<p>Current descriptors rarely focus on point cloud normals and struggle to achieve a balance among robustness, compactness, and descriptiveness. To address this, we present a 3D local descriptor named Normal Vector Rotation Projection Statistical (NRPS). We propose a comprehensive solution that includes a highly repeatable Local Reference Frame (LRF) and a 3D descriptor, both heavily relying on point cloud normals. Normal vectors contain rich information but are often overlooked due to their directional ambiguity. Taking inspiration from point cloud reconstruction where globally consistent normal directions are required, we adopt this established technique to compute globally consistent outward-pointing normals for our descriptor. We create a highly robust LRF using an improved covariance matrix and point cloud normals. The NRPS descriptor is generated by rotating and projecting normal, then analyzing normal direction distributions across different spatial regions and viewpoints. During the statistical process, we implement soft assignment for spatial region boundary points and normal direction division boundary points to enhance NRPS’s stability. Experimental results demonstrate that both our LRF and NRPS descriptor exhibit strong robustness against noise and resolution interference, outperforming both classical and state-of-the-art descriptors. The code and datasets are available at <a href="https://github.com/FanMingjiang2001/NRPS-descriptor-and-datasets">https://github.com/FanMingjiang2001/NRPS-descriptor-and-datasets</a>.</p>