  Reliable localization is an essential capability for marine robots navigating
in GPS-denied environments. SLAM, commonly used to mitigate dead reckoning
errors, still fails in feature-sparse environments or with limited-range
sensors. Pose estimation can be improved by incorporating the uncertainty
prediction of future poses into the planning process and choosing actions that
reduce uncertainty. However, performing belief propagation is computationally
costly, especially when operating in large-scale environments. This work
proposes a computationally efficient planning under uncertainty frame-work
suitable for large-scale, feature-sparse environments. Our strategy leverages
SLAM graph and occupancy map data obtained from a prior exploration phase to
create a virtual map, describing the uncertainty of each map cell using a
multivariate Gaussian. The virtual map is then used as a cost map in the
planning phase, and performing belief propagation at each step is avoided. A
receding horizon planning strategy is implemented, managing a goal-reaching and
uncertainty-reduction tradeoff. Simulation experiments in a realistic
underwater environment validate this approach. Experimental comparisons against
a full belief propagation approach and a standard shortest-distance approach
are conducted.
