  Currently two-way and three-way spacecraft Doppler tracking techniques are
widely used and playing important roles in control and navigation for deep
space missions. Starting from one-way Doppler model, we extend the models of
two-way and three-way Doppler by making them include possible violations of the
local Lorentz invariance (LLI) and the local position invariance (LPI) in order
to test the Einstein equivalence principle which is the cornerstone of general
relativity and all other metric theories of gravity. After taking the finite
speed of light into account, which is so-called light-time solution (LTS), we
have these models depending on the time of reception of the signal only for
practical convenience. We find that possible violations of LLI and LPI can not
affect two-way Doppler under linear approximation of LTS although this
approximation is sufficiently good for most cases in the solar system. We also
show that, in three-way Doppler, possible violations of LLI and LPI associate
with two stations only, which suggests that it is better to set the stations at
places with significant differences in velocities and gravitational potentials
to obtain high level of sensitivity for tests.
