Fast Algebraic Calibration of MEMS Tri-axis Magnetometer for Initial Alignment Using Least Square Method
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ORIGINAL ARTICLE
Fast Algebraic Calibration of MEMS Tri‑axis Magnetometer for Initial Alignment Using Least Square Method Hyo‑Joong Kim1 · Keum‑Cheol Kwon1 · Duk‑Sun Shim1 Received: 11 March 2020 / Revised: 10 July 2020 / Accepted: 7 August 2020 / Published online: 18 August 2020 © The Korean Institute of Electrical Engineers 2020
Abstract Magnetometer is an important sensor for attitude estimation in low-cost, high performance navigation systems and the application extends with inertial sensors to indoor navigation, mobile devices, health monitoring, and so on. Magnetometer calibration is an essential procedure before using it. This paper proposes a fast algebraic calibration algorithm without external reference system after obtaining an ellipsoid fitting from arbitrary rotations of MEMS magnetometer, and also proposes a calibrated measurement to calculate heading for initial alignment. Keywords Magnetometer · Calibration · Ellipsoid fitting · Least square method · MEMS
1 Introduction Magnetometers are a key aiding sensor for attitude estimation in low-cost, high performance navigation systems [1]. The application of magnetometers covers attitude and heading reference system (AHRS), inertial navigation system (INS), and extends with inertial measurement units (IMU) to indoor navigation [2], mobile devices [3], health monitoring [4], accurate 3D positioning [5], low cost compass system [6], and so on. Magnetometer calibration is an essential problem and many calibration techniques have been presented in the literature [1, 7–17]. A classic calibration technique is the swinging algorithm [7], which computes scalar parameters using least square algorithm. However, the swinging algorithm has some drawbacks since it requires external heading information [1] and is limited to use with two-axis systems [8]. A maximum likelihood estimator (MLE) is formulated in [1] to iteratively find the optimal calibration parameters without requiring external attitude references. The magnetometer * Duk‑Sun Shim [email protected] Hyo‑Joong Kim [email protected] Keum‑Cheol Kwon [email protected] 1
School of Electrical and Electronics Engineering, ChungAng University, Seoul, South Korea
measurement model in [9] includes a parameter matrix consisting of scale factors and non-orthogonality corrections, and another parameter of bias vector, which are estimated through extended Kalman filter and Unscented filter. In Ref. [10], the magnetometer measurement model includes scale factors and bias, and the calibration procedure involves arbitrary rotations of the sensor platform and a visual 2D projection of measurements. An adaptive least square estimation provides a consistent solution to the ellipsoid fitting and then magnetometer’s calibration parameters are derived in [11]. In Ref. [12], the ellipsoid coefficient matrix is derived from the measurements and magnetometer’s calibration parameters are derived by using the constant intersection angle method. References [13] provides calibration parameters of a magnetometer as a formula a
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