Trace-Norm Regularized Multi-Task Learning for Sea State Bias Estimation
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Trace-Norm Regularized Multi-Task Learning for Sea State Bias Estimation ZHONG Guoqiang1), *, QU Jianzhang1), WANG Haizhen1), LIU Benxiu1), JIAO Wencong1), FAN Zhenlin1), MIAO Hongli2), and HEDJAM Rachid3) 1) Department of Computer Science and Technology, Ocean University of China, Qingdao 266100, China 2) Department of Physics, Ocean University of China, Qingdao 266100, China 3) Department of Computer Science, Sultan Qaboos University, P. O. B 36, AlKhod 123, Muscat, Oman (Received June 21, 2019; revised January 30, 2020; accepted March 30, 2020) © Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2020 Abstract Sea state bias (SSB) is an important component of errors for the radar altimeter measurements of sea surface height (SSH). However, existing SSB estimation methods are almost all based on single-task learning (STL), where one model is built on the data from only one radar altimeter. In this paper, taking account of the data from multiple radar altimeters available, we introduced a multi-task learning method, called trace-norm regularized multi-task learning (TNR-MTL), for SSB estimation. Corresponding to each individual task, TNR-MLT involves only three parameters. Hence, it is easy to implement. More importantly, the convergence of TNR-MLT is theoretically guaranteed. Compared with the commonly used STL models, TNR-MTL can effectively utilize the shared information between data from multiple altimeters. During the training of TNR-MTL, we used the JASON-2 and JASON-3 cycle data to solve two correlated SSB estimation tasks. Then the optimal model was selected to estimate SSB on the JASON-2 and the HY-2 70-71 cycle intersection data. For the JSAON-2 cycle intersection data, the corrected variance (M) has been reduced by 0.60 cm2 compared to the geophysical data records (GDR); while for the HY-2 cycle intersection data, M has been reduced by 1.30 cm2 compared to GDR. Therefore, TNR-MTL is proved to be effective for the SSB estimation tasks. Key words
sea state bias (SSB); radar altimeter; geophysical data records (GDR); trace-norm; multi-task learning
1 Introduction One of the goals of remote sensing is to measure the sea surface height (SSH) using satellite altimeter technology. The SSH measurement is very important for determining and monitoring ocean currents and eddies (Wunsch and Stammer, 1998), climate change, wave height and wind speed, and for studies in geodesy and ocean geophysics (Barrick, 1972). Sea level has continued to rise in recent years, mainly due to the melting of polar glaciers and the thermal expansion of upper seawater, which is induced by climate changes. Studies have showed that global sea level has risen by 10 to 20 centimeters over the past 100 years and will accelerate in the future (Dasgupta et al., 2009). Sea level rising has a significant impact on the socio-economy, natural environment and ecosystems in the coastal areas. First of all, sea level rising may submerge some low-lying coastal areas. Second, it may increase the intensity of storm surges. Freq
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