  This paper considers a radio-frequency (RF)-based simultaneous localization
and source-seeking (SLASS) problem in multi-robot systems, where multiple
robots jointly localize themselves and an RF source using distance-only
measurements extracted from RF signals and then control themselves to approach
the source. We design a Rao-Blackwellized particle filter-based algorithm to
realize the joint localization of the robots and the source. We also devise an
information-theoretic control policy for the robots to approach the source. In
our control policy, we maximize the predicted mutual information between the
source position and the distance measurements, conditioned on the robot
positions, to incorporate the robot localization uncertainties. A projected
gradient ascent method is adopted to solve the mutual information maximization
problem. Simulation results show that the proposed SLASS framework outperforms
two benchmarks in terms of the root mean square error (RMSE) of the estimated
source position and the decline of the distances between the robots and the
source, indicating more effective approaching of the robots to the source.
