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Bias-Eliminated PnP for Stereo Visual Odometry: Provably Consistent and Large-Scale Localization

Guangyang Zeng, Yuan Shen, Ziyang Hong, Yuze Hong, Viorela Ila, Guodong Shi, Junfeng Wu

TL;DR

This work addresses large-scale stereo visual odometry with unreliable triangulation by developing a bias-eliminated weighted PnP estimator that is provably $\sqrt{n}$-consistent. By decoupling pose estimation from 3D point triangulation and rigorously propagating uncertainty, the authors integrate the Bias-Eli-W PnP into a stereo VO pipeline called CurrentFeature Odometry, augmented with epipolar bundle adjustment. The approach yields substantial improvements in both relative pose error and absolute trajectory error on KITTI and Oxford RobotCar benchmarks, and demonstrates robustness under erratic motions. The combination of uncertainty-aware bias correction, current-frame feature triangulation, and epipolar BA offers a practical pathway to reliable large-scale localization in challenging robotic scenarios.

Abstract

In this paper, we first present a bias-eliminated weighted (Bias-Eli-W) perspective-n-point (PnP) estimator for stereo visual odometry (VO) with provable consistency. Specifically, leveraging statistical theory, we develop an asymptotically unbiased and $\sqrt {n}$-consistent PnP estimator that accounts for varying 3D triangulation uncertainties, ensuring that the relative pose estimate converges to the ground truth as the number of features increases. Next, on the stereo VO pipeline side, we propose a framework that continuously triangulates contemporary features for tracking new frames, effectively decoupling temporal dependencies between pose and 3D point errors. We integrate the Bias-Eli-W PnP estimator into the proposed stereo VO pipeline, creating a synergistic effect that enhances the suppression of pose estimation errors. We validate the performance of our method on the KITTI and Oxford RobotCar datasets. Experimental results demonstrate that our method: 1) achieves significant improvements in both relative pose error and absolute trajectory error in large-scale environments; 2) provides reliable localization under erratic and unpredictable robot motions. The successful implementation of the Bias-Eli-W PnP in stereo VO indicates the importance of information screening in robotic estimation tasks with high-uncertainty measurements, shedding light on diverse applications where PnP is a key ingredient.

Bias-Eliminated PnP for Stereo Visual Odometry: Provably Consistent and Large-Scale Localization

TL;DR

This work addresses large-scale stereo visual odometry with unreliable triangulation by developing a bias-eliminated weighted PnP estimator that is provably -consistent. By decoupling pose estimation from 3D point triangulation and rigorously propagating uncertainty, the authors integrate the Bias-Eli-W PnP into a stereo VO pipeline called CurrentFeature Odometry, augmented with epipolar bundle adjustment. The approach yields substantial improvements in both relative pose error and absolute trajectory error on KITTI and Oxford RobotCar benchmarks, and demonstrates robustness under erratic motions. The combination of uncertainty-aware bias correction, current-frame feature triangulation, and epipolar BA offers a practical pathway to reliable large-scale localization in challenging robotic scenarios.

Abstract

In this paper, we first present a bias-eliminated weighted (Bias-Eli-W) perspective-n-point (PnP) estimator for stereo visual odometry (VO) with provable consistency. Specifically, leveraging statistical theory, we develop an asymptotically unbiased and -consistent PnP estimator that accounts for varying 3D triangulation uncertainties, ensuring that the relative pose estimate converges to the ground truth as the number of features increases. Next, on the stereo VO pipeline side, we propose a framework that continuously triangulates contemporary features for tracking new frames, effectively decoupling temporal dependencies between pose and 3D point errors. We integrate the Bias-Eli-W PnP estimator into the proposed stereo VO pipeline, creating a synergistic effect that enhances the suppression of pose estimation errors. We validate the performance of our method on the KITTI and Oxford RobotCar datasets. Experimental results demonstrate that our method: 1) achieves significant improvements in both relative pose error and absolute trajectory error in large-scale environments; 2) provides reliable localization under erratic and unpredictable robot motions. The successful implementation of the Bias-Eli-W PnP in stereo VO indicates the importance of information screening in robotic estimation tasks with high-uncertainty measurements, shedding light on diverse applications where PnP is a key ingredient.

Paper Structure

This paper contains 18 sections, 2 theorems, 14 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. System overview
  4. Front end
  5. Back end
  6. Triangulation and uncertainty estimation
  7. Bias-eliminated weighted PnP
  8. Epipolar bundle adjustment
  9. Simulations and Experiments
  10. Simulation
  11. Consistency of bias-eliminated PnP
  12. Rationality of utilizing the latest KF for pose tracking
  13. Effect of the epipolar BA
  14. Experiments on real datasets
  15. KITTI Dataset
  16. ...and 3 more sections

Key Result

Theorem 1

The bias-eliminated estimator $(\hat{R}_c^{\rm BE},\hat{t}_c^{\rm BE})$ is $\sqrt{n}$-consistent, i.e., $\hat{R}_c^{\rm BE}-R_c^o=O_p(1/\sqrt{n}$), $\hat{t}_c^{\rm BE}-t_c^o=O_p(1/\sqrt{n})$.

Figures (7)

  • Figure 1: System overview. L and R refer to the left and right images, respectively, and KF and CF denote the keyframe and current frame, respectively.
  • Figure 2: Illustration of frame tracking. The orange circles represent feature-matching uncertainties and the blue ellipses denote the triangulation uncertainties.
  • Figure 3: Illustration of epipolar BA. For two KFs, we utilize stereo images, while for OFs, we only use the left image. Epipolar constraints for each pair of images with matched features are involved in BA, and point-to-epipolar-line distances are optimized.
  • Figure 4: Consistency of the bias-eliminated PnP estimator. The units of the RMSEs of noise std, rotation, and translation are pixel, $^\circ$, and m.
  • Figure 5: Average pose error of each frame when using different numbers of KFs for the line trajectory.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Definition 1: $\sqrt{n}$-Consistency in Probability
  • Theorem 1
  • proof
  • Lemma 1