Enhancement of the Total Least Squares Method for Feature Extraction in 2D LiDAR Mapped Environments

Feature-based Simultaneous Localization and Mapping (SLAM) using 2D Light Detection and Ranging (LiDAR) in structured indoor environments commonly relies on the extraction of straight segments and corners from raw scan data. The quality of these landmarks depends not only on the fitting algorithm, but also on how uncertainty is modeled and propagated from line estimates to derived corner features. Although the magnitude of LiDAR uncertainty has been widely studied, the influence of line parameterization and geometric conditioning on uncertainty propagation has received less attention. In particular, the scale ambiguity inherent to implicit line representations can degrade numerical conditioning and affect the stability of the propagated covariance estimates. This paper proposes a novel Weighted Conformal Total Least Squares (WCTLS) formulation for line extraction from 2D LiDAR data. Unlike conventional approaches, the proposed method enforces a geometrical normalization that removes scale ambiguity and improves the conditioning of the estimation problem. The method is compared with Unweighted Total Least Squares (UTLS) and Weighted Total Least Squares (WTLS) using real indoor datasets and repeated scans acquired from fixed sensor positions. The results show that all three formulations provide equivalent geometric corner locations, whereas the proposed WCTLS method consistently reduces the propagated uncertainty of the estimated corner coordinates. In addition, repeatability analysis over 100 scans per environment shows that WCTLS yields lower median corner ellipse areas and reduced dispersion across scans, without increasing computational complexity.