A In-Situ Soil Moisture Sensing: Optimal Sensor Placement and Field Estimation

We study the problem of optimal sensor placement in the context of soil moisture sensing. We show that the soil moisture data possesses some unique features that can be used together with the commonly used Gaussian assumption to construct more scalable, robust and better performing placement algorithms. Specifically, there exists a coarse-grained monotonic ordering of locations in their soil moisture level over time, both in terms of its first and second moments, a feature much more stable than the soil moisture process itself at these locations. This motivates a clustered sensor placement scheme, where locations are classified into clusters based on the ordering of the mean, with the number of sensors placed in each cluster determined by the ordering of the variances. We show that under idealized conditions the greedy mutual information maximization algorithm applied globally is equivalent to that applied cluster by cluster, but the latter has the advantage of being more scalable. Extensive numerical experiments are performed on a set of 3-dimensional soil moisture data generated by a state-of-the-art soil moisture simulator. Our results show that our clustering approach outperforms applying the same algorithms globally, and is very robust to lack of training and errors in training data.