  Gravitational-wave observations of binary neutron star mergers and their
electromagnetic counterparts provide an independent measurement of the Hubble
constant, $H_0$, through the standard-sirens approach. Current methods of
determining $H_0$, such as measurements from the early universe and the local
distance ladder, are in tension with one another. If gravitational waves are to
break this tension a thorough understanding of systematic uncertainty for
gravitational-wave observations is required. To accurately estimate the
properties of gravitational-wave signals measured by LIGO and Virgo, we need to
understand the characteristics of the detectors noise. Non-gaussian transients
in the detector data and rapid changes in the instrument, known as
non-stationary noise, can both add a systematic uncertainty to inferred
results. We investigate how non-stationary noise affects the estimation of the
luminosity distance of the source, and therefore of $H_0$. Using a population
of 200 simulated binary neutron star signals, we show that non-stationary noise
can bias the estimation of the luminosity distance by up to 2.4\%. However,
only $\sim$15\% of binary neutron star signals would be affected around their
merger time with non-stationary noise at a similar level to that seen in the
first half of LIGO-Virgo's third observing run. Comparing the expected bias to
other systematic uncertainties, we argue that non-stationary noise in the
current generation of detectors will not be a limiting factor in resolving the
tension on $H_0$ using standard sirens. Although, evaluating non-stationarity
in gravitational-wave data will be crucial to obtain accurate estimates of
$H_0$.
