In-situ soil moisture sensing: Measurement scheduling and estimation using compressive sensing

We consider the problem of monitoring soil moisture evolution using a wireless network of in-situ underground sensors. To reduce cost and prolong lifetime, it is highly desirable to rely on fewer measurements and estimate with higher accuracy the original signal (soil moisture temporal evolution). In this paper we explore results from the compressive sensing (CS) literature and examine their applicability to this problem. Our main challenge lies in the selection of two matrices, the measurement matrix and a representation basis. The physical constraints of our problem make it highly nontrivial to select these matrices, so that the latter can sufficient sparsify the underlying signal while at the same time be sufficiently incoherent with the former, two common pre-conditions for CS techniques to work well. We construct a representation basis by exploiting unique features of soil moisture evolution. We show that this basis attains very good tradeoff between its ability to sparsify the signal and its incoherence with measurement matrices that are consistent with our physical constraints. Extensive numerical evaluation is performed on both real, high-resolution soil moisture data and simulated data, and through comparison with a closed-loop scheduling approach. Our results demonstrate that our approach is extremely effective in reconstructing the soil moisture process with high accuracy and low sampling rate.