In wireless sensor networks, sensors that do not provide valuable information about internal or external events in the network can be deactivated to optimize their limited energy consumption and that of the entire network. This study presents an innovative and efficient method for selecting sensors that provide informative data, considering both the total received information and communication overhead. To achieve this, we mathematically model energy depletion in sensors based on the number of transmitted bits from nodes and incorporate this model into the cost function, leading to the formulation of a novel optimization problem. By leveraging convex relaxation, this problem is transformed into a semidefinite optimization framework. To evaluate the proposed method, a combination of the extended Kalman filter and a sensor selection algorithm based on the generalized Fisher information matrix is employed for the trajectory estimation of a simulated nonlinear moving target. The obtained results demonstrate that the proposed algorithm significantly outperforms one of the most recent approaches in this domain, which does not consider communication overhead.