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An Observability-Constrained Magnetic Field-Aided Inertial Navigation System -- Extended Version

Chuan Huang, Gustaf Hendeby, Isaac Skog

TL;DR

The paper addresses yaw observability and uncertainty consistency in magnetic field–aided inertial navigation by extending the observability-constrained EKF to MAINS. It preserves the system's unobservable subspace by minimally modifying the Jacobians through a constrained optimization, ensuring the yaw direction remains non-observable and the uncertainty remains consistent. Empirical results from simulations and real-world tests show improved estimation accuracy and better alignment between perceived and true uncertainty, especially for yaw, with some residual position instabilities attributed to calibration. The approach enhances reliability of navigation outputs when fusing magnetic-field-based odometry with inertial data, aiding control and decision processes in autonomous systems.

Abstract

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an observability-constrained magnetic field-aided inertial navigation system is proposed to address the issue of erroneous yaw observability, which leads to inconsistent estimates of yaw uncertainty. The proposed method builds upon the previously proposed observability-constrained extended Kalman filter and extends it to work with a magnetic field-based odometry-aided inertial navigation system. The proposed method is evaluated using simulation and real-world data, showing that (i) the system observability properties are preserved, (ii) the estimation accuracy increases, and (iii) the perceived uncertainty calculated by the EKF is more consistent with the true uncertainty of the filter estimates.

An Observability-Constrained Magnetic Field-Aided Inertial Navigation System -- Extended Version

TL;DR

The paper addresses yaw observability and uncertainty consistency in magnetic field–aided inertial navigation by extending the observability-constrained EKF to MAINS. It preserves the system's unobservable subspace by minimally modifying the Jacobians through a constrained optimization, ensuring the yaw direction remains non-observable and the uncertainty remains consistent. Empirical results from simulations and real-world tests show improved estimation accuracy and better alignment between perceived and true uncertainty, especially for yaw, with some residual position instabilities attributed to calibration. The approach enhances reliability of navigation outputs when fusing magnetic-field-based odometry with inertial data, aiding control and decision processes in autonomous systems.

Abstract

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an observability-constrained magnetic field-aided inertial navigation system is proposed to address the issue of erroneous yaw observability, which leads to inconsistent estimates of yaw uncertainty. The proposed method builds upon the previously proposed observability-constrained extended Kalman filter and extends it to work with a magnetic field-based odometry-aided inertial navigation system. The proposed method is evaluated using simulation and real-world data, showing that (i) the system observability properties are preserved, (ii) the estimation accuracy increases, and (iii) the perceived uncertainty calculated by the EKF is more consistent with the true uncertainty of the filter estimates.
Paper Structure (13 sections, 51 equations, 4 figures, 1 algorithm)

This paper contains 13 sections, 51 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preserve Observability Properties
  3. Application to the MAINS
  4. State-Space Model
  5. Linearized Error State Model
  6. Unobservable subspace and Interpretations
  7. Suggested Modifications of the Jacobians
  8. Experimental Evaluation
  9. Simulation Setup and Result
  10. Experimental Setup and Result
  11. Summary & Conclusions
  12. The Unobservable Subspace Basis
  13. Interpretation of the Unobservable Subspace

Figures (4)

  • Figure 1: Example of the perceived yaw uncertainty calculated by the EKF used to realize magnetic field-odometry-aided INS in huang2023mains (black line). Also shown is the perceived yaw uncertainty of the proposed observability-constrained EKF algorithm (red line), as well as the initial uncertainty (blue line).
  • Figure 2: The sensor board used in the MAINS. It has 30 PNI https://www.pnicorp.com/rm3100/ magnetometers and an Osmium MIMU 4844 IMU.
  • Figure 3: Monte Carlo simulation results. The RMSE results are the average value calculated from 50 independent simulations.
  • Figure 4: Results from real-world experiment. The RMSE results are the average value calculated from using 12 randomly selected initialization states.