Trace-Norm Regularized Multi-Task Learning for Sea State Bias Estimation

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 cm ² compared to the geophysical data records (GDR); while for the HY-2 cycle intersection data, M has been reduced by 1.30 cm ² compared to GDR. Therefore, TNR-MTL is proved to be effective for the SSB estimation tasks.