Error Calibration Method Research Articles

The Asynchronous Gimbal-Rotation-Based Calibration Method for Lever-Arm Errors of Two Rotational Inertial Navigation Systems

The Asynchronous Gimbal-Rotation-Based Calibration Method for Lever-Arm Errors of Two Rotational Inertial Navigation Systems

Binocular Vision-based Three-dimensional Contouring Error Calibration Method for NC Machine Tools

Binocular Vision-based Three-dimensional Contouring Error Calibration Method for NC Machine Tools

Online calibration of ultra-short baseline installation error in dynamic environment

The ultra-short base-line system is widely used in the navigation of ships and underwater vehicles. The installation error between the sensor and inertial measurement unit (IMU) are the main sources of positioning inaccuracy. In high-precision navigation, the installation error is not negligible. A method based on Kalman filter is designed to estimate the installation error of USBL in real time. The detailed derivation of Kalman filter for the calibration is presented in the paper. Then the observability analysis is carried out to verify the feasibility of the method. Simulation results show that the method proposed in this paper can calibrate the installation error between the ultra-short baseline and inertial measurement unit in real time and online. The positioning accuracy is improved by compensating the installation error. Therefore, the error calibration method proposed in this paper is effective and can greatly improve the positioning accuracy of USBL.

Multichannel Phase Calibration for Linear Array Based on Extended <inline-formula> <tex-math notation="LaTeX">$\omega K$</tex-math> </inline-formula> Algorithm and Minimum-Entropy Method

Millimeter-wave imaging techniques have been used for security inspection at important checkpoints. With the increase of working frequencies of the imaging systems, the precise multichannel phase calibration becomes more and more important. Most of the traditional algorithms are used for the calibration of passive receiving antenna array, based on the signal model of far-field plane wave. However, the near-field spherical wave model should be utilized for the active wideband near-field imaging applications. Consequently, the traditional calibration algorithms cannot be used in wideband near-field imaging systems. The metal plate is usually employed for the calibration of wideband near-field imaging systems, but the precision is very sensitive to the flatness of the surface of the metal plate, which will result in additional phase error after calibration. In this letter, a multichannel phase error estimation and calibration method is proposed for the wideband linear array system. By using an extended $\omega K$ algorithm and the minimum-entropy method, the additional phase error of each channel after preliminary calibration is estimated and calibrated. Simulations and experimental results show the effectiveness of the proposed method.

A Novel Tri-Axial MEMS Gyroscope Calibration Method over a Full Temperature Range.

The micro-electro-mechanical inertial measurement unit (MEMS-IMU) has gradually become a research hotspot in the field of mid-low navigation, because of its advantages of low cost, small size, light weight, and low power consumption (CSWap). However, the performance of MEMS-IMUs can be severely degraded when subjected to temperature changes, especially gyroscopes. In order to make full use of the navigation accuracy, this paper proposes an optimized error calibration method for a tri-axial MEMS gyroscope across a full temperature range. First of all, a calibration error model is established which includes package misalignment error, sensor-to-sensor non-orthogonality error, scale factor, and bias. Then, a simple three-position positive/reversed test is undertaken by carrying out a single-axis temperature-controlled turntable at different reference temperature points. Lastly, the error compensation vector is obtained using the least squares method to establish an error matrix. It is worth mentioning that the error compensation vector at a known temperature point can be calculated through Lagrange interpolation; then, the outputs of the tri-axial MEMS gyroscope can be well compensated, eliminating the need for a recalibration step. The experimental results confirm the effectiveness of the proposed method, which is feasible and operational in engineering applications, and has a certain reference value.

A Phase Tunable Rotary Traveling Wave Oscillator: Analysis and Calibration

In this paper, a new phase error analysis is introduced for rotary traveling wave oscillators (RTWOs). Two new analytical approaches are used to extract closed-form equations for the RTWOs phase error arising from asymmetric resonator and inequality of negative transconductors. Derived equations show that the phase error can be cancelled and even controlled by adjusting the bias current of negative transconductors without any undesirable changing in oscillation frequency. This characteristic is then used for introducing a new phase error calibration method for RTWOs. This calibration method is not limited by the problems that limit the usage of the prior calibration technique. Our theoretical results are compared with accurate simulations to evaluate the validity of the proposed analysis and accuracy of the closed-form equations. Simulations have been done in 0. 18- $\mu$ m CMOS technology with a 1.8-V supply voltage. The evaluations show good agreement between analytical phase-error equations and simulation results. Also, appropriate simulations confirm the validity of the calibration method that is introduced in this paper.

A Self-Calibration Method for the Installation Errors of Rotation Axes Based on the Asynchronous Rotation of Rotational Inertial Navigation Systems

The attitude accuracy of the rotational inertial navigation system (RINS) is affected by the oscillatory attitude error caused by the installation error of the rotation axes. Data on the specific force, gyro measurement, attitude, or velocity errors are necessary to estimate the installation error. However, these errors are difficult to obtain and even unavailable in autonomous navigation. As the configuration consisting of two RINSs has been installed in the same vessel, we propose a self-calibration method to address the installation error solely using the attitude difference of two RINSs. We then constructed the Kalman filter based on the attitude difference model of two RINSs. The asynchronous time of the rotation sequence of two RINSs is optimized to improve the observability degree of the Kalman model. The proposed algorithm is examined by undertaking a test using two RINSs. Results indicate that the estimation accuracy of the installation error is at 6 arcsec level. The oscillatory attitude errors of RINS 1 are reduced from 305 to 6 arcsec, and those of RINS 2 are decreased from 131 to 6 arcsec after 350 s. The test results prove the effectiveness of the proposed installation error calibration method.

Inclinometer Assembly Error Calibration and Horizontal Image Correction in Photoelectric Measurement Systems.

Inclinometer assembly error is one of the key factors affecting the measurement accuracy of photoelectric measurement systems. In order to solve the problem of the lack of complete attitude information in the measurement system, this paper proposes a new inclinometer assembly error calibration and horizontal image correction method utilizing plumb lines in the scenario. Based on the principle that the plumb line in the scenario should be a vertical line on the image plane when the camera is placed horizontally in the photoelectric system, the direction cosine matrix between the geodetic coordinate system and the inclinometer coordinate system is calculated firstly by three-dimensional coordinate transformation. Then, the homography matrix required for horizontal image correction is obtained, along with the constraint equation satisfying the inclinometer-camera system requirements. Finally, the assembly error of the inclinometer is calibrated by the optimization function. Experimental results show that the inclinometer assembly error can be calibrated only by using the inclination angle information in conjunction with plumb lines in the scenario. Perturbation simulation and practical experiments using MATLAB indicate the feasibility of the proposed method. The inclined image can be horizontally corrected by the homography matrix obtained during the calculation of the inclinometer assembly error, as well.

System-Level Calibration for the Star Sensor Installation Error in the Stellar-Inertial Navigation System on a Swaying Base

The star sensor installation error has a great influence on the attitude accuracy of the stellar-inertial navigation system and should be precisely calibrated. However, it is difficult to realize the installation error without a proper reference on a swaying base, which becomes a limitation for operation accuracy and reaction ability improvement. In this paper, a star sensor installation error calibration method on a swaying base is proposed. The measurement equation is established using accelerometer information, gravity and direct star vector observations in the inertial frame. The state equation is deduced according to the navigation error model. The installation error can be calibrated in the inertial frame instead of the zero-velocity information with respect to the Earth. The simulations and experimental results indicate that the proposed method performs much better than the traditional method on a swaying base. The calibration accuracy can be within 1 arc-s in simulation, and the stability is approximately 5 arc-s in the experiment. High accuracy can be achieved without precise external devices and artificial references. The proposed method is very suitable for mooring ships and for readiness on duty vehicles. The on-line accuracy and rapid-response ability can be significantly improved.

Integrated Calibration for the Cross Magnetic Gradiometer

The magnetic gradiometer onboard a maneuverable vehicle is subjected to not only magnetometer errors and misalignment errors but also magnetic interference of vehicle. Measurement precision of the magnetic gradiometer is greatly affected by those errors, so an integrated error calibration method is proposed in this paper. Firstly, considering vector magnetometer errors and magnetic interference, an integrated error calibration model for vector magnetometer is established, and ellipsoid fitting parameters are calculated by the least square algorithm under ellipsoid restriction, then the error calibration matrices are solved by the Cholesky factorization. Secondly, the misalignment error calibration matrices are obtained by solving the Orthogonal Procrustes problem. Finally, simulations and experiments with a cross magnetic gradiometer are performed to verify effectiveness and robustness of the proposed method. Results show that the proposed method can effectively calibrate the cross magnetic gradiometer, and measurement accuracy of the cross magnetic gradiometer is increased greatly.

Equivalence Of Self-report And Accelerometer Measures Following A Physical Activity Intervention.

The International Physical Activity Questionnaire (IPAQ) is a validated and widely used self-report physical activity (PA) measure, however findings about validity have been somewhat equivocal. PURPOSE: This study evaluated the agreement of the IPAQ measure with a novel and objective activity monitoring method known as Sojourns Including Posture (SIP). The SIP method is based on the same bout detection method as the more established Sojourn method but incorporates data from the ActivPAL to provide more robust information about transitions between Sedentary and Light activity. The aim was to investigate differences between self-reported moderate (MPA), vigorous (VPA), and sedentary (SED) minutes to SIP data, to inform whether participants were able to accurately self-report PA and SED time. METHODS: A sample of 93 inactive adults (53% female; 42 ± 9.1 mean age) participated in this study. Participants received a wearable device to track PA. Post-intervention, individuals wore accelerometers for 1 week, and self-reported PA and SED via the IPAQ. Minutes of MPA, VPA, and SED from each measure were compared using Pearson correlations, equivalence testing, and Bland-Altman plots, with the SIP method as the criterion. RESULTS: The overall Pearson correlation between the measures was low to moderate (r = 0.37, P < .05). The mean MPA via IPAQ was 96.9 ± 87.8 minutes per day compared to 57.3 ± 24.4 minutes per day measured by SIP. Mean VPA from the IPAQ was 8.99 ± 6.76 minutes, while the SIP method reported 14.44 ± 9.51 minutes. The mean SED via the IPAQ was 456.6 ± 156.93 minutes compared to 546.13 ± 104.42 minutes measured by SIP. Equivalence testing demonstrated that the MPA, VPA, and SED methods were not equivalent at the ±10% equivalence zone. A Bland Altman plot was constructed to visualize the MPA data using 95% limits of agreement that are between -121.1 and 200.4. More data points trended below the mean of 39.65, suggesting proportional bias that self-report overestimated activity. CONCLUSIONS: This study provides some support for the use of the IPAQ, but confirms the common observation in self-report instruments with participants tending to overestimate their participation in MPA and underestimate sedentary time. The use of measurement error modeling and calibration methods may be needed to address this error in future studies.

Error Analysis and Calibration Method of a Multiple Field-of-View Navigation System.

The Multiple Field-of-view Navigation System (MFNS) is a spacecraft subsystem built to realize the autonomous navigation of the Spacecraft Inside Tiangong Space Station. This paper introduces the basics of the MFNS, including its architecture, mathematical model and analysis, and numerical simulation of system errors. According to the performance requirement of the MFNS, the calibration of both intrinsic and extrinsic parameters of the system is assumed to be essential and pivotal. Hence, a novel method based on the geometrical constraints in object space, called checkerboard-fixed post-processing calibration (CPC), is proposed to solve the problem of simultaneously obtaining the intrinsic parameters of the cameras integrated in the MFNS and the transformation between the MFNS coordinate and the cameras’ coordinates. This method utilizes a two-axis turntable and a prior alignment of the coordinates is needed. Theoretical derivation and practical operation of the CPC method are introduced. The calibration experiment results of the MFNS indicate that the extrinsic parameter accuracy of the CPC reaches 0.1° for each Euler angle and 0.6 mm for each position vector component (1σ). A navigation experiment verifies the calibration result and the performance of the MFNS. The MFNS is found to work properly, and the accuracy of the position vector components and Euler angle reaches 1.82 mm and 0.17° (1σ) respectively. The basic mechanism of the MFNS may be utilized as a reference for the design and analysis of multiple-camera systems. Moreover, the calibration method proposed has practical value for its convenience for use and potential for integration into a toolkit.

An on-machine error calibration method for a laser micromachining tool

In this paper, an on-machine error calibration method, covering error modeling and measurement, is proposed to evaluate and compensate the errors caused by the mechanical and optical system equipped in the micromachining center using the femtosecond laser. Through preliminary tests by dicing silicon wafer, it has revealed that the squareness, laser beam misalign and focal position offset, are the main causes to result in the inaccuracy of micromachining. Consequently, an error modeling method is proposed to evaluate the error distribution in the workspace, and hereafter a comprehensive error vector of the laser beam, combining the squareness errors of Z-axis with the laser beam misalign, is generated by the variable substitution method. Subsequently, an increment error model in the instant local coordinates is established to satisfy the requirement of the programming method commonly used in the laser machine tools. Furthermore, a series of holes and grooves are machined on the femtosecond laser micromachining center to validate the proposed approach and model. The machining dimensions including diameters, distances and angles, are measured on-machine to identify the squareness errors, laser beam misalign and focal position offset according to the proposed error model. Finally, the experimental results show that, comparing to the uncompensated tests, the machining accuracy has been significantly improved with the proposed method.

Improved Channel Error Calibration Algorithm for Azimuth Multichannel SAR Systems

Multichannel synthetic aperture radar systems in azimuth can effectively suppress azimuth ambiguity and are promising in high-resolution wide-swath imaging. However, unavoidable channel errors will significantly degrade the performance of ambiguity suppression. Conventional subspace calibration methods usually estimate phase error via decomposing a Doppler-variant covariance matrix from one Doppler bin, and then average these errors estimated from several Doppler bins to improve the estimation accuracy, which will result in a large computational load. This letter presents an improved channel error calibration method, which works on the undersampled data of the individual azimuth channel. By a proposed matrix transformation method, the Doppler-variant covariance matrices will be transformed into a constant covariance matrix. Therefore, the improved calibration algorithm needs to estimate and decompose the new covariance matrix only once. The computation load could be greatly reduced. Moreover, the new covariance matrix can be estimated by training samples not only from range bins but also from Doppler bins, which will improve the estimation accuracy. Theoretical analysis and experiments based on simulations and measurements showed the high accuracy, efficiency, and robustness of the improved method, particularly in low signal-to-noise ratio.

Array error calibration methods in downward-looking linear-array three-dimensional synthetic aperture radar

In order to achieve high-precision three-dimensional (3-D) imaging with an airborne downward-looking linear-array 3-D synthetic aperture radar (LA-3D-SAR), a uniform virtual antenna array can be obtained by aperture synthesis of the cross-track sparse multiple-input-multiple-output array. However, the actual 3-D imaging quality is unavoidably degraded by array errors such as the multichannel amplitude-phase errors due to the nonideal antenna characteristics, and the virtual element position errors due to vibrations and motion measurement deviations. We investigate the effects of these errors on the forms and the degrees of image quality degradation and consider the use of corresponding calibration methods to eliminate the effects of errors. For the multichannel amplitude-phase errors, the target response is subject to an integrated sidelobe level increase introduced by the phase error, which can be calibrated based on external (parallel or point target) calibrators, as proposed in the paper. For the virtual element position errors, they mainly the result of contrast degradation and noise in the image along the cross-track direction and have little impact on the range and along-track directions. The imaging performance is more sensitive to the error component in the height direction as compared to other components, the precision requirement of which should be established as the calibration reference. A calibration method based on time-divided active calibrators is proposed to estimate and correct the virtual element position errors. Both numerical simulations and real data experiments have shown the validity of the analyses as well as the effectiveness of the proposed calibration methods.

A Novel Strategy for Large-Scale Metabolomics Study by Calibrating Gross and Systematic Errors in Gas Chromatography-Mass Spectrometry.

Metabolomics is increasingly applied to discover and validate metabolite biomarkers and illuminate biological variations. Combination of multiple analytical batches in large-scale and long-term metabolomics is commonly utilized to generate robust metabolomics data, but gross and systematic errors are often observed. The appropriate calibration methods are required before statistical analyses. Here, we develop a novel correction strategy for large-scale and long-term metabolomics study, which could integrate metabolomics data from multiple batches and different instruments by calibrating gross and systematic errors. The gross error calibration method applied various statistical and fitting models of the feature ratios between two adjacent quality control (QC) samples to screen and calibrate outlier variables. Virtual QC of each sample was produced by a linear fitting model of the feature intensities between two neighboring QCs to obtain a correction factor and remove the systematic bias. The suggested method was applied to handle metabolic profiling data of 1197 plant samples in nine batches analyzed by two gas chromatography-mass spectrometry instruments. The method was evaluated by the relative standard deviations of all the detected peaks, the average Pearson correlation coefficients, and Euclidean distance of QCs and non-QC replicates. The results showed the established approach outperforms the commonly used internal standard correction and total intensity signal correction methods, it could be used to integrate the metabolomics data from multiple analytical batches and instruments, and it allows the frequency of QC to one injection of every 20 real samples. The suggested method makes a large amount of metabolomics analysis practicable.

An investigation of highly accurate and precise robotic hole measurements using non-contact devices

Industrial robots arms are widely used in manufacturing industry because of their support for automation. However, in metrology, robots have had limited application due to their insufficient accuracy. Even using error compensation and calibration methods, robots are not effective for micrometre (μ m) level metrology. Non-contact measurement devices can potentially enable the use of robots for highly accurate metrology. However, the use of such devices on robots has not been investigated. The research work reported in this paper explores the use of different non-contact measurement devices on an industrial robot. The aim is to experimentally investigate the effects of robot movements on the accuracy and precision of measurements. The focus has been on assessing the ability to accurately measure various geometric and surface parameters of holes despite the inherent inaccuracies of industrial robot. This involves the measurement of diameter, roundness and surface roughness. The study also includes scanning of holes for measuring internal features such as start and end point of a taper. Two different non-contact measurement devices based on different technologies are investigated. Furthermore, effects of eccentricity, vibrations and thermal variations are also assessed. The research contributes towards the use of robots for highly accurate and precise robotic metrology.

Bandwidth-efficient calibration method for nonlinear errors in M-channel time-interleaved ADCs

In order to enhance the effective resolution of time-interleaved analog-to-digital converters (TI-ADCs), both linear and nonlinear channel mismatches should be carefully calibrated. This paper concentrates on a bandwidth-efficient background calibration method for nonlinear errors in M-channel TI-ADCs. It utilizes the least-mean square algorithm as well as a certain degree of oversampling to achieve adaptive mismatch tracking. The calibration performance and computational complexity are investigated and evaluated through behavioral-level simulations. Furthermore, a calibration strategy for narrow-band input signals is proposed and verified as an improvement of the basic calibration structure for such signals.

Calibration algorithm for multiplicative modelling errors using constant modulus auxiliary signals

In this paper, the active calibration method for multiplicative modelling errors using phase-modulated (also called constant modulus) auxiliary sources is presented. Compared with some existing calibration methods, the proposed approach can exploit the constant modulus characteristic of the sources and has significantly better performance. For the purpose of incorporating the constant modulus information into the procedure for finding array error parameters, the maximum likelihood criterion is chosen as the optimisation function and a concentrated alternating iteration algorithm is developed, which has rapid convergence rate. In addition, to reduce the effects of azimuth deviations of the auxiliary sources, the study proceeds to extend the novel algorithm to the scenario where the true azimuths of the sources deviate slightly from the nominal values with a prior known Gaussian distribution. The Cramer–Rao bound (CRB) expressions for the unknowns are derived for the case when it is known that the sources are phase-modulated. Simulation results show that the performance of the proposed algorithms are considerably better than that of subspace-based calibration methods and closely follows the CRB for array error estimation.

A Study of a Normalized Error Calibration Method Based on Parallel High-Speed Data Acquisition System

For Offset error and Gain error brought by multi-channel parallel alternate technology in high-speed data acquisition system, this paper proposes a progressive dynamic balance of error normalized calibration method. And in the high-speed data acquisition system of 1GSPS experimental platform consisting of 8 ADC, the program is carried out by experiments. The results show that the method is simple, practical and stable and meets the design requirements.