Defining a Unified Height System for Africa using Relativistic Geodetic Approaches.

Establishing an International Height Reference Frame (IHRF) has been a major goal of the International Association of Geodesy (IAG) for a long time. The scope of this study is to define a unified height system for Africa using the advantages of relativistic geodetic approaches via spatial time-frequency links. We propose a ground clock network connected with the ACES (Atomic clocks ensemble in Space) by frequencies transfer. The gravitational potential of the ACES will be determined using a gravity field model. The ground stations include stationary clocks as the backbone of the frame. Frequency transfer between the ACES and these stations will be simulated. The gravitational potential differences between the ACES and the ground stations will be computed using the tri-frequency combination method. Finally, the gravitational potential of the ground stations will be determined and converted to orthometric height. The TFC uses the uplink of carrier frequency 13.475 GHz (Ku band) and downlinks of carrier frequencies 14.70333 GHz (Ku band) and 2248 MHz (S-band) to transfer frequency signals. Here we present a simulation experiment. In this experiment, we use the international space station (ISS) orbit data, ionosphere and troposphere models, regional gravitational potential and geoid for Africa, solid Earth tide model, and simulated clock data by a conventionally accepted stochastic noises model. We consider various effects, including the Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by the atmosphere, and Shapiro effect, with accuracy levels of decimetres. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228, and the Natural Science Foundation of Hubei Province of China under Grant 2019CFB611.