Sensor scheduling for energy constrained estimation in multi-hop Wireless Sensor Networks

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central fusion center. The fusion center computes an estimate of the process state by means of a Kalman filter. In this paper we assume that the WSN admits a tree topology with fusion center at the root node. At each time step only a subset of sensors can be selected to transmit their observations to the fusion center due to limited energy budget. We propose a stochastic sensor selection algorithm to randomly select a subset of sensors according to certain probability distribution, which is chosen to minimize the expected next step estimation error covariance matrix while maintaining the connectivity of the network. One of the main advantages of the stochastic formulation over the traditional deterministic formulation is that the stochastic formulation provides smaller expected estimation error than the deterministic formulation. Further, we prove that the optimal stochastic sensor selection problem can be relaxed into a convex optimization problem and thus solved efficiently. We also provide a possible implementation of our algorithm which does not introduce any communication overhead. Finally a numerical example is provided to show the effectiveness of the proposed approach.