Calibration strategy and generality test of three-axis magnetometers

Calibration strategy will influence the calibration performance of three-axis magnetometers. In this paper, three different calibration strategies (symmetrical calibration, orthogonal calibration and random calibration) are introduced and verified by simulation and experiments. The experimental system mainly consists of three-axis fluxgate magnetometer (MAG3300), 2D nonmagnetic rotation equipment and proton magnetometer. The scalar value of magnetic field was obtained with proton magnetometer and considered to be the true value. Calibration performance of three different calibration strategies were analyzed and compared. Experimental results show that after calibration the scalar RMS error has dropped 88.5%, 85.5% and 87.6% respectively. To check the generality of the estimated error parameters, another site was chosen to be a validation position, and the calibration performance of three calibration strategies were tested and compared. After calibration, the scalar RMS error has dropped 83.2%, 78.9% and 78.8% respectively. Thus the symmetrical calibration is considered to be the best calibration strategy among three calibration strategies.     

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.     

三轴磁通门磁梯度仪转向差校正方法研究

三轴磁通门传感器应用广泛,但其自身固有的零偏误差、灵敏度误差以及三轴非正交误差对其磁场测量精度有着较大的影响。针对磁通门梯度仪中磁传感器自身的性能参数和摆放方位不一致问题,提出了转向差的校正方法:分别建立了磁通门传感器误差的自校准和互校准数学模型,并采用神经网络算法和最小二乘算法对模型参数进行求解。仿真和试验结果表明,整个校正过程简单可行,在不需要三轴无磁转台以及恒定磁场标准装置等复杂试验设备情况下,利用磁通门梯度仪在稳定的地磁场环境下采集多组磁场数据,能有效降低磁梯度仪转向差引起的测量误差。     

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.     

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。     

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。     

三分量磁通门梯度仪校准算法研究

针对三轴磁通门传感器非正交、灵敏度不一致、零偏以及构成梯度仪的两个磁通门传感器位置不一致引起的测量误差问题,建立了误差模型;基于地磁矢量模值短时不变原理,采用线性化最小二乘算法进行一个磁通门传感器参数的辨识;基于校准后三分量差值F范数最小原理,采用多元线性回归的方法进行另一个磁通门传感器参数以及两个磁通门传感器相对位置关系参数的辨识。实验结果表明,该方法能够将两个磁通门中最大总场误差从1 194.4 n T降低到30.0 n T,将三分量梯度仪最大输出误差从529.1 n T降低到13.4 n T,有效地改善了梯度仪性能。     

磁力仪温度误差的径向基神经网络补偿模型

磁通门磁力仪参数受温度影响明显,直接影响传感器测量精度,需要研究补偿方法,提高测量精度。采用无磁高低温试验箱测量磁通门传感器温度特性;提出基于径向基神经网络的温度误差补偿方法,分别建立磁通门磁力仪零漂误差补偿模型和刻度因子误差补偿模型。结果表明,径向基神经网络能良好逼近磁通门传感器参数的温度特性;与BP神经网络相比,径向基神经网络在零漂补偿中训练时间更短,精度更高,重复性更好,零漂误差的抑制能力更强。补偿后,磁通门磁力仪零漂误差从7.105 5 nT减少到0.766 1 nT;刻度因子误差从6.3E-3减少到7.2E-5;测量值温度误差由213.6 nT补偿到9.1 nT。提出建立通用的温度补偿模型,在不同磁场环境下经过反复测试,采用训练过的模型补偿后,温度误差均降低一个数量级,提高了磁通门磁力仪温度性能和精度。     

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。     

Fabrication and characterization of a new MEMS fluxgate sensor with nanocrystalline magnetic core

This paper presents a new MEMS fluxgate sensor with a Fe-based nanocrystalline ribbon magnetic core and 3D micro-solenoid coils. The excitation coils were placed vertically to the sensing coil on the chip plane. Second harmonic operation principle was adopted in this fluxgate sensor. The total size of the fluxgate sensor was 6.25 mm × 4.85 mm × 120 μm. A simple testing system was established to characterize the fabricated devices. A band pass filter was used to pick up the second harmonic signals in the sensing coils. When excitation rms current of 120 mA and the operational frequency of 200 kHz were selected for the testing of the fabricated devices, the sensitivity of the developed fluxgate sensor was 1005 V/T in the linear range of −500 μT to +500 μT. Due to the combination of the 3D structure coils with the nanocrystalline core, relatively low sensor noise was achieved. The noise power density was 544 pT/Hz^0.5@1 Hz and the noise rms level was 9.68 nT in the frequency range of 25 mHz-10 Hz.     

A sensitive fluxgate magnetometer

A sensitive magnetometer whose fluxgate transducer is assembled using finished winding components produced by the radioelectronics industry is described. The maximum scale value of the magnetometer is 100 μT; the self-noise does not exceed 10 nT. During 8 h of operation, the zero shift is no more than 10 nT. At an 18-V supply voltage, the input dc is no more than 45 mA.     

平面十字磁梯度张量系统的两步线性校正

磁梯度张量系统的测量精度受限于磁传感器的零漂、灵敏度差异和三轴非正交性等系统误差以及各传感器轴系间的非对准误差。构建了平面十字磁梯度张量系统的误差参数线性模型,提出了两步线性校正法。利用两个非线性变量转换构建单磁传感器系统误差的线性方程组,对误差参数进行最小二乘估计,将传感器实际输出校正为各自理想正交输出;利用旋转矩阵构建各传感器理想正交轴间非对准误差的线性方程组并求出最小二乘解,将各传感器输出校正到参考平台框架正交坐标系上。两步校正过程均无数学简化。仿真与实验表明,相比忽略二阶及以上高阶小量的常规线性校正,提出的张量系统两步线性校正法更为精确,误差参数仿真估计准确率高于93%,实测校正后总场强度均方根误差小于13 n T,张量分量均方根误差小于90 n T/m。     

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°。     

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°。     

一阶数控球形反馈磁张量梯度仪动态特性研究

磁通门张量探头在非零的地磁场环境下存在稳定性差、非线性误差大等不足。为克服此类缺陷,需采用磁补偿技术使磁通门工作在零磁场环境。以提高磁通门张量探头的探测精度为目的,采用球形线圈及对应的驱动模块作为磁补偿装置,利用一阶数字控制系统的方法建立磁补偿装置的数学模型,并对其进行参数优化实现最优控制。实验结果显示,当带有球形反馈线圈磁通门张量探头的稳态误差在52.56 nT之内时,系统的带宽将扩展至4.75 Hz,该结果能够同时满足磁张量梯度仪的探测精度及带宽要求,提高了其在航空地球物理探测中的应用价值。     

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。     

Improved system for the automatic calibration of standard resistors in the meg-ohm range

An automated measuring system has been developed to improve the calibration of high value standard resistors in the meg-ohm range at the National Institute for Standards (NIS), Egypt. This system is suitable for the calibration of the standard resistors from 100 kΩ to 100 MΩ using the DMM-based method by the substitution technique where the unknown resistor and the standard resistor are indirectly compared in the same position using a dummy resistor as a short-term reference standard. The system operation is automatically controlled by using a Lab VIEW program which is especially developed for this purpose. The uncertainty for the high value standard resistors measurement of this system is estimated. The performance of this system is also evaluated by comparing the measurement results obtained from this technique with those obtained by the direct comparison DMM-based method. It is found that the measurement uncertainty of with this method spans from 4.1 × 10⁻⁶ to 27 × 10⁻⁶, while it spans from 40 × 10⁻⁶ to 110 × 10⁻⁶ for the direct comparison method. The relative differences of the deviation from nominal values of the working standards resistors measured by the two methods are found to be within their expanded uncertainties.     

Multiport vector network analyzer calibration using the generalized 3-term error model

A generalized 3-term error model, where only three error matrixes are defined, is proposed for the calibration of n-port vector network analyzer (VNA) with n + 1 measurement channels. In this model, the node is replaced by the complex vector, and correspondingly the branch gain is represented by the complex square matrix. According to this error model, which also obeys the fundamental rules of flow graph, the formula for actual scattering matrix of an n-port DUT can be deduced. Finally, the actual S-parameters of a four-port device can be corrected and they are compared with the measurement results by Agilent VNA E5071B. The good agreement attests the precision of the calibration algorithm.     

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。     

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...