Differential 6-DOF Pose Estimation with Provable First-Order Immunity to Camera Calibration Errors

2026-08-05

AI Summary

This work addresses the sensitivity of conventional 3D-to-2D methods to extrinsic calibration errors in estimating minute motions, which hinders high-precision six-degree-of-freedom (6-DOF) pose estimation. The authors propose a differential 6-DOF pose estimation approach that directly computes relative platform motion from inter-frame image displacements and known 3D control points, bypassing absolute pose estimation and supporting both monocular and multi-camera systems. Theoretical analysis demonstrates for the first time that translational extrinsic errors are entirely canceled out, while rotational errors introduce only bounded perturbations; the study further derives observability conditions, the Cramér–Rao lower bound, and an unbiased consistent estimator. Experiments show that under 0.5-pixel noise, the monocular system achieves 10.09 arcsec rotation RMSE and 3.70 mm translation RMSE in 0.34 ms, and the binocular system attains 10.58 arcsec and 3.91 mm in 0.27 ms—significantly outperforming existing PnP methods.

Abstract

Accurate six-degree-of-freedom (6-DOF) motion estimation is essential for robotic manipulation, autonomous systems, and structural displacement monitoring. Conventional 3D-2D methods estimate absolute camera poses independently at each time and recover platform motion through camera-to-platform extrinsics, making them sensitive to extrinsic calibration errors, especially for micromotion. We present a differential pose estimation method that directly recovers platform motion from inter-frame image displacements and known 3D control points. By differencing perspective projection equations, using a depth-invariance approximation, and modeling motion on SE(3), the method avoids independent absolute-pose estimation and supports both monocular and multi-camera systems. We prove that translational extrinsic errors cancel exactly, while rotational errors induce a bounded perturbation determined by calibration error, motion magnitude, and observation geometry. We also derive generic observability conditions, a Cramer-Rao lower bound, and a bias-eliminated consistent estimator, and characterize the validity limits of the approximations. Extensive synthetic and real-world experiments establish a new state of the art for 6-DOF platform micromotion estimation, outperforming representative PnP and generalized-PnP methods in accuracy, calibration robustness, and computational efficiency. With five control points and 0.5-pixel image noise, the monocular solver obtains a combined pitch-yaw rotation RMSE of 10.09 arcsec, a translation RMSE of 3.70 mm, and a runtime of 0.34 ms. The binocular solver achieves a rotation RMSE of 10.58 arcsec, a translation RMSE of 3.91 mm, and a runtime of 0.27 ms. Code will be released upon publication at https://github.com/zyoungszu/pami2026.

Problem

• 6-DOF pose estimation
• camera calibration errors
• micromotion
• extrinsic calibration
• differential motion estimation

Innovation

• differential pose estimation
• 6-DOF motion
• calibration error immunity
• SE(3) modeling
• micromotion estimation