The data for an energy management system (EMS) in an integrated energy system (IES) is obtained through state estimation. This is then the basis for optimal scheduling, protection and control. At present, the dynamic models of gas and heat networks are rarely considered in such state estimation, and the method lacks robustness. This paper develops dynamic state estimation models for gas and heat networks, and proposes a unified method for the electricity-gas-heat network, one which takes into account robustness while ensuring accuracy. First, the state transition equations in matrix form are formulated according to finite difference models considering the dynamic characteristics of the gas and heat networks. Then, combined with a quasi-steady state model of the electric power system, a unified state estimation method and multi-time-scale measurement strategy in the Kalman filter framework are proposed. In addition, the prediction accuracies of the electric power and gas systems are improved through adaptive adjustment. The kernel density estimation method is used to adjust the measurement weights and filter out bad data to ensure robust state estimation. Finally, simulation results show that the proposed method not only can improve the estimation accuracy by improving prediction accuracy, but also is robust to various types of bad data.