In-situ Soil Moisture Sensing: Measurement Scheduling and Estimation Using Sparse Sampling

摘要

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 (the temporal evolution of soil moisture). In this article, we explore the use of results from the theory of sparse sampling, including Compressive Sensing (CS) and Matrix Completion (MC), in this application context. We first consider the problem of reconstructing the soil moisture process at a single location using CS. Our physical constraint leads to very sparse measurement matrices, which makes finding a suitable representation basis very challenging: it needs to make the underlying signal sufficiently sparse while at the same time being sufficiently incoherent with the measurement matrix, two common preconditions for CS techniques to work well. We construct a representation basis by exploiting unique features of soil moisture evolution and show that this basis attains a very good tradeoff between its ability to sparsify the signal and its incoherence with measurement matrices that are consistent with our physical constraints. We next consider the problem of jointly reconstructing soil moisture processes at multiple locations, assuming sparse measurements can be taken at each location. We show that the spatial soil moisture process enjoys a low-rank property, a priority for MC. Accordingly, we introduce a spatiotemporal measurement matrix and apply the MC framework to reconstruct the soil moisture field. 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, for a single location, a uniform measurement scheduling followed by CS recovery results in a very nice tradeoff between estimation accuracy, sampling rate, flexibility, and feasibility in implementation. When multiple locations are available, our results show that joint reconstruction using MC in general produces better estimation accuracy than using a single location alone, but it requires the use of independent and random measurement schedules across locations. We also show that these sparse sampling techniques can be augmented so as to be robust against sporadic data outliers/corruption caused by, for example, intermittent sensor faults.