LAUSR

In this paper, we study the level set estimation of a spatial-temporally correlated random field by using a small number of spatially distributed sensors. The level sets of a random field are defined as regions where data values exceed a certain threshold. The identification of the boundaries of such sets is an important theoretical problem with a wide range of applications such as spectrum sensing, urban sensing, and environmental monitoring, etc. We propose a new active sparse sensing and inference scheme, which can achieve rapid and accurate extraction of level sets in a large random field by using a small number of data samples strategically and sparsely selected from the field. A Gaussian process (GP) prior model is used to capture the spatial–temporal correlations inherent in the random field. It is first shown that the optimal level set estimation can be achieved by performing a GP regression with all data samples and then thresholding the regression results. We then investigate the active sparse sensing scheme, where a central controller dynamically selects a small number of sensing locations according to the information revealed from past measurements, with the objective to minimize the expected level set estimation error probability. The expected estimation error probability is explicitly expressed as a function of the selected sensing locations, and the results are used to formulate the optimal sensing location selection problem as a combinatorial problem. Two low complexity greedy algorithms are developed by using analytical upper bounds of the expected estimation error probability. Both simulation and experiment results demonstrate that the greedy algorithms can achieve significant performance gains over baseline passive sensing algorithms and the GP upper confidence bound level set estimation algorithm.