In this paper the authors consider state estimation carried over a sensor network. A fusion center forms a local multihop tree of sensors and fuses the data into a state estimate. A set of sensor trees with desired properties is constructed, and those sensor trees are scheduled in such a way that the network lifetime is maximized. The sensor tree construction and scheduling algorithms are shown to have low polynomial time complexity which leads to efficient implementation in practice. The scheduling algorithm is also shown to return the optimal solution. Examples are provided to demonstrate the algorithms.