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Invariant Smoothing for Localization: Including the IMU Biases

Paul Chauchat, Silvère Bonnabel, Axel Barrau

TL;DR

This article brings the recently introduced Two Frames Group (TFG) to bear on the problem of Invariant Smoothing, to better take into account the IMU biases, as compared to the state-of-the-art in localization and navigation.

Abstract

In this article we investigate smoothing (i.e., optimisation-based) estimation techniques for robot localization using an IMU aided by other localization sensors. We more particularly focus on Invariant Smoothing (IS), a variant based on the use of nontrivial Lie groups from robotics. We study the recently introduced Two Frames Group (TFG), and prove it can fit into the framework of Invariant Smoothing in order to better take into account the IMU biases, as compared to the state-of-the-art in robotics. Experiments based on the KITTI dataset show the proposed framework compares favorably to the state-of-the-art smoothing methods in terms of robustness in some challenging situations.

Invariant Smoothing for Localization: Including the IMU Biases

TL;DR

This article brings the recently introduced Two Frames Group (TFG) to bear on the problem of Invariant Smoothing, to better take into account the IMU biases, as compared to the state-of-the-art in localization and navigation.

Abstract

In this article we investigate smoothing (i.e., optimisation-based) estimation techniques for robot localization using an IMU aided by other localization sensors. We more particularly focus on Invariant Smoothing (IS), a variant based on the use of nontrivial Lie groups from robotics. We study the recently introduced Two Frames Group (TFG), and prove it can fit into the framework of Invariant Smoothing in order to better take into account the IMU biases, as compared to the state-of-the-art in robotics. Experiments based on the KITTI dataset show the proposed framework compares favorably to the state-of-the-art smoothing methods in terms of robustness in some challenging situations.
Paper Structure (19 sections, 2 theorems, 27 equations, 1 figure, 1 table)

This paper contains 19 sections, 2 theorems, 27 equations, 1 figure, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Smoothing on Lie groups
  3. Smoothing on Lie groups
  4. Group affine Dynamics and Invariant Smoothing
  5. Localization with an IMU using the TFG
  6. Considered simplified problem
  7. Making the system group affine
  8. Theoretical results
  9. Application to biased IMU based localization
  10. Computing the Jacobians
  11. Differences with other parametrisations
  12. Experimental Results
  13. Implementation details
  14. Results
  15. Conclusion
  16. ...and 4 more sections

Key Result

Proposition 1

Let $\chi_{i+1}:=f_i(\chi_i)$ for group affine dynamics eq:group_affine_def. We have with $\mathbf{F}_i=\bf\mathbf{Ad}_{\boldsymbol{\Upsilon}_i^{-1}}\mathbf{M}$ a linear operator, and $\mathbf{M}$ from eq:LGLA.

Figures (1)

  • Figure 1: Convergence and consistency comparison of smoothing based on three parametrisations: using the TFG (ours), $SE_2(3)$chauchat2022smoothing, and NavState (GTSAM dellaert2016new), with a window size of 5. For 50 Monte Carlo runs over the KITTI trajectory 01, during the transitory phase after an initialization with random yaw, the yaw error and the $3\sigma$ envelope obtained from the estimated covariance are plotted over time. Consistent trajectories are in blue, inconsistent ones in red.

Theorems & Definitions (3)

  • Definition 1
  • Proposition 1: from barrau2019linear, discrete-time log-linear property
  • Proposition 2: from barrau2022geometry