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.     

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。     

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。     

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.     

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。     

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。     

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.     

A new digital background calibration for redundant radix-4 pipelined ADCs by modeling of adaptive filter for linear and nonlinear errors

In this paper a new digital background correction and calibration technique for redundant multi-bit pipeline stages is presented. In this method output voltage of each stage in converter is defined as sum of the ideal product and error signal, which error voltage include of linear non-ideal section or first order error and nonlinearity undesired signal or third order error. Linear error is formed by capacitor mismatch, op-amp offset, comparator offset and finite op-amp gain effects. Nonlinear error is deformed the output voltage depend on the nonlinear results of open loop residue amplifier. Correction begins with separately calculation and cancelation of the nonlinear and linear errors respectively. For calibration of each stage at first step, the nonlinear effects in digital output of backend ADC is eliminated and then by digital modeling of first order analog error the influence of this unfavorable signal is diminished from digital equivalent of input voltage. Therefore for cancelation of non-ideal impairment in each stage a digital filter consist of linear and nonlinear channel in digital domain is designed. The first order and third order coefficients of designed digital function are unknown and should by a pertinent method be estimated simultaneously. Adaptive filter are best choose for this method. Simulation results show that INL/DNL parameters of 14-bit radix-4 pipelined converter are improved from 17LSB/3LSB to 0.45LSB/0.41LSB after calibration. The SNDR/SFDR parameters are increased from 30 dB/36 dB to 83 dB/90 dB.     

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°。     

A multilevel calibration technique for an industrial robot with parallelogram mechanism

This paper presents a multilevel calibration technique for improving the absolute accuracy of an industrial robot with a parallelogram mechanism (ABB IRB2400). The parallelogram structural error is firstly modeled based on the partial differential of the position function of a general four-bar linkage and the linearization of the position constraints of the parallelogram mechanism, the model coefficients are fitted from experimental data. Secondly, an absolute kinematic calibration model is established and resolved as a linear function of all the kinematic parameters, as well as the base frame parameters and tool parameters. Finally, contrary to most other similar works, the robot joint space (rather than Cartesian space) is divided into a sequence of fan-shaped cells in order to compensate the non-geometric errors, the positioning errors on the grid points are measured and stored for the error compensation on the target points. After the multilevel calibration, the maximum/mean point positioning errors on 284 tested configurations (evenly distributed in the robot common workspace) are reduced from 1.583/0.420 mm to 0.172/0.066 mm respectively, which is almost the same level as the robot bidirectional repeatability.     

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。     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

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。     

Calibration of a 3D-ball plate

The presented 3D-ball plate is used for testing machine tools with a workspace of 500 mm × 500 mm × 320 mm. The artefact consists of a 2D-ball plate which is either located by a kinematic correct coupling on a base plate or on a spacer. The spacers are placed between the base plate and the ball plate and are also kinematic coupled to the other elements of the artefact. The kinematic couplings provide a high repeatability of the measurement setup. Because of the specific application the known calibration procedures for 2D-ball plates are not applicable.A calibration method for the pseudo-3D-artefact on a coordinate measuring machine (CMM) is presented, with the aim to minimise the influence of geometric CMM errors. Therefore a computer simulation is used to analyse the effects of these disturbing errors on the calibration of the ball plate and the spacers. Using a reversal method, the plate is measured at four different horizontal positions after rotating the ball plate around its vertical axis. A couple of the CMM errors, e.g., a squareness error C0Y between the X- and Y-axis of the CMM, can be eliminated by that method—others have to be determined with additional measurements, e.g., the positioning errors EXX or EYY of the X- and Y-axis, respectively. The paper also contains a measurement uncertainty estimation for the calibration by use of experiments, tolerances and Monte Carlo-simulations. The achieved uncertainty for ball positions in the working volume is less than 2.1 μm (coverage factor k = 2).     

Optimization of surface roughness and flank wear using the Taguchi method in milling of Hadfield steel with PVD and CVD coated inserts

In this paper, the Taguchi method and regression analysis have been applied to evaluate the machinability of Hadfield steel with PVD TiAlN- and CVD TiCN/Al₂O₃-coated carbide inserts under dry milling conditions. Several experiments were conducted using the L₁₈ (2 × 3 × 3) full-factorial design with a mixed orthogonal array on a CNC vertical machining center. Analysis of variance (ANOVA) was used to determine the effects of the machining parameters on surface roughness and flank wear. The cutting tool, cutting speed and feed rate were selected as machining parameters. The analysis results revealed that the feed rate was the dominant factor affecting surface roughness and cutting speed was the dominant factor affecting flank wear. Linear and quadratic regression analyses were applied to predict the outcomes of the experiment. The predicted values and measured values were very close to each other. Confirmation test results showed that the Taguchi method was very successful in the optimization of machining parameters for minimum surface roughness and flank wear in the milling the Hadfield steel.     

Designing and producing large-volume liquid gamma-ray standard sources for low radioactive pollution measurements of seawater samples by comparison between experimental and simulation results

In order to in-situ measurement of large volume water samples, using of a portable HPGe detector was considered. Because of necessity of efficiency calibration of the detector for the geometry (100 L), the large volume standard sources were prepared. Before making large volume standard sources (100 L), the Monte Carlo method has been applied in order to optimizing the calibration procedures and in agreement with experiment results, has been caused reducing the amount of produced radioactive wastes. First, the efficiency of the portable coaxial P-type HPGe detector for 1 L liquid standard sources in Marinelli beaker geometry was simulated. Then, the experimental efficiency calibration was carried out using the detector for those 1 L liquid standard sources in Marinelli beaker geometry. The detector dead layer was determined by comparison of the simulation and experimental efficiency curve results. Then, a relation between simulation and experimental measurements, that is, between pulse-height per emitted particle, F8 tally, and estimated amount of spiked radioactive solution into the 1 L distilled water in Marinelli beaker was found. Then, the efficiency calibration of the large volume liquid standard sources was simulated. The estimated amount of spiking radioactive solution into the large volume distilled water (100 L) has been taken into account dividing experimental efficiencies (in Marinelli beaker) by the simulated efficiencies (in 100 L). Finally, by spiking the large volume distilled water with the radioactive solution, efficiency calibration of the potable HPGe detector for 100 L geometry was done.     

Improved machine tool linear axis calibration through continuous motion data capture

Machine tool calibration is becoming recognised as an important part of the manufacturing process. The current international standards for machine tool linear axes calibration support the use of quasi-static calibration techniques. These techniques can be time consuming but more importantly a compromise in quality due to the practical restriction on the spatial resolution of target positions on the axis under test. Continuous motion calibration techniques have the potential to dramatically increase calibration quality. Through taking several measurement values per second while the axis under test is in motion, it is possible to measure in far greater detail. Furthermore, since machine tools normally operate in dynamic mode, the calibration data can be more representative if it is captured while the machine is in motion. The drawback to measuring the axis while in motion is the potential increase in measurement uncertainty. In the following paper, different methods of continuous motion calibration are discussed. A time-based continuous motion solution is proposed as well as a novel optimisation and correlation algorithm to accurately fuse the data taken from quasi-static and continuous motion measurements. The measurement method allows for minimal quasi-static measurements to be taken while using a continuous motion measurement to enhance the calibration process with virtually no additional time constraints. The proposed method does not require any additional machine interfacing, making it a more readily accessible solution for widespread machine tool use than other techniques which require hardware links to the CNC. The result of which means a shorter calibration routine and enhanced results. The quasi-static and continuous motion measurements showed correlation to within 1 μm at the quasi-static measurement targets. An error of 13 μm was detailed on the continuous motion, but was missed using the standard test. On a larger, less accurate machine, the quasi-static and continuous motion measurements were on average within 3 μm of each other however, showed a standard deviation of 4 μm which is less than 1% of the overall error. Finally, a high frequency cyclic error was detected in the continuous motion measurement but was missed in the quasi-static measurement.     

Evaluation of aspects affecting measurement of three-axis accelerometers

In order to set integrated procedures involving geotechnical and structural aspects finalized to buildings diagnostics, uncertainty aspects are discussed concerning three-axis accelerometers and inclinometers for a distributed sensor network. This network allows to operate in a selective manner, preferring the most critical situations. To this aim, the main aspects affecting the measurement uncertainty of sensors to be used for building diagnostic should be known. As the firstly step of the uncertainty evaluation procedure, we focused on the calibration of sensors used for the task. The requirement of low cost and complexity of sensors and test benches was considered. Experimental results show that satisfactory calibration accuracy could be achieved, also for the low frequency range, 0–10 Hz. Systematic errors are minimized and main parameters affecting uncertainty are identified, such as: the motion positioning of the accelerometer with respect to the vertical axis, the imposed motion law, the parameter used as the reference and, finally, the real radial positioning of the sensor. Requirements to be satisfied by the sensor are also analysed.     

Measurement and analysis of fluorescent whitening agent content in soybean milk based on image techniques

This paper presents a method for measuring and quantitatively analyzing the fluorescent whitening agent in soybean milk based on image techniques. After collecting the fluorescent images of the soybean milk samples, the top seven wavelet moment invariants are selected according to the sample training and experimental comparison. Then calculate the standard templates of the 49 classes of calibration samples with different fluorescent whitening agent content ranging from 0.02 mg/ml to 0.5 mg/ml. The minimum distance method is carried out to match the testing sample with the calibration template, which realizes the quantitative analysis. To verify the effectiveness of the presented method, the prediction experiment is carried out. Results show that the absolute errors are within 0.005 mg/ml and the relative errors are within 5%, which means this method can measure the fluorescent whitening agent in soybean milk. This research presents a new approach for detecting the illegal fluorescence additive in food production.