Accurate knowledge about the motion state of preceding vehicles (PVs) contributes to the optimization of planning and decision making of autonomous vehicles, which in turn further enhances road safety. Existing studies generally rely on information from special sensors mounted on the ego vehicle to estimate PVs state. With the evolution of information technology, the use of vehicle-to-vehicle (V2V) communication to estimate the PVs state has attracted more and more attention. However, the problem of how to reduce the communication rate while ensuring the estimation accuracy of PVs state with the limited communication bandwidth has not been addressed yet. In addition, traditional studies on lateral state estimation of PVs assume that the longitudinal velocity of the PV is known or design an additional estimator to predict the longitudinal velocity. This results in the dynamical coupling characteristics of the vehicle not being fully considered. To address these problems, an event-triggered estimation framework by fusing an event-triggered mechanism with an embedded cubature Kalman filter based on a coupled vehicle model is proposed for PVs state estimation. Simulation and real vehicle test results demonstrate that the proposed prediction approach can strike an effective balance between the communication rate and the estimation performance. The estimation accuracy of the proposed method is still superior to that of the cubature Kalman filter, even if the communication rate drops to 37.55%.