1Estimation of Multiple Instantaneous Point Sources of Advection-Diffusion

Sensor networks have emerged as an important tool for the monitoring of physical fields of interest. In this setting, sensors obtain spatiotemporal samples of the field which can then be fused so as to infer certain properties of the field. This paper considers advection-diffusion fields for which the advection-diffusion equation is a well-known model. Specifically, we consider the problem of estimating in both space and time, the sources of the resulting field and demonstrate that this source identification problem can be formulated as a system governed by a weighted sum of complex exponentials. This system under certain conditions can be solved in order to recover the unknown source parameters. Finally, we validate our findings through numerical simulations in the noisy setting for both single and multiple point sources. Index Terms — Spatiotemporal sampling, advection-diffusion equation, sensor networks, diffusion fields, Prony’s method. 1