A Stochastic Optimization Approach to Magnetometer Calibration With Gradient Estimates Using Simultaneous Perturbations

Triaxial magnetometers are indispensable part of every attitude sensing equipment for providing heading information. However, magnetometer measurements are affected by a number of error sources such as soft iron, hard iron, sensor nonorthogonality, and bias. These erroneous measurements, if not properly calibrated, deteriorate the quality of attitude estimates. In this paper, we present a new approach to calibrate triaxial magnetometer measurements by posing the calibration problem as a stochastic optimization problem. A scalar objective function is derived which involves magnetometer calibration parameters corresponding to all distortions. In order to recursively solve for optimized calibration parameters, a modified version of simultaneous perturbation stochastic approximation for the gradient is proposed for faster convergence. The proposed approach places no restrictions on the number of parameters involved and offers a complete solution by solving for all calibration parameters. The proposed approach is tested and validated using experimental data and the performance is compared against a reference approach.