Spatial Sensor Selection via Gaussian Markov Random Fields

This paper addresses the problem of selecting the most informative sensor locations out of all possible sensing positions in predicting spatial phenomena by using a wireless sensor network. The spatial field is modeled by Gaussian Markov random fields (GMRFs), where sparsity of the precision matrix enables the network to benefit from computation. A new spatial sensor selection criterion is proposed based on mutual information (MI) between random variables at selected locations and those at unselected locations and interested but unlikely sensor placed positions, which enhances resulting prediction. The GMRF-based optimality criterion is then proven to be computationally and efficiently resolved, especially in a large-scale sensor network, by a polynomial time approximation algorithm. More importantly, with demonstrations of monotonicity and submodularity properties of the MI set function in the proposed selection criterion, our near-optimal solution is also guaranteed by at least within(1-1/e) of the optimal performance. The effectiveness of the proposed approach is compared and illustrated using two real-life large data sets with promising results.