In this paper, consensus problem is investigated for a class of discrete-time wireless sensor networks, with which the topologies are connected. Each sensor updates its state that is based on the states of itself and its neighbours, the information that each sensor received is corrupted by additive noise, and data can be gotten by a sink node directly or indirectly. Based on the local measurement among the sink node and its neighbours, an expected state is provided. According to errors among the expected state and the states of all sensors, the adaptive consensus protocols are provided. By Gershgorin's theorem and the Lyapunov functional method, a sufficient condition has been derived to ensure system to achieve the expected value. Simulation results are provided to verify the reliability of the proposed methods.