Abstract: To solve the problems of non-Gaussian noise in measurement data, limited accuracy of estimation results, and low efficiency in power system state estimation, a robust forecasting-aided state estimation method (FASE) for power system based on deep learning framework and kernel ridge regression (KRRSE) is proposed. Firstly, according to the historical operation data of the power system, the convolutional neural network based on attention mechanism combined with the neural network of long-short term memory (ATT-CNN-LSTM) is used to formulate the prediction model. Secondly, the support vector machine(SVM) is used to detect abnormal and missing data and realize data classification, and output state estimate result based on the ATT-CNN-LSTM model under abnormal condition. Thirdly, the nonlinear mapping function between the quantity measurement and the state quantity is established by using the kernel ridge regression model, which can filter out the non-Gaussian noise in measurement data. Finally, case studies on the IEEE 118-bus system and 300-bus system verify the high accuracy and robustness of the proposed KRRSE method.