A Relaxation Approach to Dynamic Sensor Selection in Large-Scale Wireless Networks

Wireless sensor networks (WSNs) require more complex sensor selection strategies than other distributed networks to perform optimal state estimation. In addition to constraints associated with distributed state estimation, wireless sensor networks have limitations on bandwidth, energy consumption, and transmission range. This paper introduces and empirically evaluates a dynamic sensor selection strategy. A discrete-time Kalman filter is used for state estimation. At each time step, a subset of sensors is selected to gather data on the following time step because of power and bandwidth constraints that prohibit using all of the sensors. A standard criterion for selecting this subset of sensors is to maximize the information to be gained by minimizing a function of the next-step error covariance matrix.  We propose a relaxation of this non-convex combinatorial optimization problem and  demonstrate its applicability to large-scale sensor networks. The proposed dynamic sensor selection strategy is compared empirically to other dynamic and static sensor selection strategies with respect to state estimation performance of a convection-dispersion field arising from the problem of surface-based monitoring of CO$_2$ sequestration sites.