Optimal Experimental Design for In-Field Calibration of a Nine-Parameter Tri-Axial Magnetometers Model

This study presents an in-depth analysis of the Optimal Experimental Design for in-field calibration of tri-axial magnetometers, with a particular focus on the 9-parameter inclination-based calibration model and its implementation through 12-observation schemes. Initially, the paper examines various experimental schemes applicable to different global locations, and integrates theoretical analysis with simulation and experimental results. Then, the information matrix for the proposed 9-parameter model under the outlined 12-observation scheme is derived. Based on that the G-optimality of the proposed scheme is proved. Subsequent simulation studies rigorously evaluate the scheme’s resilience to variations in the bias angles between actual placement and ideal position, as the bias angles change from 0° to 90°, the relative efficiency decreases from 1 to 3.7586 × 10 ^-33 . Finally, the practical application situation of the 9-parameter calibration model and 12-observation scheme is experimentally verified by using commercial Inertial Measurement Unit devices in diverse locations. This research not only proposes a suite of numerical solutions for ideal conditions but also offers a pragmatic guide for assessing actual device placement in field applications.