SE(2)-MambaLoc: Regression-Based LiDAR Localization via SE(2)-Equivariant Feature Learning and Mamba Diffusion

Regression-based LiDAR Localization has achieved impressive accuracy but remains challenging due to viewpoint variations and computational inefficiency. This paper introduces SE(2)-MambaLoc, an end-to-end regression-based framework combining SE(2)-equivariant feature learning and Mamba diffusion models for robust and efficient Bird’s-Eye-View (BEV) LiDAR localization. Our approach first constructs a BEV height-weighted density map (BEV-HWDM) to preserve elevation-aware structural features while reducing storage demands. An SE(2)-equivariant feature extractor (SEFE), built on a modified ResNet18, interleaves lightweight decoupled SE(2) group convolution blocks, which are decomposed into kernel generators and positional encoders, with standard residual stages. It replaces the classification head with parallel inception bottleneck and context anchor attention modules to produce a sequence of rotation-robust spatial BEV descriptors without data augmentation. For pose regression, we reformulate localization as an iterative denoising process using a Mamba diffusion model. By treating the spatial feature map as a sequence of tokens, our Mamba backbone captures the geometric dependencies between the pose and the environmental context with linear-time complexity, avoiding the quadratic bottleneck of Transformers. Extensive experiments on Oxford Radar RobotCar and NCLT datasets demonstrate that our proposed SE(2)-MambaLoc achieves superior orientation (yaw) accuracy over state-of-the-art (SOTA) methods with comparable position accuracy and a 49% reduction in training time. Ablation studies validate the effectiveness of BEV-HWDM, SEFE, and Mamba diffusion components, underscoring their roles in enhancing robustness and efficiency.