Multi-energy flow state estimation is an important research field of energy Internet. At present, the research on the state estimation of electricity-water coupling system has just started, and there are still some problems, such as poor adaptability to the working conditions of water network, inadequate utilization of electricity-water coupling information and so on. For this reason, a bilinear least square (WLS) state estimation method for water network considering the correction of friction coefficient is proposed in this paper. Based on the virtual measurement of the water pump and the bi-directional transmission of coupling information, a bilinear WLS state estimation method is proposed, which is suitable for discrete operation, cooperative operation and joint operation of electricity-water coupling system. The effectiveness of the proposed bilinear WLS estimation is verified by 11-node water network and two electricity-water coupling systems formed by coupling with IEEE-14 node and IEEE-118 node power system. The results of numerical examples prove the necessity of correcting friction coefficient in water network state estimation, the superiority of bilinear WLS estimation method in computational efficiency and adaptability of low flow rate water network, and the effectiveness of cooperative estimation and joint estimation in improving the accuracy, data consistency and observability of power system and water network state estimation.