Delay-tolerant vs. delay-constrained estimation of spatial random fields

In this paper, we design a number of encoding strategies suitable for the estimation of spatial random fields via wireless sensor networks. We address two cases of interest, namely, (i) delay-constrained applications, in which the observations collected in a particular timeslot must be immediately encoded and conveyed to the Fusion Center (FC); and (ii) delay-tolerant applications where the time horizon is enlarged to the observations collected in L consecutive timeslots. For the delay-tolerant case, we derive a closed-form expression of the number of observations to be allocated to each timeslot and the correspoding attainable distortion. Numerical results confirm that the distortion associated to delay-tolerant encoding strategies is substantially lower.