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The perturbation effects on the magnetometer can be described as soft iron and hard iron effects. Hard iron ef- fects are a stationary perturbation by other near-by sources, leading to a locally different magnetic field strengths, which results in a shift of the center of the measured ideal sphere. Soft iron effects are distortions in the magnetic field itself, they result in tilting and stretching of different parts of the ideal sphere measurements, forming an ellipsoid. As such, the perturbed measurements lie on a ellipsoid with offset b and shape R, for a average magnetic field strength of B, re- sulting that the uncalibrated measurements u follow approximately the following conic equation: (u-b)R(u—b) = B² Calibration takes place using a least-squares approach of the real measurements relative to a sphere. Having u being the vector of uncalibrated magnetometer measurements, the calibrated, sphere measurement are denoted by the vector m. Matrix A is the square root of perturbation in shape R and b is the offset of the center. m = (u-b)A (4.38)

The perturbation effects on the magnetometer can be described as soft iron and hard iron effects. Hard iron ef- fects are a stationary perturbation by other near-by sources, leading to a locally different magnetic field strengths, which results in a shift of the center of the measured ideal sphere. Soft iron effects are distortions in the magnetic field itself, they result in tilting and stretching of different parts of the ideal sphere measurements, forming an ellipsoid. As such, the perturbed measurements lie on a ellipsoid with offset b and shape R, for a average magnetic field strength of B, re- sulting that the uncalibrated measurements u follow approximately the following conic equation: (u-b)R(u—b) = B² Calibration takes place using a least-squares approach of the real measurements relative to a sphere. Having u being the vector of uncalibrated magnetometer measurements, the calibrated, sphere measurement are denoted by the vector m. Matrix A is the square root of perturbation in shape R and b is the offset of the center. m = (u-b)A (4.38)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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I need help coding in MATLAB. Can you code an example of calibration problem of magnetometers? Assume the uncalibrated values.

The perturbation effects on the magnetometer can be described as soft iron and hard iron effects. Hard iron ef- fects are a stationary perturbation by other near-by sources, leading to a locally different magnetic field strengths, which results in a shift of the center of the measured ideal sphere. Soft iron effects are distortions in the magnetic field itself, they result in tilting and stretching of different parts of the ideal sphere measurements, forming an ellipsoid. As such, the perturbed measurements lie on a ellipsoid with offset b and shape R, for a average magnetic field strength of B, re- sulting that the uncalibrated measurements u follow approximately the following conic equation: (u-b)R(u—b) = B² Calibration takes place using a least-squares approach of the real measurements relative to a sphere. Having u being the vector of uncalibrated magnetometer measurements, the calibrated, sphere measurement are denoted by the vector m. Matrix A is the square root of perturbation in shape R and b is the offset of the center. m = (u-b)A (4.38)
Transcribed Image Text:The perturbation effects on the magnetometer can be described as soft iron and hard iron effects. Hard iron ef- fects are a stationary perturbation by other near-by sources, leading to a locally different magnetic field strengths, which results in a shift of the center of the measured ideal sphere. Soft iron effects are distortions in the magnetic field itself, they result in tilting and stretching of different parts of the ideal sphere measurements, forming an ellipsoid. As such, the perturbed measurements lie on a ellipsoid with offset b and shape R, for a average magnetic field strength of B, re- sulting that the uncalibrated measurements u follow approximately the following conic equation: (u-b)R(u—b) = B² Calibration takes place using a least-squares approach of the real measurements relative to a sphere. Having u being the vector of uncalibrated magnetometer measurements, the calibrated, sphere measurement are denoted by the vector m. Matrix A is the square root of perturbation in shape R and b is the offset of the center. m = (u-b)A (4.38)
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