A Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame
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A Geometric Approach to Strapdown Magnetometer
Calibration in Sensor Frame
J.F. Vasconcelos, Member, IEEE, G. Elkaim, Member, IEEE, C. Silvestre Member, IEEE,
P. Oliveira Member, IEEE, and B. Cardeira Member, IEEE
Abstract
In this work a new algorithm is derived for the onboard calibration of three-axis strapdown magnetometers. The proposed calibration method is written in the sensor frame, and compensates for the combined effect of all linear time-invariant distortions, namely soft iron, hard iron, sensor non-orthogonality, bias, among others. A Maximum Likelihood Estimator (MLE) is formulated to iteratively find the optimal calibration parameters that best fit to the onboard sensor readings, without requiring external attitude references. It is shown that the proposed calibration technique is equivalent to the estimation of a rotation, scaling and translation transformation, and that the sensor alignment matrix is given by the solution of the orthogonal Procrustes problem. Good initial conditions for the iterative algorithm are obtained by a suboptimal batch least squares computation. Simulation and experimental results with low-cost sensors data are presented and discussed, supporting the application of the algorithm to autonomous vehicles and other robotic platforms.
Index Terms
Calibration; Magnetic fields; Maximum likelihood estimators; Least-squares algorithm.
I. I NTRODUCTION
Magnetometers are a key aiding sensor for attitude estimation in low-cost, high performance navigation systems [1], [2], [3],
[4], with widespread application to autonomous air, ground and ocean vehicles. These inexpensive, low power sensors allow for accurate attitude estimates by comparing the magnetic field vector observation in body frame coordinates with the vector representation in Earth frame coordinates, available from geomagnetic charts and software [5]. In conjunction with vector observations provided by other sensors such as star trackers or
A Geometric Approach to Strapdown Magnetometer
Calibration in Sensor Frame
J.F. Vasconcelos, Member, IEEE, G. Elkaim, Member, IEEE, C. Silvestre Member, IEEE,
P. Oliveira Member, IEEE, and B. Cardeira Member, IEEE
Abstract
In this work a new algorithm is derived for the onboard calibration of three-axis strapdown magnetometers. The proposed calibration method is written in the sensor frame, and compensates for the combined effect of all linear time-invariant distortions, namely soft iron, hard iron, sensor non-orthogonality, bias, among others. A Maximum Likelihood Estimator (MLE) is formulated to iteratively find the optimal calibration parameters that best fit to the onboard sensor readings, without requiring external attitude references. It is shown that the proposed calibration technique is equivalent to the estimation of a rotation, scaling and translation transformation, and that the sensor alignment matrix is given by the solution of the orthogonal Procrustes problem. Good initial conditions for the iterative algorithm are obtained by a suboptimal batch least squares computation. Simulation and experimental results with low-cost sensors data are presented and discussed, supporting the application of the algorithm to autonomous vehicles and other robotic platforms.
Index Terms
Calibration; Magnetic fields; Maximum likelihood estimators; Least-squares algorithm.
I. I NTRODUCTION
Magnetometers are a key aiding sensor for attitude estimation in low-cost, high performance navigation systems [1], [2], [3],
[4], with widespread application to autonomous air, ground and ocean vehicles. These inexpensive, low power sensors allow for accurate attitude estimates by comparing the magnetic field vector observation in body frame coordinates with the vector representation in Earth frame coordinates, available from geomagnetic charts and software [5]. In conjunction with vector observations provided by other sensors such as star trackers or