Direct and Indirect Estimation of the Variance–Covariance Matrix of the Parameters of a Fitted Ellipse and a Triaxial Ellipsoid

Πάνου, Γεώργιος; Agatza-Balodimou, A. M.

doi:10.1061/(asce)su.1943-5428.0000342

Cited by 14 publications

(3 citation statements)

References 12 publications

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“…Equation ( 9) is consistent with the equation of spatial ellipsoids, and G and K of can be obtained using an ellipsoid fitting algorithm when |H g | is known [22]. The value of |H g | can be obtained by the magnetic total field magnetometer.…”

Section: Calibration Methodsmentioning

confidence: 65%

Calibration of strapdown magnetic vector measurement systems based on a plane compression method

Cheng

Wang

et al. 2023

Meas. Sci. Technol.

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The strapdown magnetic vector measurement system which can obtain the magnetic vector field and the attitude information simultaneously has widely applied in geophysical prospecting. A high-performance calibration of systematic errors including magnetometer error and misalignment error is essential for this system. The traditional methods calibrate these two errors separately, having the problems of cumbersome steps and be dependent on special data acquisition ways such as rotation, rolling-over, incline, etc. An original method combining plane compression with ellipsoid fitting is proposed in this paper, which can simultaneously complete the calibration calculation of magnetometer error and misalignment error by one experiment. It can be done using a set of attitude-independent spatial scatter point data and no additional mechanical equipment is required. The mathematical analysis of this method has been done to study the elements decreasing the measurement accuracy of the system, and numerical simulation and field experiments are performed to validate the above analysis. The results indicate that the method can do contribution to the accuracy improvement of magnetic vector measurement system.

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Section: Calibration Methodsmentioning

confidence: 65%

Calibration of strapdown magnetic vector measurement systems based on a plane compression method

Cheng

Wang

et al. 2023

Meas. Sci. Technol.

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“…When using U-Net for target segmentation, jagged edges in the edge area exist. Therefore, according to the prior knowledge that the physical shape of the cornea is an ellipse, the least squares method is used to fit the ellipse with the smallest algebraic distance between the segmentation boundary points ( 19 ) and to realize the smooth fitting of the segmentation results, then the final cornea segmentation results are obtained.…”

Section: Methodsmentioning

confidence: 99%

A Novel System for Measuring Pterygium's Progress Using Deep Learning

et al. 2022

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Pterygium is a common ocular surface disease. When pterygium significantly invades the cornea, it limits eye movement and impairs vision, which requires surgery to remove. It is medically recognized that when the width of the pterygium that invades the cornea is >3 mm, the patient can be treated with surgical resection. Owing to this, this study proposes a system for diagnosing and measuring the pathological progress of pterygium using deep learning methods, which aims to assist doctors in designing pterygium surgical treatment strategies. The proposed system only needs to input the anterior segment images of patients to automatically and efficiently measure the width of the pterygium that invades the cornea, and the patient's pterygium symptom status can be obtained. The system consists of three modules, including cornea segmentation module, pterygium segmentation module, and measurement module. Both segmentation modules use convolutional neural networks. In the pterygium segmentation module, to adapt the diversity of the pterygium's shape and size, an improved U-Net++ model by adding an Attention gate before each up-sampling layer is proposed. The Attention gates extract information related to the target, so that the model can pay more attention to the shape and size of the pterygium. The measurement module realizes the measurement of the width and area of the pterygium that invades the cornea and the classification of pterygium symptom status. In this study, the effectiveness of the proposed system is verified using datasets collected from the ocular surface diseases center at the Affiliated Eye Hospital of Nanjing Medical University. The results obtained show that the Dice coefficient of the cornea segmentation module and the pterygium segmentation module are 0.9620 and 0.9020, respectively. The Kappa consistency coefficient between the final measurement results of the system and the doctor's visual inspection results is 0.918, which proves that the system has practical application significance.

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“…where M = ( C −1 ) T C −1 , the function of the error coefficient of the geomagnetic sensor is the coefficient of the ellipsoid equation. At this time, the coefficients and offsets in (4) can be solved by singular value decomposition [27,28] and then substituted into (2) to obtain the corrected geomagnetic data.…”

Section: Geomagnetic Sensor Error Modelingmentioning

confidence: 99%

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

Jiang,

Tan

2024

Meas. Sci. Technol.

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Aiming at the problems that the traditional single ellipsoid fitting fails to eliminate the errors of the geomagnetic sensor and does not consider the geomagnetic anomaly information, etc., this paper proposes a Robust Least Squares combined with the Levenberg-Marquardt (LM-RLS) algorithm to fit an accurate ellipsoid to achieve accurate data calibration. According to the geomagnetic sensor error model, the total amount of geomagnetism is used as the constraint, the fitted ellipsoid coefficients of Robust Least Squares (RLS) are used as the initial values, and the LM algorithm is used to calculate the magnetic field dispersion points to the nearest point of the fitted ellipsoid surface. Then, the initial calibration value is solved by the criterion of the minimum weighted sum of squares of the closest point distance. Finally, the accurate ellipsoid is obtained to realize data calibration. The results of the dynamic experiment show that after the ellipsoid is precisely fitted by the LM-RLS algorithm, the sum of the absolute values of the distance from the magnetic field discrete data to the ellipsoid surface is reduced by 48.33% (RLS) and 43.10% (RWTLS). The relative errors of the magnetic field in the X, Y, and Z axes are reduced from 0.48%, 0.78%, 1.48% (RLS) and 0.30%, 0.58%, 1.14% (RWTLS) to 0.10%, 0.04%, 0.16 %, respectively. The accuracy of geomagnetic calibration is improved by 68.06% (RLS) and 61.02% (RWTLS) in the dynamic experiment. The algorithm improves the accuracy of geomagnetic measurement, which provides a new idea for the calibration of three-axis geomagnetic sensors.

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Direct and Indirect Estimation of the Variance–Covariance Matrix of the Parameters of a Fitted Ellipse and a Triaxial Ellipsoid

Cited by 14 publications

References 12 publications

Calibration of strapdown magnetic vector measurement systems based on a plane compression method

Calibration of strapdown magnetic vector measurement systems based on a plane compression method

A Novel System for Measuring Pterygium's Progress Using Deep Learning

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

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