Gravity fields derived from GPS tracking of the three Swarm satellites have shown artifacts near the geomagnetic equator, where the carrier phase tracking on the L2 frequency is unable to follow rapid ionospheric path delay changes due to a limited tracking loop bandwidth of only 0.25 Hz in the early years of the mission. Based on the knowledge of the loop filter design, an analytical approach is developed to recover the original L2 signal from the observed carrier phase through inversion of the loop transfer function. Precise orbit determination and gravity field solutions are used to assess the quality of the correction. We show that the a posteriori RMS of the ionosphere-free GPS phase observations for a reduced-dynamic orbit determination can be reduced from 3 to 2 mm while keeping up to 7% more data in the outlier screening compared to uncorrected observations. We also show that artifacts in the kinematic orbit and gravity field solution near the geomagnetic equator can be substantially reduced. The analytical correction is able to mitigate the equatorial artifacts. However, the analytical correction is not as successful compared to the down-weighting of problematic GPS data used in earlier studies. In contrast to the weighting approaches, up to 9–10% more kinematic positions can be retained for the heavily disturbed month March 2015 and also stronger signals for gravity field estimation in the equatorial regions are obtained, as can be seen in the reduced error degree variances of the gravity field estimation. The presented approach may also be applied to other low earth orbit missions, provided that the GPS receivers offer a sufficiently high data rate compared to the tracking loop bandwidth, and provided that the basic loop-filter parameters are known.

从三颗Swarm卫星的GPS跟踪得出的重力场显示出地磁赤道附近的伪影，其中L2频率上的载波相位跟踪无法跟随电离层路径延迟的快速变化，这是因为在卫星中仅0.25 Hz的有限跟踪环路带宽任务的初期。基于环路滤波器设计的知识，开发了一种分析方法，通过环路传递函数的求逆，从观察到的载波相位中恢复原始L2信号。精确的轨道确定和重力场解决方案用于评估校正的质量。我们显示，用于减少动态轨道确定的无电离GPS相位观测的后验RMS可以从3 mm减小到2 mm，而与未经校正的观测相比，离群筛选中最多可以保留7％的数据。我们还表明，地磁赤道附近的运动轨道和重力场解中的伪影可以大大减少。分析校正能够减轻赤道伪影。但是，与早期研究中使用的有问题的GPS数据的权重降低相比，分析校正的效果不佳。与加权方法相比，对于2015年3月受严重干扰的月份，可以保留多达9-10％的运动位置，并且可以获得更强的赤道区域重力场估计信号，从重力场估计的减小的误差程度方差可以看出。假设与跟踪环路带宽相比，GPS接收机提供足够高的数据速率，并且假设基本环路滤波器参数已知，则所提出的方法也可以应用于其他低地球轨道飞行任务。