In the deformation monitoring based on satellite positioning, the extraction of the effective deformation signal which needs plenty of computing resources is very important. Mobile-edge computing can provide low latency and near-edge computing agility for the deformation monitoring process. In this paper, we propose an edge computing network architecture to reduce the satellite observation time while maintaining a certain positioning accuracy. In such architecture, the state transition equation is established for monitoring, and the Kalman filter is used to reduce the error caused by the reduction of the observation time. At the same time, the method of determining the initial filter value and the filtering process are given. Through the actual monitoring of a certain section of railway track, the feasibility of the proposed method is proved.