Point cloud registration is a key technology for light detection and ranging (LiDAR) positioning. To address the challenges of the traditional iterative closest point (ICP) algorithm in point cloud registration in scenarios with sparse geometric features and degenerated environments, this paper proposes an optimization method for LiDAR point cloud registration considering the reliability of geometric features. This method consists of two modules: 1) A curvature-based feature extraction module that constructs a local neighborhood covariance matrix and decomposes its eigenvalues to calculate the maximum and minimum principal curvatures of the point cloud, while introducing the principal curvature difference and normal vector angle to construct a curvature consistency error function. By quantifying geometric feature differences, it effectively filters out ambiguous candidate matching points in repetitive structures, resolves matching ambiguities under noise interference, ensures the geometric consistency of feature registration, and provides high-quality feature pairs for subsequent registration; 2) A feature reliability-based point cloud registration module that uses three factors—feature fitting error, local curvature, and spectral entropy—to quantify feature fitting quality, forms a unified reliability weight through a Bayesian model, and constructs a weighted point cloud registration optimization framework based on this weight. The weight adjustment mechanism suppresses the interference of low-quality features, thereby reducing the errors introduced into the registration results. Experimental validation on both self-built and public KITTI datasets shows that the proposed method reduces 3D positioning errors by 47% compared to conventional point-line (PL)/point-plane (PP) ICP methods in indoor degraded scenes, significantly improving positioning accuracy and robustness in challenging environments. Ablation experiments further confirm the importance of multi-feature collaborative optimization, and the algorithm maintains optimization times within 20 ms for ten thousand-level feature pairs, meeting real-time requirements.