Monte Carlo Simulation
A Monte Carlo numerical simulation was conducted to replicate 6,000 measurements from a MEMS AHRS during the sinusoidal motions of a vehicle. This simulation was designed to emulate a magnetometer calibration platform for an articulated vehicle or one with pitching capabilities in the Wide Angular Movement (WAM) dataset, a magnetometer calibration for a roll-and-pitch stable vehicle in the Mid Angular Movement (MAM) dataset, and a survey for a vehicle with the same capabilities as described in WAM for the Low Angular Movement (LAM) dataset.
Each experiment lasted 600 s, with simulated data generated at a 10 Hz rate and magnetometer measurements (\(\sigma_{mag} = 10\) mG) and angular rate sensor (\(\sigma_{gyro} = 10\) mrad/s) corrupted by Gaussian noise.
The true magnetic field vector is \(\mathbf{m_0} = [227,\, 52, \,412]^T\) mG, the soft-iron upper triangular terms are given by \(\mathbf{a} = [1.10,\, 0.10,\, 0.04,\, 0.88,\, 0.02,\, 1.22]^T\), the hard-iron bias is \(\mathbf{m_b} = [20,\, 120,\, 90]^T\) mG, and the gyroscope bias is \(\mathbf{w_b} = [4,\, -5,\, 2]^T\) mrad/s.
Note
For further details on the simulation, please refer to the section V. Numerical Simulation Evaluation in the paper.