We present an extension to the Global Positioning System (GPS) broadcast navigation message user equations for computing GPS space vehicle (SV) velocity and acceleration. Although similar extensions have been published, the extension presented herein includes a distinct kinematic method for computing SV acceleration, which significantly reduces the complexity of the equations and improves the mean magnitude results by approximately one order of magnitude by including oblate Earth perturbation effects. Additionally, detailed analyses and validation results using multiple days of precise ephemeris data and multiple broadcast navigation messages are presented. Improvements in the equations for computing SV position are also included, removing ambiguity and redundancy in the existing user equations. The recommended changes make the user equations more complete and more suitable for implementation in a wide variety of programming languages employed by GPS users. Furthermore, relativistic SV clock error rate computation is enabled by the recommended equations. A complete, stand‐alone table of the equations in the format and notation of the GPS interface specification is provided, along with benchmark test cases to simplify implementation and verification.

中文翻译：

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根据广播的导航消息计算GPS卫星速度和加速度

我们提出了对全球定位系统（GPS）广播导航消息用户方程的扩展，用于计算GPS航天器（SV）的速度和加速度。尽管已发布了类似的扩展名，但本文介绍的扩展名包括一种用于计算SV加速度的独特的运动学方法，该方法可以显着降低方程式的复杂性，并通过包括扁圆的地球扰动效应将平均幅度结果提高大约一个数量级。此外，还提供了使用多天的精确星历数据和多条广播导航消息进行的详细分析和验证结果。还包括用于计算SV位置的方程式的改进，从而消除了现有用户方程式中的歧义和冗余。推荐的更改使用户方程式更加完整，更适合于以GPS用户使用的多种编程语言来实现。此外，相对论的SV时钟错误率计算通过推荐的公式实现。提供了完整，独立的等式表，其中包括GPS接口规范的格式和符号，以及基准测试用例，以简化实施和验证。