Sparse sensing for distributed gaussian detection

An offline sampling design problem for Gaussian detection is considered in this paper. The sensing operation ismodeled by a selection vector, whose sparsity order is determined by the prescribed global error probability. Since the numerical optimization of the error probability is difficult, equivalent simpler costs, viz., the Kullback-Liebler distance and Bhattacharyya distance are optimized. The sensing problem is formulated and solved sub-optimally using convex optimization techniques. It is shown that the sensing problem can be solved optimally for conditionally independent Gaussian observations. Further, we show that for non-identical sensor observations, the number of sensors required to achieve a certain detection performance decreases as the sensors become more correlated.