Angle Measurement Error Research Articles

Revised astrometric calibration of the Gemini Planet Imager

We present a revision to the astrometric calibration of the Gemini Planet Imager (GPI), an instrument designed to achieve the high contrast at small angular separations necessary to image substellar and planetary-mass companions around nearby, young stars. We identified several issues with the GPI Data Reduction Pipeline (DRP) that significantly affected the determination of angle of north in reduced GPI images. As well as introducing a small error in position angle measurements for targets observed at small zenith distances, this error led to a significant error in the previous astrometric calibration that has affected all subsequent astrometric measurements. We present a detailed description of these issues, and how they were corrected. We reduced GPI observations of calibration binaries taken periodically since the instrument was commissioned in 2014 using an updated version of the DRP. These measurements were compared to observations obtained with the NIRC2 instrument on Keck II, an instrument with an excellent astrometric calibration, allowing us to derive an updated plate scale and north offset angle for GPI. This revised astrometric calibration should be used to calibrate all measurements obtained with GPI for the purposes of precision astrometry.

A Novel Approach to Separate Geometric Error of the Rotary Axis of Multi-axis Machine Tool Using Laser Tracker

It is highly desirable to enhance machining accuracy for multi-axis machine tool, in which the geometric accuracy of rotary axis is a main contributing factor. Thus, how to achieve the fast and accurate identification of each geometric error of rotary axis, as well as its correction and compensation has become a key issue. This paper presents a novel method of geometric error separation of the rotary axis by means of laser tracker. For this method, the direction variation of the vectors composed by some adjacent measuring points during the rotation of turntable is measured, and rotary axis’s six geometric errors including three linear displacement and three angular displacement errors can be accurately identified on the basis of the mapping relationship between the vector’s direction variation and each geometric error. Meanwhile, the multi-station and time-sharing measurement is adopted based on GPS principle, aiming to overcome the effect of angle measurement error using laser tracker. Eventually, the geometric error separation mathematical model on rotary axis with this novel method is established, and the corresponding measurement algorithms containing the base station calibration and the measuring point determination based on the hybrid genetic algorithm, as well as each geometric error separation algorithm are deduced respectively. Furthermore, the numerical simulations are conducted to examine the validity of the derived algorithms. Results of the comparative experiment demonstrate that high-efficiency and high-precision measurement for the geometric error of the rotary axis can be accomplished by the proposed approach.

A Novel High-Gain Sum and Difference Conical Beam-Scanning Reflector Antenna

A novel sum and difference (SD) conical beam-scanning reflector antenna is proposed in this paper. The reflector surface, illuminated by two omnidirectional horns, is a body of revolution obtained by revolving the generating parabola about a symmetry axis. The horns stacked along the symmetry axis of the reflector are fed by a nest coaxial waveguide. Teflon lens is used to improve the side lobe levels and reflection coefficients of the feed horns. By tilting the generating parabola and using the offset feeding method, two conical beams, with different beam pointing angles, were generated. A compact feed network was also designed to feed the two horns, which includes two rectangular TE10 mode-to-coaxial TEM mode transitions and a Magic-T to implement SD beams. The scanning performance of conical beams can be achieved by mechanically moving the feed antennas along the symmetry axis and taking full advantage of offset focus characteristic of the parabolic reflector. The error in angle measurement was also discussed. The SD conical beam-scanning antenna was formed by a parabolic dish with a radius of 18 λ operating at 24 GHz. The proposed antenna was designed, simulated, and fabricated. The measured results show that the difference beam null-depth is -25 dB and the sum beam gain is 15 dBi at 40°. The sum beam gain varies by less than 1.5 dB across the scan coverage from 30.8° to 45.2°. The measured results are found to be in good agreement with the simulated ones.

Development of wearable posture monitoring system for dynamic assessment of sitting posture.

There have been increasing cases of people seeking treatment for neck and back pain. The most common cause of neck and back pain is due to long-term poor sitting posture. The most common poor sitting posture cases are humpback, and head and neck being too far forward. It is easy to cause neck and back pain and other symptoms. Therefore, the development of wearable posture monitoring system for dynamic assessment of sitting posture becomes both helpful and necessary. In addition to recording the wearer's posture when sitting with quantitative assessment, it is needed to execute real-time action feedback for correctness of posture, in order to reduce neck and back pain due to long-term poor sitting posture. This study completed an instant recording and dynamic assessment of position measurement and feedback system. The system consists of a number of dynamic measurement units that can describe the posture trajectory, which integrates three-axis gyro meter, three-axis accelerometer, and magnetometer in order to measure the dynamic tracking. In the reliability analysis experiment, angle measurement error is less than 2%. The correlation coefficient between correlation analysis and Motion Analysis (MA) is 0.97. It is shown that the motion trajectory of this system is highly correlated with MA. In the feasibility test of sitting position detection, it is possible to detect the sitting position from the basic action of the walking, standing, sitting and lying down, and the sensitivity reaches 95.84%. In the assessment of the sitting position, the information published by the Canadian Centre for Occupational Health and Safety was used, as well as the recommendations of professional physicians as a basis for evaluating the threshold of the sitting measurement parameters and immediately feedback to the subjects. The system developed in this study can be helpful to reduce neck and back pain due to long-term poor sitting posture.

Acquisition Algorithm of Spatial Control Parameter Tilt Angle for On-line Insulator

Most vision control of the existing power-line insulator robot system needs to be realized indirectly through the remote computer. The vision system itself does not have the ability of vision control, and the level of automation is low. In order to improve the visual control ability and automation level of the power-line insulator robot, an on-line spatial control parameter acquisition algorithm for insulator is presented based on target extraction. The algorithm can be embedded in the hardware platform of visual system to automatically measure tilt angle of insulators. The results of hardware implementation show that the proposed algorithm can measure tilt angle parameters relatively accurately on the hardware platform of visual system. The error of tilt angle measurement is 0.4°~4°, which achieves the desired effect and design requirements.

An Error Evaluation Method for the Ship Angular Flexure Measurement Based on the Principle of Relevance

Due to the lack of true ship angular flexure data, it is difficult to evaluate its measurement error of the angular velocity matching method in practice. In this paper, the cause of the measurement error of the ship flexure angle is analyzed in theory, and an evaluation method for the ship angular flexure measurement error based on the principle of relevance is proposed. The proposed method provides a prediction formula to describe the estimation error of the static flexure angle based on the off-diagonal elements of the error covariance matrix P in Kalman filtering. In addition, the optimized coefficient F is introduced to make the prediction error range better describe the real error variation. The optimized coefficient F ensures that the proposed formula has good prediction effects in all three directions. Simulations based on the actual measured ship flexure data are carried out, and the simulation results verify the capability of the prediction formula. The proposed method can be used in the evaluation of the ship flexure measurement error.

Influence of foot position on the measurement of first metatarsal axial rotation using the first metatarsal axial radiographs

BackgroundThe purpose of this study was to clarify 1) the measurement error of the pronation angle using the first metatarsal axial radiograph with the pronation angle along the longitudinal axis of the first metatarsal as the reference standard, 2) the influence of variability in the foot position on the measurement error, and 3) the intra- and interrater reliability of pronation angle measurement using digitally reconstructed radiographs. MethodsDigitally reconstructed radiographs of the first metatarsal were generated from the computed tomography images of 10 feet without hallux valgus (non-HV group) and 10 feet with hallux valgus (HV group). In total, 135 images were created at different degrees of supination, plantarflexion, and adduction from each foot to simulate the first metatarsal axial view. Then, the pronation angle of the first metatarsal was measured. The measurement error was determined using the mean error and 95% limits of agreement. Simple linear regression analysis was used to test the correlations of the measurement error with pronation, plantarflexion and adduction angles. The intra- and interrater reliability of measurement was assessed using the intraclass correlation coefficient and minimum detectable change values. ResultsThe mean measurement errors were 0.1° for both the non-HV and HV groups. There was no significant correlation of the measurement error with pronation, plantarflexion or adduction angles for both groups. Additionally, the intraclass correlation coefficients for the intra- and interrater reliability were more than 0.9 in both the non-HV and HV groups with the minimum detectable change values ranging from 0.7° to 1.4°. ConclusionThe measurement error of first metatarsal pronation using the axial view was clinically acceptable. The measurements were not influenced by the variability in foot position while obtaining the radiograph. The first metatarsal axial view could be used to quantify the first metatarsal coronal rotation.

Target positioning of UAV airborne optoelectronic platform based on nonlinear least squares

The target positioning algorithm of the traditional unmanned aerial vehicle (UAV) airborne optoelectronic platform introduces a large number of angle measurement errors, resulting in low target positioning accuracy. In this paper, a hybrid nonlinear algorithm of least squares and Gauss-Newton is proposed. Firstly, the Gauss-Newton iterative nonlinear target localization algorithm based on laser ranging value is derived. Then the rough solution of linear least square is used as the initial value of the nonlinear Newton iteration method for target location estimation. The algorithm combines the advantages of the simple and easy implementation of the least squares method and the high convergence accuracy of the Gauss-Newton method, and satisfies the requirements of the Gauss-Newton method for the initial value accuracy. Experimental results of measured data show that the longitude error of fixed target positioning results of this method is less than 1.37×10-5 degrees, the latitude error is less than 6.31×10-5 degrees, and the height error is less than 1.78 meters. And the processing time of each positioning is within 6 ms, which meets the requirements of real-time positioning.

Alternative method for measuring the phase retardation and fast axis of a wave plate

An alternative method is proposed for simultaneously measuring the phase retardation and fast axis angle of a wave plate by utilizing a radially polarized symmetric light beam. A horizontal polarized laser is passed through a spatial filter, a zero-order vortex half-wave retarder, for measuring the light beam. An analyzer and a charge-coupled device are used for the measurement. The charge-coupled device captures two intensity variation patterns before and after a wave plate to be tested is rotated by 45° in any initial fast axis angle direction. Through analysis of the intensity values, the phase retardation and fast axis angle of the wave plate to be tested can be accurately determined using mean calculation. To validate the proposed method, half-wave and quarter-wave plates were measured experimentally. The measurement errors of phase retardation and fast axis angle were approximately 0.087° and 0.094°, respectively.

Validation for the Method Measuring Lateral Stability Angle Belonging Tractors and Agricultural Machines

The article presents the results of validation for the method of mea­suring the lateral stability in tractors, trailers and agricultural machines. The method was developed in the testing laboratory of the State Scientific Institution «Leonid Pogorely Ukrainian Research Institute for Forecasting and Testing Equipment and Technologies for Agricultural Production», Kharkov branch. The method developed for measuring the angle of lateral stability is based on measuring the mass of the machine on boards in a horizontal and inclined position. Evaluation of lateral stability is carried out through an indirect indicator — the ratio of the mass of the machine bead in a horizontal position and inclined. The application of the develo­ped method does not require determination of the coordinates of the cen­ter of mass of the machine and the use of platform stands, but provides only for measuring the mass of the machine in a horizontal position and at an angle when lifting one of the sides. A method for calculating the metrological characteristics of the proposed method is given. The error in measuring the angle of transverse stability of the proposed method consists of the error in measuring the mass of the machine and the uncertainty in measuring the angle of elevation of the machine’s edge. These values are independent and uncorrelated. The measurement error of the lateral stability angle is determined for the range of the real values masses of the machines and the angle at which they can be lifted aboard in safety conditions. As a result, validation is established. The method of measuring the lateral stability of a machine by successively weighing its sides is sui­table for use. Its following characteristics. Requirements for the accuracy of measuring instruments: the measurement error of the angle of inclination of the machine — no more than ± 0,1°; measurement error of the mass of the machine — no more than ± 4 kg. The total absolute error of the me­thod: when the mass of the machine is (2000)—(2300) kg — not more than 1,5°; with a mass (2300)—(10000) kg — 1,0°; with a mass of 10,000 kg or more — 0,5°. The range of measured values of the lateral stability angle is (25—45)°. The angle at which the machine climbs is (5—15)°. The scope of application of the method: tractors, trailers, agricultural machines. Table — 4. Figure — 4. References — 10.

Monopulse forward‐looking imaging algorithm based on Levenberg–Marquardt optimisation

With precise angle measurement, traditional monopulse techniques for forward-looking imaging can acquire exact angle information of one single target within a radar beam. However, when multiple targets exist in a beam, it is difficult to resolve them. To address this problem, a novel monopulse forward-looking imaging algorithm based on Levenberg–Marquardt (LM) optimisation is proposed. The core idea of this algorithm is to solve maximum likelihood estimation problem based on LM optimisation (ML-LM) to obtain the direction of arrival (DOA) estimation of unresolved targets. First, the echo model of two targets within a forward-looking radar beam is established, then the imaging framework of the proposed algorithm is introduced. Finally, the advantages of ML-LM are illustrated based on a series of evaluation criterion, including angle measurement error for various values of signal-to-noise ratio (SNR), angle interval adaptability and computational efficiency. The simulation results show that two targets within a forward-looking radar beam can be resolved and relocated accurately utilising the proposed algorithm. Meanwhile, the comparison with other algorithms shows it has higher DOA estimation accuracy, less computational complexity and a wider range of angle interval adaptability.

A New Method of Angle Measurement Error Analysis of Rotary Encoders

In this article, a method of error source analysis and detection to improve the angle measurement accuracy of rotary encoders in precision measuring instruments is proposed. The angle measurement error caused by the installation eccentricity of the grating disk and the radial error motion of the rotating shaft is analyzed, and the error model is built. The method of measuring the radial error motion is introduced, and the visual system and image processing technology is proposed to detect the eccentricity. The verification experiment by the use of an autocollimator and a polygon is carried out. The residual error after comparison within ±6″ accounts for 9% of the angle measurement error. The proposed error model is verified, and the angle measurement error can be predicted if the installation eccentricity and radial error motion are known.

Evaluating the feasibility of two post-hoc correction techniques for mitigating posture-induced measurement errors associated with wearable motion capture

Wearable motion capture systems are commonly used to measure body kinematics outside of laboratory settings. However, commercially available systems are designed to be used with typically developed adult populations, and assume users begin with a typical standing posture. Individuals with cerebral palsy and other neuromuscular pathologies often present atypical postures that can introduce significant errors in kinematics measurements from wearable motion capture. This study examines two post-hoc correction techniques for rectifying posture-induced errors in kinematic data: (1) Direct three-dimensional realignment of the measured body segment orientations, or (2) adding the initial static joint angle to the dynamic joint angle measurements. Gait kinematics were measured for eight able-bodied participants using a commercial wearable motion capture system. Participants walked with a typical gait, simulated crouch gait, and simulated equinus. The resulting kinematics from the uncorrected and post-hoc corrected trials were compared against simultaneously recorded measurements from an optoelectric motion capture system. Both correction techniques significantly decreased the posture-induced errors in lower-limb joint angle measurements. This work establishes a basis for the application of post-hoc correction techniques, aimed at improving the performance of wearable kinematic measurement systems when used with individuals having non-typical postures.

LiDAR measurement system and the calibration method of loading robot

To carry out the measurement of vehicle body position and dimension of loading robot before loading, an intelligent vehicle body measurement system based on two-dimensional LiDAR was provided, and the calibration method of this system was studied as a key point. The two-dimension LiDAR was driven by rotating the platform, and the three-dimensional information of car body measured was obtained by using the single two-dimensional laser radar. In allusion to the complexity of calibration method of LiDAR measurement system and the difficulty in making calibration pieces, a system parameter calibration method was proposed based on 321 coordinate system building method, and mathematical models of calibration was established, with the principle and procedure of calibration method in detail. Measurement system was set up in a laboratory to carry out calibration experiment and measurement experiment on simulation vehicle body, and the measurement experiment for real vehicle body was conducted outside. The experiment result shows that the maximum measurement error of vehicle body size and length of this measurement system was 26.4 mm; maximum angle measurement error was 0.18 degree, which fully meets the precision requirements of loading.

LMS Adaptive Filtering of Drilling Tool Vibration Signal

As the dynamic measurement of attitude parameter of the steerable drilling tool under vibration may be not accurate, the Least Mean Square (LMS) adaptive filtering algorithm is adopted to filter the influence of drilling tool vibration on the attitude measurement in this paper. The simulation results show that the measurement error of inclination angle after LMS adaptive filtering can be less than 0.1°, and the measurement error of tool face angle is less than 6°, which could effectively improve the attitude measurement accuracy of vertical steerable drilling tools; the results of inverse analysis on actual drilling data show that the actual measurement error of inclination angle after LMS adaptive filtering is about 3°, which is much smaller than that before filtering. It shows that LMS adaptive filtering can effectively filter the vibration signal of drilling tools and greatly improve the dynamic measurement accuracy of the tool attitude.

Effects of additives on atmospheric pressure gliding arc applied to the modification of polypropylene

The polypropylene (PP) strips were modified with the industrial gliding arc discharge working in air flow at 50 Hz. The experiments aimed at increased wettability and improved strength of the epoxy adhesive DP190 bond with PP. While working only in dry air, the deterioration of the plasma treatment uniformity was observed at higher treatment speeds than 100 mm/s. At the same time, the tensile strength of the adhesive bond and the atomic concentrations of O and N decreased whereas the water contact angle (WCA) measurement error increased. The fast camera measurements revealed that the PP surface was treated by the direct contact with active plasma filaments. The non-uniformity of the PP surface treatment for increased treatment speed can be explained by taking into account the stochastic character of the filament propagation direction and the characteristic time scales of the process.As an improvement of the gliding arc treatment technology a new geometry utilizing the gas cross flow was proposed with the help of gas dynamic simulations. The addition of argon cross flow led to an improvement of the treatment uniformity and, for the optimized conditions, the measured tensile strength of the adhesive bond to PP was 6.5 times higher than for the untreated PP sample. The treatments with the cross flow of argon mixed with water vapors and volatile organic compounds (VOCs), ethanol and isopropanol, did not increase the tensile strength of the adhesive joint even though the wettability was higher for the mixtures with VOCs. Since the concentration of functional groups measured by X-ray photoelectron spectroscopy was well correlated with the tensile strength of adhesive joints, WCA measurements cannot be used as the only parameter judging the success of the plasma treatment aimed at an improvement of adhesive joint strength.

On the size-dependent behavior of drop contact angle in wettability alteration of reservoir rocks to preferentially gas wetting using nanofluid

Wettability alteration of rock surfaces toward gas wetting have been recognized as a practical approach for maximizing the production from the gas condensate reservoirs. Most of the reported work in this area applied the so called sessile drop contact angle measurement technique to examine the change in wetting state of a surface. However, the size-dependent wetting behavior of drop which could affect the exact determination of wettability and wettability changes was not well discussed in the previous studies. Therefore, in this work, the size dependency of contact angle for four different liquid-solid-gas systems; i.e., water-calcite-air, water-treated calcite-air (nanofluid treated calcite), oil-calcite-air, and oil-treated calcite-air, were investigated. To provide a better understanding of the displacement of reservoir gas and liquid following the wettability alteration process, a dynamic contact angle measurement approach was designed. The effect of drop size and surface roughness on the wetting state of calcite rock samples at the initial and altered condition of wettability was then investigated through experimental and modeling approaches. The surface roughness of calcite samples and drop contact angles were determined using Atomic Force Microscopy and Low bond axisymmetric drop shape analysis method, respectively. Analysis of results demonstrated that size dependency of contact angle imposed an error as high as 22.2° on the measurement of achieved wettability alteration in the case of water-calcite/treated calcite-air system. On the basis of calculated pseudo-line tension from the modeling schemes, it was also revealed that the surface roughness had a significant impact on wettability measurements. Both low and high pseudo-line tension values of order 10−9 and 10−6 N, respectively, could dictate some level of errors in contact angle measurements. However, high values were supposed to have a considerable degree of importance in gas condensate applications. The results of this study could provide a better understanding of the contact angle measurement experiments for petroleum engineers to evaluate the wettability alteration schemes.

Automatic measurement algorithm of scoliosis Cobb angle based on deep learning

Aiming at the subjective experience of the physician, the high measurement error in the Cobb angle measurement of scoliosis X-ray images and the X-ray image of spine is difficult to segment. A deep learning based scoliosis Cobb angle measurement algorithm which can automatically calculate Cobb angle without the physician’s manual definition is proposed. A DU-Net detection and segmentation network is proposed in this paper to remove the unrelated regions and to segment the spine contour in the spine X-ray image. The aggregated channel features in pedestrian detection algorithm is introduced to scoliosis image to realize the spine region detection. And the DU-Net network is training to segment spine contour. Therefore, the spine curve can be fitted by the spine contour and the Cobb angle can be automatically measured by the tangent line of spine curve. As a result, the Cobb angle measure methods yields an average error of 2.9° to reference Cobb angle which are measured manually by special orthopaedist. The detection algorithm in this paper yields an average precision of 98.5% and a recall of 99.5%. Moreover, the DU-Net reach an average Dice coefficient to reference segmentation of 90.28%, an IOU of 82.29% and a precision of 86.30%.

Scan angle error measurement based on phase-stepping algorithms in scanning beam interference lithography.

In this paper, a doubled-period grating (DPG) method is proposed to measure the scan angle error in scanning beam interference lithography (SBIL), together with a high-resolution two-dimensional stage and phase-stepping algorithms. A reference grating, which was the doubled period of the interference field, is adapted to diffract the incident left and right beams to form an interferogram captured by a CCD camera. The phase-stepping algorithm was applied to calculate the phase of the interferogram. First, by translating the stage, the reference grating lines were adjusted parallel to the scan direction by comparing the phase of the interferogram between the starting point and the ending point. Next, by rotating the stage step by step, the phase of the interferogram was obtained at each step as well as the phase slope. The scan angle error was considered to be least when the slope was minimum. Finally, a grating mask with a size of 100×100 mm2 was fabricated to verify the feasibility of the method. The scan angle error was measured with a precision of less than 12.65 μrad, which indicates the effectiveness of the proposed method to fabricate high-quality gratings in the future.

Impact of the Measurement Errors on Synchrophasor-Based WAMS Applications

Data from Phasor Measurement Units (PMUs) inform powerful diagnostic tools that can help avert catastrophic failures in the power grid. Because of this, PMU measurement errors are particularly problematic, and it is critical to understand their impact. However, there is limited understanding of how much the PMU measurement errors affect the performance of various synchrophasor-based applications, and thus the ability of these applications to fulfill the users' requirements effectively is also unclear. This paper examines internal and external factors contributing to PMU phase angle and frequency measurement errors. A generic method is proposed to evaluate the impact of measurement errors on application performance. The impact of measurement errors on several synchrophasor-based Wide Area Monitoring System (WAMS) applications are analyzed as examples. These applications include power system disturbance location, oscillation detection, islanding detection, and dynamic line rating. The analysis demonstrated that the proposed method can be used to quantify the measurement error impact and analyze the performance degradation of these applications due to the measurement error. It also reveals that the impact of measurement error depends on the type, algorithm, and parameters of applications.