Computing GPS satellite velocity and acceleration from the broadcast navigation message

Abstract

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.