Using field data to design a sensor network

Distributed sensing and data acquisition in field applications is a labor intensive and expensive process. In such applications, measurements need to be performed in thousands of points. To design a sensor network for soil moisture measurement, we introduce a two step design procedure; in the first step, the data of soil moisture experiments known as SMEX03 (in Little Washita watershed, Oklahoma) is used to approximate the spatial variability of moisture data. Based on the numerical data of SMEX03, the spatial correlation of soil moisture is approximated. Our numerical analysis shows that the spatial correlation of moisture measurements of two points behaves similar to an exponentially decaying function of the distance of those points. The analysis also shows that the moisture measurements for the points with distance up to 150m show a high correlation, while the spatial correlation is practically zero for points that are more than 400m apart. In the second step, we use the spatial correlation of soil moisture to design a sensor network. It is assumed that the sensors are placed sparsely in the field, but it is desirable to estimate the soil moisture at any arbitrary point of the field based on the measurements of the nearby sensors. We use a linear estimator, and give the coefficients that minimize its variance. The value of the minimum variance of the linear estimator depends on the location. We give a closed form formula for the coefficients of the linear minimum variance estimator and the upper bound for the its variance as a function of spatial separation of sensors. Assuming a known value for the maximum allowable moisture estimation variance, we find the optimal placement of the sensors. The results show that in a grid like placement of the sensors in the field, with average separation of distance of 50-100m between neighboring sensor pairs, the soil moisture can be approximated with a good accuracy at any arbitrary point of the field, while increasing the distance of neighboring senors beyond 200m degrades the performance significantly.