A Low-Dimensional Accelerometer-Magnetometer Alignment Method for Ultralow-Frequency Magnetic-Field-Based Positioning Systems

Ultralow-frequency magnetic-field-based positioning systems (ULF-MPSs), which feature high penetrability, enable accurate positioning free of cumulative errors, rendering them well-suited for non-line-of-sight (NLOS) environments. To reduce the sensitivity to the relative attitude between the magnetic source and the sensor unit, these systems typically fuse magnetometer and accelerometer data to extract attitude information. However, theoretical analysis and experiments in this article demonstrate that accelerometer-magnetometer misalignment errors propagate through attitude estimation, thereby increasing positioning deviations and compromising the algorithm's robustness against relative attitude fluctuations. For these issues, a low-dimensional alignment method featuring four independent unknown parameters is proposed, implemented with a rotation quaternion-based alignment model and a two-step optimization algorithm. The method requires only five sets of attitude measurements for reliable and stable misalignment parameter estimation, making it a practical alternative to existing algorithms for mobility-limited platforms. Underground experiments conducted with a mobile platform show that when the proposed method is applied to the scenario with slightly larger inter-sensor misalignment angles, the Euclidean position deviations over the eight test points within a 15 × 5 m² area decrease on average by 55.1 %, from 0.69 to 0.31 m; the standard deviation of normalized position deviations for six attitudes at the same position falls by 93.6 %, from 2.52 % to 0.16 %. Comparable improvements are obtained for minor misalignment angles, confirming the proposed alignment method's effectiveness in reducing positioning deviations and improving the attitude robustness of ULF-MPSs.