Diffusion SLAM: Localizing Diffusion Sources From Samples Taken by Location-Unaware Mobile Sensors

We consider diffusion fields induced by multiple localised and instantaneous sources. We assume a mobile sensor samples the field, uniformly along a piecewise linear trajectory, which is unknown. The problem we address is the estimation of the amplitudes and locations of the diffusion sources, as well as of the trajectory of the sensor. We first propose a method for diffusion source localisation and trajectory mapping (D-SLAM) in 2D, where we assume the activation times of the sources are known and the evolution of the diffusion field over time is negligible. The reconstruction method we propose maps the measurements obtained using the mobile sensor to a sequence of generalised field samples. From these generalised samples, we can then retrieve the locations of the sources as well as the trajectory of the sensor (up to a 2D orthogonal geometric transformation). We then relax these assumptions and show that we can perform D-SLAM also in the case of unknown activation times, from samples of a time-varying field, as well as in 3D spaces. Finally, simulation results on both synthetic and real data further validate the proposed framework.