FSS-EMD-MIO: robust map-free magnetic-inertial odometry via Fibonacci sphere-sampled equivalent dipole modeling for indoor navigation

Abstract Achieving stable and high-precision positioning in environments where Global Navigation Satellite System (GNSS) is denied remains a significant challenge. Magnetic field odometry has emerged as an effective solution; however, existing methods mostly rely on polynomial model, which is often inadequate for accurately characterizing the complex spatial variations of indoor magnetic fields. To address this limitation, this paper proposes a robust magnetic-inertial odometry (MIO) method based on the Fibonacci sphere-sampled equivalent magnetic dipole model (FSS-EMD), denoted as FSS-EMD-MIO. The method employs Fibonacci sphere sampling to construct the FSS-EMD, which can more accurately capture local magnetic field variations and magnetic anomaly distributions. Furthermore, by deriving the spatial gradient of the FSS-EMD, an analytical relationship between magnetic observations and the displacement, velocity, and attitude of the carrier is established. An Adaptive Error State Kalman Filter (AESKF) that integrates the magnetic dipole model, magnetometer array observations, and the inertial navigation system is then designed, enabling high-precision indoor autonomous positioning without reliance on prior maps. Experimental results using public datasets demonstrate that the proposed method achieves a horizontal positioning RMSE below 1.27 m, outperforming state‑of‑the‑art methods by an average of 46%, with improvements ranging from 11 to 82% under different sensor height and motion direction. In addition, the method exhibits strong robustness across different heights and motion directions. This study provides a novel and reliable solution for infrastructure-free indoor positioning.