This paper presents a real-time robust power system forecasting-aided state estimation method based on the Bayesian framework, deep learning, and Gaussian mixture model to dynamically estimate the non-Gaussian measurement noise in the real-time power system. The approach is data driven and model independent. A non-linear mapping function between measurement and state is formulated based on the historical operating data of the power system and the Gaussian process. Then combine the anomaly detection technology in machine learning and the Gaussian mixture model to accurately judge and delete the abnormal data in measurement information. Thus, a power system state forecasting model based on long-short term memory neural network is established, which can solve the problem of missing data combining power flow calculation. Numerical simulations carried out on the IEEE 118-bus and IEEE 300-bus test system reveal that the proposed method has high accuracy and robustness.