This paper studies a design problem of how a group of wireless sensors are selected and scheduled to transmit data efficiently over a multi-hop network subject to energy-saving consideration, when they are observing multiple independent discrete-time linear systems. Each time instant, some sensors are selected to transmit their measurements to a remote estimator. We formulate an optimization problem, minimizing a linear combination of the averaged estimation error and the averaged transmission energy consumption to obtain suitable network scheduling and estimation algorithms. Necessary conditions for optimality are derived and these conditions help trim the feasible solution space so that the optimal solution can be computed efficiently. A numerical example is provided to demonstrate the theoretical results.