  Accurately estimating the positions of multi-agent systems in indoor
environments is challenging due to the lack of Global Navigation Satelite
System (GNSS) signals. Noisy measurements of position and orientation can cause
the integrated position estimate to drift without bound. Previous research has
proposed using magnetic field simultaneous localization and mapping (SLAM) to
compensate for position drift in a single agent. Here, we propose two novel
algorithms that allow multiple agents to apply magnetic field SLAM using their
own and other agents measurements.
  Our first algorithm is a centralized approach that uses all measurements
collected by all agents in a single extended Kalman filter. This algorithm
simultaneously estimates the agents position and orientation and the magnetic
field norm in a central unit that can communicate with all agents at all times.
In cases where a central unit is not available, and there are communication
drop-outs between agents, our second algorithm is a distributed approach that
can be employed.
  We tested both algorithms by estimating the position of magnetometers carried
by three people in an optical motion capture lab with simulated odometry and
simulated communication dropouts between agents. We show that both algorithms
are able to compensate for drift in a case where single-agent SLAM is not. We
also discuss the conditions for the estimate from our distributed algorithm to
converge to the estimate from the centralized algorithm, both theoretically and
experimentally.
  Our experiments show that, for a communication drop-out rate of 80 percent,
our proposed distributed algorithm, on average, provides a more accurate
position estimate than single-agent SLAM. Finally, we demonstrate the
drift-compensating abilities of our centralized algorithm on a real-life
pedestrian localization problem with multiple agents moving inside a building.
