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.

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