Cooperative localization uses odometry and inter-robot measurements to estimate the motion of a robot team. These measurements describe only relative geometry, but the team's estimated position and orientation can drift together over time, i.e., gauge drift. In this work, we study correction of this gauge drift using a radio attenuation map registered in the same world coordinate frame used for robot poses. Specifically, we propose Radio-to-Pose Information (RPI), an interface that converts power residuals and their pose derivatives into a Gaussian information matrix and vector pair. RPI builds on the insight that received power is sensitive to shared displacement in the world map. The pose estimator uses the interface together with odometry and inter-robot measurements to update poses and minimize uncertainty. We characterize the shared motions detectable from the map and observed links. For an uncertain shared map, RPI keeps correlations across robots and time and reproduces joint Gaussian pose estimates and covariances. Across $1000$ simulated Gaussian trials, RPI matches the results of joint estimation. Across 32 paired trials with a registered map, RPI reduces common-position RMSE from $0.542$m to $0.140$m in a $50\times50$m arena compared with a baseline that uses radio only to weight relative measurements.

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