Accurate spatial alignment is a key requirement for situated Augmented Reality (AR) in urban planning, where citizens and planners can visualize proposed designs in real outdoor environments. However, existing AR localization approaches often rely on smartphone GNSS, vendor-specific cloud anchors, or cloud-based visual positioning, which introduce accuracy limitations, privacy concerns, or dependencies that restrict their use in participatory planning workflows. This paper presents a privacy-aware on-device localization pipeline for outdoor urban planning scenarios. The approach aligns LiDAR scans captured on smartphones with prescanned reference point cloud tiles to enable stable and accurate placement of urban planning models. Approximate GNSS is used only to retrieve a relevant reference tile, while all preprocessing and registration steps are performed locally on the device. The pipeline combines voxel downsampling, local geometric descriptors, and global registration to estimate alignment without relying on GNSS for pose estimation or on cloud-based visual localization services. A mobile demonstrator was developed to support situated AR in urban planning scenarios, allowing users to explore design proposals directly in context. Initial validation under controlled conditions showed that the system can recover translations and rotations with errors on the order of a few centimeters, while processing times remained suitable for mobile use. The approach was also deployed in an urban planning case study and enabled stable outdoor visualization of planning elements on-site.