e consider an estimation network of many distributed sensors, where each senor takes a noisy measurement of some unknown parameter. Due to energy limitation, the network selects only a subset of sensors for data fusion as long as the distortion is tolerable. In this paper, we present a sampling framework based on linear minimum variance unbiased estimation. The framework enables the system to achieve a desired estimation fidelity level and to improve the network lifetime. Simulations illustrate the effectiveness of the proposed sampling schemes.