignment errors between different magnetometers according to the rotation matrix comprising conversion of different orthogonal coordinate system. After calibration, outputs of tri-axial magnetometers are acquired along the ideally platform frame-orthogonal coordinate system and these enable calibration of magnetic gradient tensor system. Simulations and experiments show that the proposed linear calibration method can accurately solve the detailed error parameters and decrease measurement errors of magnetic gradient tensor system remarkably.     

十字形磁梯度张量系统的误差校正

针对十字形磁梯度张量系统中的单磁力仪误差(三轴灵敏度偏差、非正交误差和零点漂移误差)以及磁力仪之间存在的不对正误差,提出了十字形磁梯度张量系统的误差校正方法。首先,建立单磁力仪误差模型,采用基于椭球约束的最小二乘拟合算法对磁力仪的测量数据进行拟合从而得到椭球拟合参数;然后,接着利用Cholesky分解得到单磁力仪误差校正矩阵;最后在单磁力仪误差校正的基础上,利用正交Procrustes方法对不同磁力仪间的测量数据进行拟合从而得到磁力仪间的不对正误差校正矩阵。对提出的方法进行仿真与实测实验验证,实验结果表明:经过校正,磁梯度张量各分量的最大波动量由10 049nT/m降到52nT/m。提出的校正方法可以基本消除十字形磁梯度张量系统的误差,提高测量结果的准确度,且方法操作简单,不需要高精度的三轴无磁转台等设备,具有较高的实用价值。     

矢量磁力仪本体磁性现场校正算法研究

海洋磁力仪的本体磁性校正是磁力仪应用系统的核心技术,尤其当载体磁性发生改变后,其现场的校正算法是影响其应用有效性的关键。先分析了搭载有三轴磁通门磁力仪的水下勘探系统的主要磁干扰源,描述了相应的磁校正模型,简明扼要地介绍了椭球拟合、粒子群、遗传及粒子群遗传混合等算法,并逐一通过MATLAB予以实现。最后使用水下载体在西南印度洋的作业数据对上述算法进行功能性验证。由校正前后的数据波动情况、均方根误差值和相对误差值可知,磁校正领域混合算法校正效果相对较佳,能提高磁力仪传感器的测量有效性。     

基于椭球拟合的三轴磁传感器快速标定补偿方法

考虑到现有多轴磁传感器的标定补偿方法中普遍存在操作时间长、计算量较大、标定设备要求高、场地要求面积大等问题,提出一种基于椭球拟合的三轴磁传感器误差标定补偿方法。首先,分析传感器误差产生机理,并在此基础上,建立传感器误差模型,推导出各误差系数的计算公式,并利用椭球拟合的方法对三轴磁传感器进行测试标定与误差补偿。实验结果表明,该方法能够正确、有效地标定补偿三轴磁传感器的不正交误差、灵敏度误差以及零偏误差,具有操作简捷、省时、精度高等特点。     

An accurate probe pre-travel error compensation model for five-axis on-machine inspection system

On a five-axis CNC machine tool, the pretravel errors of touch-trigger probes are severely affected by gravity and must be compensated to ensure the required measurement accuracy. The situation is more complex than that of the three-axis on-machine inspection system. This paper proposes a simple and accurate modeling and compensation method for the probe pretravel error of a five-axis on-machine inspection system. First, the pretravel error for the 5-axis CNC tool is decoupled into three parts, which are analyzed based on the probe's mechanical structure. Then, a new calibration point selection strategy is proposed to obtain the accurate reference sphere center. Finally, we carry out calibration tests to validate the proposed method. The compensation results show that the proposed compensation method for the probe pretravel error under the influence of gravity (PPEUG) can improve the accuracy considerably.     

三轴数字MEMS加速度计现场标定方法

微机电系统(micro electro mechanical systems,简称MEMS)加速度传感器作为低成本惯性测量单元在物体姿态监测中有着广泛应用。根据三轴数字加速度传感器的输出数学模型,详细推导了如何计算数学模型中标度因数、安装误差系数以及零偏值。提出一种基于长方体的六位置简单标定方法,对比三轴转台精确标定结果表明六位置简单标定法简单易行,精度较高,易于单片机实现,适合不具备三轴转台的场所,且该方法对MEMS三轴数字加速度计的校准具有很好的通用性。     

基于两步修正法的 MEMS 三轴陀螺仪标定方法

针对目前三轴陀螺仪标定存在依赖于昂贵的转台设备或标定参数不完全的问题,本文提出了一种了基于两步修正法的MEMS三轴陀螺仪标定方法。该方法首先使用六位置法对加速度计12参数模型、三轴陀螺仪比例因子、三轴陀螺仪静态零偏进行标定补偿,然后对三轴陀螺仪非正交误差模型建模,进行系统级标定。两步修正法可实现在无精密设备条件下快速准确的对各项误差进行辨识,获得良好的标定效果。仿真实验表明,本文算法所获得的非正交误差均值接近1%,标准差小于0.1%;比例因子误差均值小于0.14%,标准差小于0.004%,且具有很好的一致性。实际实验表明,65 s纯惯性导航姿态更新结果中,该标定方法的俯仰角误差精度可以达到0.624°,横滚角误差精度可以达到0.67°。     

基于自适应遗传算法的三轴光电跟踪策略

三轴光电跟踪系统由于存在一个冗余横倾轴,可以解决传统两轴光电跟踪系统存在的空间跟踪盲区,全方位跟踪空间目标。在详细分析三轴光电跟踪系统运动学特性的前提下,运用四元数方法建立了存在一个冗余自由度的运动学模型,并设计出一种新的基于自适应遗传算法的三轴跟踪策略。仿真及实验结果表明,基于自适应遗传算法的三轴跟踪策略不需要进行轴系间的运动切换即可避免跟踪盲区,真正实现了系统的三轴联动全方位连续跟踪运动;而且与现有两轴跟踪策略和三轴切换跟踪策略相比,各轴所需的转动角度减小了30%以上,因而提升了系统的跟踪性能,其跟踪快速性提高了30%以上。     

六轴IMU补偿的磁力计动态稳定校准

磁力计是用于确定机器人姿态的常用传感器之一,在使用过程中极易受到周围环境磁场和量测噪声的干扰.传统的椭球拟合能够校准环境磁场的影响,但是不能抑制量测噪声,且不能实时运行,最新的陀螺仪补偿算法弥补了这些缺点,但是由于陀螺仪存在漂移,所以也会使得磁力计数据发生漂移.文中提出一种使用六轴IMU来补偿校准磁力计的方法,首先通过...     

Offline and online strategies to improve pose accuracy of a Stewart Platform using indoor-GPS

The pose accuracy of a robot manipulator may be improved by assessing and correcting systematic errors. Both offline and online strategies can be considered. To date, there has not been a solution for the online pose error correction of parallel manipulators. Moreover, offline strategies using indoor-GPS as reference measurement system have not yet been investigated. In this paper an optimization-based kinematic calibration method and an online correction technique are proposed and implemented for a low-cost Stewart Platform. In both cases, an indoor-GPS system was used as reference measurement equipment. Performance of both strategies are compared to a kinematic calibration method based on direct parameter measurement. Pose errors are evaluated for each strategy using a robotic total station. Performance of the optimization-based calibration and the online correction technique were similar and better than the direct parameter measurement calibration. Both techniques resulted in average pose errors less or equal to 0.3 mm and 0.05°. The proposed strategies may be adapted to other similar parallel manipulators and are applicable to large sized equipment.     

基于激光干涉仪的数控机床运动误差识别与补偿

提出了数控机床运动误差的软件补偿方法。采用刚体运动假设和齐次坐标变换建立了多轴机床空间运动误差的通用模型。该模型把刀具相对于工件的空间误差表示为机床各结构件之间运动误差的位置函数。给出了全部运动误差参数的激光干扰仪识别方法，提出了一种新的roll误差测量措施，在立式加工中心上进行了运动误差的补偿实验，结果证明所提出的运动误差软件联动补偿效果显著。