LiDAR-based Scene Coordinate Regression (SCR) maps point clouds directly to 3D scene coordinates, enabling precise 6-DoF localisation without explicit map retrieval. However, existing methods produce deterministic predictions, discarding aleatoric uncertainty that could improve robustness and downstream decision-making.

We present UQ-Loc, which extends the LightLoc architecture with an anisotropic Gaussian covariance head that predicts a full 3x3 positive-definite covariance matrix per voxel. Training uses a Negative Log-Likelihood (NLL) loss augmented with a kNN-based spatial smoothness regulariser, while inference employs a modified SC2-PCR solver with uncertainty-weighted seed scoring and a Mahalanobis-distance inlier test.

We adopt Expected Calibration Error (ECE) as a principled metric for evaluating the quality of the predicted uncertainty. Experiments demonstrate that UQ-Loc achieves consistent improvement in 6-DoF localization accuracy while producing well-calibrated covariances.