Convex Relaxation Method for Sensor Placement in Multiclass Monitoring Networks

The design of a sensor network plays an important role in monitoring a physical field. This task becomes more difficult as the network consists of different classes of sensors with their corresponding uncertainties. In this article, the rankMax sensor placement method is proposed for scenarios where high-quality instruments are used along with low-cost sensors (LCSs) in a multiclass monitoring network. The novelty of the method relies on exploiting a closed form of the inverse of the Fisher information matrix (FIM) in terms of rank-1 matrices that allow expressing a convex relaxation of the sensor placement problem. The method performance is evaluated on an air pollution dataset for small and large monitoring networks and compared with a straightforward extension of the convex relaxation method proposed by Joshi and Boyd. The results show that the rankMax method outperforms the multiclass Joshi-Boyd (MCJB) method about 91% of the time, being particularly useful when there are not many reference instruments in the network.