The Surface Water and Ocean Topography (SWOT) mission generates dense altimetry data that, when used in geoid gradient component estimations through least-squares collocation (LSC), lead to an ill-conditioned problem. Such problems also arise in geodetic network designs. This study introduces the Tikhonov-L-curve regularization to effectively address this challenge. By pinpointing the maximum curvatures of the L-curve, we discern optimal regularization parameters, countering issues stemming from the dense data of SWOT and the resulting ill-conditioned covariance matrices. Our approach not only stabilizes LSC solutions but also achieves gradient accuracies at 1-microrad levels compared to theoretical values. Additionally, we experimented with a strategic removal process that selectively eliminates adjacent geoid gradients. This technique considerably improves geoid gradient component determinations, especially evident at a threshold distance of 0.755 km within an 8′× 8′ data selection window. While our findings are rooted in simulated SWOT data, they are pivotal for future research intending to employ real SWOT data, anticipated by late 2023. This work serves as a precursor for marine gravity field determinations, emphasizing the importance of stabilized LSC solutions to avoid misleading seafloor signatures due to data compactness.

地表水和海洋地形 (SWOT) 任务生成密集的测高数据，当通过最小二乘搭配 (LSC) 用于大地水准面梯度分量估计时，会导致病态问题。此类问题也出现在大地测量网络设计中。本研究引入了 Tikhonov-L 曲线正则化来有效应对这一挑战。通过精确定位 L 曲线的最大曲率，我们可以识别最佳正则化参数，解决由 SWOT 密集数据和由此产生的病态协方差矩阵引起的问题。我们的方法不仅稳定了 LSC 解决方案，而且与理论值相比，梯度精度达到了 1 微拉德水平。此外，我们还尝试了一种战略性去除过程，可以选择性地消除相邻的大地水准面梯度。该技术显着改进了大地水准面梯度分量的确定，尤其是在 8'× 8' 数据选择窗口内的 0.755 km 阈值距离处明显。虽然我们的研究结果植根于模拟 SWOT 数据，但它们对于未来打算采用真实 SWOT 数据的研究至关重要，预计到 2023 年底。这项工作可以作为海洋重力场测定的先驱，强调稳定 LSC 解决方案的重要性，以避免误导由于数据紧凑性而产生的海底特征。