Wang Jin, Yan Shiwei, Tu Rui, Zhang Pengfei
College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China.
Chinese Academy of Surveying and Mapping, Beijing 100830, China.
Sensors (Basel). 2025 Apr 30;25(9):2863. doi: 10.3390/s25092863.
Determining the sea surface height using Global Navigation Satellite System (GNSS) buoys is an important method for satellite altimetry calibration. The buoys observe the absolute height of the sea surface using GNSS positioning technology, which is then used to correct the systematic deviation of the altimeter of the orbiting satellite. Due to the challenging observational conditions, such as significant multipath errors in GNSS code observation and complex variations in buoy position and attitude, gross errors in GNSS buoy positioning reduce the accuracy and stability of the calculated sea surface heights. To accurately detect and remove these gross errors from GNSS coordinate time series, the complementary ensemble empirical mode decomposition (CEEMD) method and the interquartile range (IQR) method were adopted to enhance the accuracy and stability of GNSS sea surface altimetry. Firstly, the raw GNSS sequential coordinate series are decomposed into main terms, such as trend contents and periodic contents, and high-frequency noise terms using the CEEMD method. Subsequently, the high-frequency noise terms of the GNSS coordinate series are regarded as the residual sequences, which are used to detect gross errors using the IQR method. This approach, which integrates the CEEMD and IQR methods, was named CEEMD-IQR and enhances the ability of the traditional IQR method to detect subtle gross errors in GNSS coordinate time series. The results indicated that the CEEMD-IQR method effectively detected gross errors in offshore GNSS coordinate time series using GNSS buoys, presenting a significant enhancement in the gross error detection rate of at least 35.3% and providing a "clean" time series for sea level measurements. The resulting GNSS sea surface altimetry accuracy was found to be better than 1.51 cm.
利用全球导航卫星系统（GNSS）浮标确定海面高度是卫星测高校准的重要方法。浮标利用GNSS定位技术观测海面的绝对高度，然后用于校正轨道卫星高度计的系统偏差。由于观测条件具有挑战性，例如GNSS码观测中存在严重的多径误差以及浮标位置和姿态的复杂变化，GNSS浮标定位中的粗大误差会降低计算得到的海面高度的准确性和稳定性。为了从GNSS坐标时间序列中准确检测和去除这些粗大误差，采用互补总体经验模态分解（CEEMD）方法和四分位距（IQR）方法来提高GNSS海面测高的准确性和稳定性。首先，使用CEEMD方法将原始GNSS顺序坐标序列分解为主要项，如趋势项、周期项和高频噪声项。随后，将GNSS坐标序列的高频噪声项视为残差序列，利用IQR方法检测粗大误差。这种将CEEMD和IQR方法相结合的方法被命名为CEEMD - IQR，增强了传统IQR方法检测GNSS坐标时间序列中细微粗大误差的能力。结果表明，CEEMD - IQR方法有效地检测了使用GNSS浮标的近海GNSS坐标时间序列中的粗大误差，粗大误差检测率显著提高至少35.3%，并为海平面测量提供了一个“干净”的时间序列。得到的GNSS海面测高精度优于1.51厘米。
