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MSCEKF-MIO: Magnetic-Inertial Odometry Based on Multi-State Constraint Extended Kalman Filter

Jiazhu Li, Jian Kuang, Xiaoji Niu

TL;DR

The paper tackles robust, fingerprint‑free indoor positioning using a magnetometer array to model local magnetic fields and fuse these observations with inertial navigation via a Multi‑State Constraint EKF (MSCEKF). By enforcing curl‑free and divergence‑free magnetic field constraints and adding a magnetic vector attitude constraint, the method achieves accurate velocity and heading estimates without pre‑built magnetic maps. Experimental results show substantial improvements over MAINS on both public and proprietary datasets, including ~0.5 m horizontal RMSE on open data and ~2.4 m average horizontal error on longer, real‑world trajectories, with strong velocity and heading stability in magnetically rich environments. The approach offers a low‑power, cost‑effective indoor localization solution suitable for tunnels and complex indoor layouts, with future work aimed at strengthening performance under weak magnetic gradients and enabling collaborative sensing.

Abstract

To overcome the limitation of existing indoor odometry technologies which often cannot simultaneously meet requirements for accuracy cost-effectiveness, and robustness-this paper proposes a novel magnetometer array-aided inertial odometry approach, MSCEKF-MIO (Multi-State Constraint Extended Kalman Filter-based Magnetic-Inertial Odometry). We construct a magnetic field model by fitting measurements from the magnetometer array and then use temporal variations in this model-extracted from continuous observations-to estimate the carrier's absolute velocity. Furthermore, we implement the MSCEKF framework to fuse observed magnetic field variations with position and attitude estimates from inertial navigation system (INS) integration, thereby enabling autonomous, high-precision indoor relative positioning. Experimental results demonstrate that the proposed algorithm achieves superior velocity estimation accuracy and horizontal positioning precision relative to state-of-the-art magnetic array-aided INS algorithms (MAINS). On datasets with trajectory lengths of 150-250m, the proposed method yields an average horizontal position RMSE of approximately 2.5m. In areas with distinctive magnetic features, the magneto-inertial odometry achieves a velocity estimation accuracy of 0.07m/s. Consequently, the proposed method offers a novel positioning solution characterized by low power consumption, cost-effectiveness, and high reliability in complex indoor environments.

MSCEKF-MIO: Magnetic-Inertial Odometry Based on Multi-State Constraint Extended Kalman Filter

TL;DR

The paper tackles robust, fingerprint‑free indoor positioning using a magnetometer array to model local magnetic fields and fuse these observations with inertial navigation via a Multi‑State Constraint EKF (MSCEKF). By enforcing curl‑free and divergence‑free magnetic field constraints and adding a magnetic vector attitude constraint, the method achieves accurate velocity and heading estimates without pre‑built magnetic maps. Experimental results show substantial improvements over MAINS on both public and proprietary datasets, including ~0.5 m horizontal RMSE on open data and ~2.4 m average horizontal error on longer, real‑world trajectories, with strong velocity and heading stability in magnetically rich environments. The approach offers a low‑power, cost‑effective indoor localization solution suitable for tunnels and complex indoor layouts, with future work aimed at strengthening performance under weak magnetic gradients and enabling collaborative sensing.

Abstract

To overcome the limitation of existing indoor odometry technologies which often cannot simultaneously meet requirements for accuracy cost-effectiveness, and robustness-this paper proposes a novel magnetometer array-aided inertial odometry approach, MSCEKF-MIO (Multi-State Constraint Extended Kalman Filter-based Magnetic-Inertial Odometry). We construct a magnetic field model by fitting measurements from the magnetometer array and then use temporal variations in this model-extracted from continuous observations-to estimate the carrier's absolute velocity. Furthermore, we implement the MSCEKF framework to fuse observed magnetic field variations with position and attitude estimates from inertial navigation system (INS) integration, thereby enabling autonomous, high-precision indoor relative positioning. Experimental results demonstrate that the proposed algorithm achieves superior velocity estimation accuracy and horizontal positioning precision relative to state-of-the-art magnetic array-aided INS algorithms (MAINS). On datasets with trajectory lengths of 150-250m, the proposed method yields an average horizontal position RMSE of approximately 2.5m. In areas with distinctive magnetic features, the magneto-inertial odometry achieves a velocity estimation accuracy of 0.07m/s. Consequently, the proposed method offers a novel positioning solution characterized by low power consumption, cost-effectiveness, and high reliability in complex indoor environments.
Paper Structure (12 sections, 43 equations, 10 figures, 6 tables)

This paper contains 12 sections, 43 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Local Magnetic Field Modeling
  3. Magnetic-Inertial Odometry with Magnetometer Array Constraint
  4. Inertial Navigation Algorithm
  5. Multi State Constraint Extended Kalman Filter
  6. Observation model
  7. Experimental Results
  8. Results on OA dataset
  9. Results on Our dataset
  10. Analysis of N-frame Mag Constraint
  11. Analysis of the Impact of Magnetic Field Gradients
  12. Conclusions and Future Work

Figures (10)

  • Figure 1: A 2D illustration of the geometric relationship between the body frames at two consecutive times.
  • Figure 2: Algorithm flow chart of MSCEKF-MIO
  • Figure 3: Trajectory estimation results of OA dataset
  • Figure 4: Sensor array platform
  • Figure 5: Data acquisition environment
  • ...and 5 more figures