  The second postulate of special relativity states that the speed of light in
vacuum is independent of the emitter's motion. The test of this postulate so
far remains unexplored for gravitational radiation. We analyze data from the
LIGO-Virgo detectors to test this postulate within the ambit of a model where
the speed of the emitted GWs ($c'$) from a binary depends on a characteristic
velocity $\tilde{v}$ proportional to that of the reduced one-body system as $c'
= c + k\, \tilde{v}$, where $k$ is a constant. We have estimated the upper
bound on the 90\% credible interval over $k$ to be ${k \leq 8.3 \times
{10}^{-18}}$, which is several orders of magnitude more stringent compared to
previous bounds obtained from electromagnetic observations. The Bayes' factor
supports the second postulate with a strong evidence that the data is
consistent with the null hypothesis $k = 0$, upholding the principle of
relativity for gravitational interactions.
