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Long short-term memory (LSTM) is a deep learning model that has been widely applied in the field of high-precision time series prediction and is often combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 were used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that, compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86% and the average MAE is reduced by 9.44%; moreover, the average R2 increased by 17.97%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average velocity accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby demonstrating the reliability of the predicted results.<\/jats:p>","DOI":"10.3390\/rs15143694","type":"journal-article","created":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T01:27:32Z","timestamp":1690248452000},"page":"3694","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["An Improved VMD-LSTM Model for Time-Varying GNSS Time Series Prediction with Temporally Correlated Noise"],"prefix":"10.3390","volume":"15","author":[{"given":"Hongkang","family":"Chen","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, East China University of Technology, Nanchang 341000, China"}]},{"given":"Tieding","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, East China University of Technology, Nanchang 341000, China"}]},{"given":"Jiahui","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9956-4380","authenticated-orcid":false,"given":"Xiaoxing","family":"He","sequence":"additional","affiliation":[{"name":"School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China"}]},{"given":"Kegen","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Environment and Surveying, China University of Mining and Technology, Xuzhou 221000, China"}]},{"given":"Xiwen","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, East China University of Technology, Nanchang 341000, China"}]},{"given":"Xiaping","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Surveying and Mapping Science and Technology, Xi\u2019an University of Science and Technology, Xi\u2019an 710000, China"}]},{"given":"Zhengkai","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, East China Jiao Tong University, Nanchang 330013, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ohta, Y., Kobayashi, T., Tsushima, H., Miura, S., Hino, R., Takasu, T., Fujimoto, H., Iinuma, T., Tachibana, K., and Demachi, T. 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