Spatio-temporal sensor management for environmental field estimation

Abstract

We develop sparsity-enforcing spatio-temporal sensor management methods for environmental field monitoring applications. Leveraging the space–time stationarity, an environmental field can be estimated with a desired spatio-temporal resolution based on recorded measurements. If the field is non-stationary, it can be monitored dynamically based on the collected measurements and predictions made through a state model, if known a priori. We develop algorithms to implement sparse sensing, i.e., sensing only the most informative locations in space and time for both spatio-temporally stationary and non-stationary field monitoring applications. The selected sensing locations form an underdetermined measurement model which can be used to estimate the field based on the prior knowledge regarding the space–time variability of the field. The task of locating the most informative sensing locations can be performed for both multiple snapshots and a single snapshot based on the availability of prior knowledge (space–time correlation and dynamics) regarding the field, available computing power and the application. Centralized sensor placement problems for the estimation of both stationary and non-stationary fields are formulated as relaxed convex optimization problems, constrained by static or dynamic performance criteria. Finally, an iterative sparsity-enhancing saddle point method is formulated to solve both of these sensor placement problems.