Random sampling via sensor networks: Estimation accuracy vs. energy consumption

The estimation of spatial processes from sparse sensing nodes is fundamental for many applications, including environmental monitoring and crowd-sourcing. In this paper, we analyze the impact of measurement errors on the estimation of a finite-energy signal sampled by a set of sensors randomly deployed in a finite d-dimensional space according to homogeneous Poisson Point Process. The optimal linear space invariant interpolator is derived. Based on such an interpolator, analytical expressions of both the estimated signal energy spectral density and the normalized estimation mean square error are obtained. An asymptotic analysis for high sensors density with respect to the signal bandwidth is given for scenarios subjected to estimation energy constraint. The normalized estimation mean square error is derived for large wireless sensor networks with constraints on the capacity-per-volume and on battery duration.