Abstract The Global Positioning System (GPS) is a space-based radio positioning system which is capable of providing continuous position, velocity and time information to users anywhere on, or near, the surface of the Earth. The positional accuracy of GPS is limited by several sources of error, such as satellite and receiver clock offsets, signal propagation delays (due to the ionosphere and troposphere), multipath, receiver measurement noise, and instrument bias. The ionospheric delay is the predominant error source. The main objective of this work was to estimate the regional vertical Total Electron Content (vTEC) densities, using a linear combination of L1 and L2 carrier phase for higher order time delays at different thin-shell layers of the ionosphere (i.e. 60 km, 90 km, 150 km, 200 km and 450 km) over GPS stations in Ethiopia. Due to the high equatorial ionization anomaly and irregularity of the electron density distribution, we selected four GPS stations across the country. We studied longitudinal, latitudinal, and altitudinal variations in the ionosphere using GPS observables extracted by precise geodetic GAMIT-GLOBK software package. We obtained data from the 2013 to 2015 period for all stations. For daily data processing in GAMIT, we switched the International Geomagnetic Reference Field 2012 (IGRF-12) model (which consists of spherical harmonic coefficients) on and off, representing the Earth’s main field and its secular variation and ionospheric electron content along the signal path (available from the Centre for Orbit Determination in Europe (CODE)). Our results confirmed that there is latitudinal, longitudinal and altitudinal variation in the ionosphere. The density of total electron content and GPS positional error due to higher-order time delays have a positive correlation (more than 95%). The positional error, due to the higher order ionospheric delay, exceeds 4 mm for all GPS stations and reached up to 8 mm. Finally, we observed that the time delay due to the higher-order ionospheric effect in the L2 signal is twice that in the L1. We conclude that the GPS signal is affected by the higher order ionospheric delay by up to several centimetres due to its electron content and the Earth’s magnetic field.

中文翻译：

---

埃塞俄比亚全球定位系统站的高阶电离层延迟和区域总电子含量的推导

摘要 全球定位系统（GPS）是一种天基无线电定位系统，能够向地球表面上或附近任何地方的用户提供连续的位置、速度和时间信息。GPS 的定位精度受到多种误差源的限制，例如卫星和接收器时钟偏移、信号传播延迟（由于电离层和对流层）、多径、接收器测量噪声和仪器偏差。电离层延迟是主要的误差源。这项工作的主要目标是估计区域垂直总电子含量 (vTEC) 密度，使用 L1 和 L2 载流子相位的线性组合在电离层的不同薄壳层（即 60 公里、90公里、150 公里、200 公里和 450 公里）通过埃塞俄比亚的 GPS 站。由于赤道电离异常高且电子密度分布不​​规则，我们在全国选取了4个GPS站。我们使用精确大地测量 GAMIT-GLOBK 软件包提取的 GPS 观测值研究了电离层的纵向、纬度和高度变化。我们从 2013 年到 2015 年期间获得了所有站点的数据。对于 GAMIT 中的日常数据处理，我们打开和关闭了国际地磁参考场 2012 (IGRF-12) 模型（由球谐系数组成），代表地球的主磁场及其沿信号路径的长期变化和电离层电子含量（可从欧洲轨道测定中心 (CODE) 获得）。我们的结果证实电离层存在纬度、经度和高度的变化。高阶时延引起的总电子含量密度与 GPS 位置误差呈正相关（大于 95%）。由于高阶电离层延迟，所有 GPS 站的位置误差超过 4 毫米，并达到 8 毫米。最后，我们观察到 L2 信号中由于高阶电离层效应导致的时间延迟是 L1 中的两倍。我们得出的结论是，由于其电子含量和地球磁场，GPS 信号受到高阶电离层延迟的影响，最多可达几厘米。我们观察到 L2 信号中由高阶电离层效应引起的时间延迟是 L1 中的两倍。我们得出的结论是，由于其电子含量和地球磁场，GPS 信号受到高阶电离层延迟的影响，最多可达几厘米。我们观察到 L2 信号中由高阶电离层效应引起的时间延迟是 L1 中的两倍。我们得出的结论是，由于其电子含量和地球磁场，GPS 信号受到高阶电离层延迟的影响，最多可达几厘米。