3.3.1 Absolute Pose Error (APE) as Localization Metric
The EVO tool (https://github.com/MichaelGrupp/evo) is employed to assess the localization precision, with the Absolute Pose Error (APE) serving as the evaluation index. APE measures the deviation in pose estimation, including both rotational and translational errors, relative to a ground truth reference. The Absolute Pose Error (APE) at time \(i\) can be calculated using the Euclidean distance, as follows:
\(\text{APE}_{i}=\parallel SE(3)_{\text{est},i}-SE(3)_{\text{gt},i}\parallel\)     (11)
where \(SE(3)_{\text{est},i}\) denotes the estimated pose at time \(i\)and \(SE(3)_{\text{gt},i}\) represents the ground truth pose at the same time.
In this study, APE represents a combination of rotational and translational errors, calculated as a dimensionless second-order norm of pose discrepancies. Fig. 5 presents the comparative APE results, and rounded-off quantitative comparisons are provided in Table 3.