Consensus for the distributed estimation of point diffusion sources in sensor networks

In this contribution, we implement a fully distributed diffusion field estimation algorithm based on the use of average consensus schemes. We show that the field reconstruction problem is equivalent to estimating the sources of the field, and then derive an exact inversion formula for jointly recovering these sources when they are localized and instantaneous. Next we adapt this formula to the sensor network setting when only spatiotemporal samples of the field are available, and only local interactions between the sensors are allowed. To this end, we propose a robust distributed algorithm for reconstructing two-dimensional diffusion fields, sampled with a network of arbitrarily placed sensors. The proposed distributed algorithm is validated through numerical simulations in the noisy, multiple source setting.