  We study the impact of eccentricity on gravitational-wave parameter
estimation for binary neutron star systems. For signals with small eccentricity
injected into the advanced LIGO sensitivity, we perform Bayesian parameter
estimation using the circular waveform model and show how the recovered
parameters can be biased from their true values, focusing on the intrinsic
parameters the chirp mass ($M_c$), the symmetric mass ratio ($\eta$), and the
tidal deformability ($\tilde{\lambda}$). By comparing the results between the
Bayesian and the analytic Fisher-Cutler-Vallisneri (FCV) methods, we obtain the
valid criteria for the FCV approach. Employing the FCV method and using the
realistic population of binary neutron star sources distributed in the
$m_1$-$m_2$-$e_0$ space, where $e_0$ indicates the eccentricity at 10Hz, we
calculate the measurement errors ($\sigma_{\theta}$) and the systematic biases
($\Delta \theta/\sigma_{\theta}$) and obtain their generalized distributions in
the range of $0 \leq e_0 \leq 0.025$. We find that for all of the three
parameters, the biases increase with increasing $e_0$, and this increase is
faster for larger $e_0$. The bias is mainly dependent on the value of $e_0$ and
weakly dependent on the component masses, and thus the distribution shows a
narrow band in the $e_0$-$\Delta \theta/\sigma_{\theta}$ plane. We present
various posterior examples to illustrate our new findings, such as the
bimodality of posteriors. In particular, we give a specific injection-recovery
example to demonstrate the importance of including eccentricity in parameter
estimation to avoid incorrect predictions of the neutron star equation of
state.
