Optimal sizing and placement of sensor networks with coordinate error variance constraint

Accurate signal reconstruction of a spatially distributed physical field requires the use of multiple sensors placed at optimal locations. This task becomes more difficult when fewer sensors are deployed, but it is still necessary to constrain the reconstruction error. This paper proposes a new method for determining the optimal number of sensors and their placement, called Sizing and Placement with Coordinate Reconstruction Error Constraint (SP-CREC). The novelty of the method lies in the possibility to constrain different signal reconstruction errors for different regions of interest within the monitored area. A large-scale algorithm is also proposed to reduce the computational complexity when the monitoring involves a large number of sensors and locations. The performance of the proposed method is evaluated on two publicly available datasets for air pollution and sea surface temperature data, and compared with the Mean Squared Error (MSE) minimization proposed by Joshi and Boyd. The results show that the proposed method is able to find near-optimal solutions for these scenarios, which occur in many practical situations.