Near-optimal sensor placement for signals lying in a union of subspaces

Sensor networks are commonly deployed to measure data from the environment and accurately estimate certain parameters. However, the number of deployed sensors is often limited by several constraints, such as their cost. Therefore, their locations must be opportunely optimized to enhance the estimation of the parameters. In a previous work, we considered a low-dimensional linear model for the measured data and proposed a near-optimal algorithm to optimize the sensor placement. In this paper, we propose to model the data as a union of subspaces to further reduce the amount of sensors without degrading the quality of the estimation. Moreover, we introduce a greedy algorithm for the sensor placement for such a model and show the near-optimality of its solution. Finally, we verify with numerical experiments the advantage of the proposed model in reducing the number of sensors while maintaining intact the estimation performance.