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Currently two-way and three-way spacecraft Doppler tracking techniques arewidely used and playing important roles in control and navigation for deepspace missions. Starting from one-way Doppler model, we extend the models oftwo-way and three-way Doppler by making them include possible violations of thelocal Lorentz invariance (LLI) and the local position invariance (LPI) in orderto test the Einstein equivalence principle which is the cornerstone of generalrelativity and all other metric theories of gravity. After taking the finitespeed of light into account, which is so-called light-time solution (LTS), wehave these models depending on the time of reception of the signal only forpractical convenience. We find that possible violations of LLI and LPI can notaffect two-way Doppler under linear approximation of LTS although thisapproximation is sufficiently good for most cases in the solar system. We alsoshow that, in three-way Doppler, possible violations of LLI and LPI associatewith two stations only, which suggests that it is better to set the stations atplaces with significant differences in velocities and gravitational potentialsto obtain high level of sensitivity for tests.

Spacecraft Doppler tracking with possible violations of LLI and LPI: a theoretical modeling