Robust ellipsoid fitting method based on optimization of a novel nonlinear cost function in navigation systems

Mirzaei, Mojtaba; Hosseini, Iman

doi:10.1007/s40430-019-1747-2

Cited by 5 publications

(2 citation statements)

References 34 publications

(44 reference statements)

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“…Substituting the observed values into (8), the coefficients of the ellipsoid equation can be solved by the RLS [30]:…”

Section: Rlss Ellipsoid Fittingmentioning

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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“…Substituting the observed values into (8), the coefficients of the ellipsoid equation can be solved by the RLS [30]:…”

Section: Rlss Ellipsoid Fittingmentioning

confidence: 99%

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

Jiang,

Tan

2024

Meas. Sci. Technol.

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“…12 To reduce costs, many researchers focus on automatic calibration techniques, such as ellipsoid fitting. 8,13,14 The Earth’s magnetic vector is constant, and when a magnetometer rotates around a specific point, its measurement should be normally distributed on a sphere. However, magnetic interferences in the measurements cause the data distribution to take an ellipsoidal shape.…”

Section: Introductionmentioning

confidence: 99%

Vehicle heading estimation of INS/magnetometer integrated system based on constant hard iron interference calibration

Cui

Wang

et al. 2021

Measurement and Control

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The integrated INS/magnetometer measurement is widely used in low-cost navigation systems. The integration has proven more effective in suppressing the divergence of heading than relying solely on a magnetometer because this is susceptible to local magnetic field interference, reducing heading accuracy. Magnetometers sense the local magnetic field that may be interfered by the nearby ferromagnetic material or strong electric currents. Hence, the magnetometer must be calibrated in the vehicle before use. When a magnetometer is installed near power components (engines, etc.), soft iron interference can be ignored. In the vehicle’s external environment, the time-varying hard iron interference can reach 100 times the strength of the geomagnetic field, meaning that a magnetometer cannot function efficiently because its accuracy is so reduced. Hence, the constant hard magnetic interference inside the vehicle is mainly concerned in this paper. An INS/Magnetometer heading estimation algorithm based on a two-stage Kalman filter is proposed to solve the problem by combining inertial sensor and magnetometer with attitude information. In the first stage filter, the constant hard iron interference is estimated by setting upward standing the three IMU axes. In the second stage filter, the INS/Magnetometer heading estimation is implemented. Finally, the results show that the algorithm improves the accuracy of vehicle heading calculations.

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