{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:46:04Z","timestamp":1785415564795,"version":"3.56.0"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:00:00Z","timestamp":1776988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12273094"],"award-info":[{"award-number":["12273094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["12273094"],"award-info":[{"award-number":["12273094"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Since coming into full operation in 2020, the BeiDou-3 Navigation Satellite System (BDS-3) has provided global users with positioning, navigation and time-synchronization services. Satellite clock bias is a key factor that affects real-time precise point positioning (PPP), precise orbit determination and the optimization of navigation message parameters; high-precision prediction of clock bias is therefore critical for improving the accuracy and reliability of BDS-3. To further enhance the prediction accuracy and stability of satellite clock bias, we propose a hybrid model based on Mamba-LSTM. This combined model leverages the strengths of the Multimodal Adaptive Model Building Algorithm (Mamba) and the Long Short-Term Memory neural network (LSTM) to predict satellite clock bias. Using precise BDS-3 satellite clock bias data from the International GNSS Service (IGS), we carried out prediction experiments. First, we compared the proposed model\u2019s predictive performance with that of the Mamba and LSTM models. In short-term (6 h) and long-term (24 h) prediction scenarios, the average prediction RMSE of Mamba-LSTM improved by approximately 41.7% and 48% relative to Mamba, and by approximately 50.4% and 54.7% relative to the LSTM results, respectively. Next, we ran comparison experiments against traditional neural networks\u2014the BP model and the CNN model. In mid-term (12 h) and long-term (24 h) prediction scenarios, the average prediction RMSE of Mamba-LSTM improved by approximately 59.6% and 63.1% compared with BP, and by approximately 52.4% and 56.2% compared with CNN, respectively. The results indicate that the Mamba-LSTM hybrid model can significantly improve the accuracy and stability of satellite clock bias prediction.<\/jats:p>","DOI":"10.3390\/s26092643","type":"journal-article","created":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T12:29:11Z","timestamp":1777033751000},"page":"2643","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Prediction of BDS-3 Satellite Clock Bias Based on the Mamba-LSTM Model"],"prefix":"10.3390","volume":"26","author":[{"given":"Yihao","family":"Cai","sequence":"first","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hengyi","family":"Yue","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tu","family":"Yuan","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengjie","family":"Wu","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xu, X., Wang, X., Liu, J., and Zhao, Q. 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