  This paper considers a special case of the problem of identifying a static
scalar signal, depending on the location, using a planar network of sensors in
a distributed fashion. Motivated by the application to monitoring wild-fires
spreading and pollutants dispersion, we assume the signal to be Gaussian in
space. Using a network of sensors positioned to form a regular hexagonal
tessellation, we prove that each node can estimate the parameters of the
Gaussian from local measurements. Moreover, we study the sensitivity of these
estimates to additive errors affecting the measurements. Finally, we show how a
consensus algorithm can be designed to fuse the local estimates into a shared
global estimate, effectively compensating the measurement errors.
