D-SLAM: Diffusion Source Localization and Trajectory Mapping

We consider physical fields induced by a finite number of instantaneous diffusion sources, which we sample using a mobile sensor, along unknown trajectories composed of multiple linear segments. We address the problem of estimating the sources, as well as the trajectory of the mobile sensor. Within this framework, we propose a method for localizing sources of unknown amplitudes, and known activation times. The reconstruction method we propose maps the measurements obtained using the mobile sensor to a sequence of generalized field samples. From these generalized samples, we can then retrieve the locations of the sources as well as the trajectory of the sensor (up to a linear geometric transformation).