GNSS time-series prediction plays an important role in the monitoring of crustal plate movement, and dam or bridge deformation, and the maintenance of global or regional coordinate frames. Deep learning is a state-of-the-art approach for extracting high-level abstract features from big data without any prior knowledge. Moreover, long short-term memory (LSTM) networks are a form of recurrent neural networks that have significant potential for processing time series. In this study, a novel prediction framework was proposed by combining a multi-scale sliding window (MSSW) with LSTM. Specifically, MSSW was applied for data preprocessing to effectively extract the feature relationship at different scales and simultaneously mine the deep characteristics of the dataset. Then, multiple LSTM neural networks were used to predict and obtain the final result by weighting. To verify the performance of MSSW-LSTM, 1000 daily solutions of the XJSS station in the Up component were selected for prediction experiments. Compared with the traditional LSTM method, our results of three groups of controlled experiments showed that the RMSE value was reduced by 2.1%, 23.7%, and 20.1%, and MAE was decreased by 1.6%, 21.1%, and 22.2%, respectively. Our results showed that the MSSW-LSTM algorithm can achieve higher prediction accuracy and smaller error, and can be applied to GNSS time-series prediction.
Multi-scale Internet traffic forecasting using neural networks and time series methods