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Sensor placement methods for field estimation based on Gaussian processes are proposed. Generally, sensor placement methods determine the appropriate placement positions by selecting them from predefined candidate positions. Many criteria for the selection have been proposed, with which the quality of the placements is evaluated with regard to the field at the candidate positions. This means that these sensor placement methods seek to find the positions that can estimate the field at the candidate positions accurately. In practical situations, however, the candidate sensor placement region can be different from the target region for field estimation. In this paper, to make sensor placement methods applicable to this situation, we propose two sensor placement methods based on the mean squared error and on conditional entropy that can be applied to cases in which the sensor placement region is arbitrarily restricted. After formulating the sensor placement problems, two approximate algorithms are derived: the greedy algorithm and the convex-relaxation-based algorithm. The application of the proposed methods to sound field estimation is also illustrated, and their effectiveness was confirmed through numerical experiments.

Region-Restricted Sensor Placement Based on Gaussian Process for Sound Field Estimation