  Image retrieval-based cross-view localization methods often lead to very
coarse camera pose estimation, due to the limited sampling density of the
database satellite images. In this paper, we propose a method to increase the
accuracy of a ground camera's location and orientation by estimating the
relative rotation and translation between the ground-level image and its
matched/retrieved satellite image. Our approach designs a geometry-guided
cross-view transformer that combines the benefits of conventional geometry and
learnable cross-view transformers to map the ground-view observations to an
overhead view. Given the synthesized overhead view and observed satellite
feature maps, we construct a neural pose optimizer with strong global
information embedding ability to estimate the relative rotation between them.
After aligning their rotations, we develop an uncertainty-guided spatial
correlation to generate a probability map of the vehicle locations, from which
the relative translation can be determined. Experimental results demonstrate
that our method significantly outperforms the state-of-the-art. Notably, the
likelihood of restricting the vehicle lateral pose to be within 1m of its
Ground Truth (GT) value on the cross-view KITTI dataset has been improved from
$35.54\%$ to $76.44\%$, and the likelihood of restricting the vehicle
orientation to be within $1^{\circ}$ of its GT value has been improved from
$19.64\%$ to $99.10\%$.
