Global Navigation Satellite Systems (GNSS) applications require computation of the geometric range between the satellite vehicle at the time-of-signal transmission and the receiver antenna location at the time-of-signal reception. This computation requires attention to the frames of reference due to the rotation of the Earth-Centered Earth-Fixed (ECEF) frame during the time-of-signal propagation. Three range computation approaches are commonplace and will be discussed herein. The first is the Global Positioning System Interface Control Document recommendation to rotate the ECEF frames to a common reference time. The other two are forms of the Sagnac correction. The Sagnac derivations already in the literature are either limited to stationary receivers or lack the connection between the Earth-centered inertial (ECI) and ECEF frames. Neither form of the Sagnac correction exactly reproduces the geometric range. They are approximations. The literature does not currently contain an analysis of the error involved in using either form of the Sagnac correction. This article makes two contributions: (1) it presents derivations for both forms of the Sagnac correction that are valid for moving receivers and that maintain the connection between the ECI and ECEF frames; and (2) it analyzes the error of the Sagnac correction for orbits of different radius. The analysis shows that Sagnac corrections introduce range errors less than \(7.57\times 10^{-4}\) meters for GNSS satellites at medium Earth orbit.

全球导航卫星系统 （GNSS） 应用需要计算信号传输时卫星飞行器与信号接收时接收器天线位置之间的几何距离。由于在信号传播期间地心地球固定 （ECEF） 帧的旋转，此计算需要注意参考系。三种范围计算方法很常见，本文将对此进行讨论。第一个是全球定位系统接口控制文档建议，将 ECEF 帧旋转到公共参考时间。另外两个是 Sagnac 更正的形式。文献中已有的 Sagnac 推导要么局限于固定接收器，要么缺乏地心惯性 （ECI） 和 ECEF 框架之间的连接。两种形式的 Sagnac 校正都不能精确再现几何范围。它们是近似值。文献目前不包含对使用任一形式的 Sagnac 校正所涉及的错误的分析。本文做出了两个贡献：（1） 它提出了两种形式的 Sagnac 校正的推导，这些校正对移动接收器有效，并保持了 ECI 和 ECEF 帧之间的连接;（2） 它分析了不同半径轨道的 Sagnac 校正误差。分析表明，对于中地球轨道的 GNSS 卫星，Sagnac 校正引入的距离误差小于 \（7.57\times 10^{-4}\） 米。