Error Analysis for Status Update From Sensors With Temporally and Spatially Correlated Observations

This paper studies the status update performance in wireless sensor networks when status, describing the physical reality that is being sensed, is temporally and spatially correlated. The status is modeled as a time-varying Gauss-Markov Random Field (GMRF), whereby the estimation error of status update at the fusion center is analyzed. The transmission latency introduced by wireless networks is modeled as exponentially distributed random variables. We extend the existing queuing analysis results for Age of Information (AoI) with uncorrelated sources to GMRF in the considered scenario. Closed-form expressions of average remote estimation error are obtained for both one- and two-dimensional GMRFs assuming the exponential time-correlation function, both First-Come First-Served (FCFS) and Last-Come First-Served (LCFS) service disciplines, and a single wireless link. The analytical results are then extended to scenarios wherein multi-packet reception, i.e., multiple concurrent wireless links, is enabled; the difficulty of analyzing obsolete updates in this case is addressed leveraging a reasonable approximation validated by theoretical analysis in the regime where the number of sensors is far more than that of wireless links. Monte-Carlo simulation results are also presented which agree with our theoretical analysis. Based on the results, optimal time and spatial domain sampling rates (e.g., sensor density) can be obtained, providing helpful guidance to wireless sensor deployment.