The most thorough study of the $\ttbar$ threshold measurements was done in the context of the TESLA project in Ref.~\cite{Martinez_Miquel_2003}, the parameters of which are very close to those of the ILC. The study makes use of a multi-parameter fit of $m_{\rm top}$, $\Gamma_{\rm top}$, $\lambda_{\rm top}$ and $\alpha_{\rm s}$ to the top cross section, the top momentum distributions, and the forward-backward asymmetry. When constraining the value of $\alpha_s(m_{\rm Z})$ to its currently measured value, the study obtained statistical uncertainties of $\Delta m_{\rm top} = 31$~MeV, $\Delta\Gamma_{\rm top} = 34$~MeV, and a relative uncertainty on the Yukawa coupling $\lambda_{\rm top}$ of the order of 40\%. The dominant experimental systematic uncertainties on the mass stem from the knowledge of $\alpha_s(m_{\rm Z})$ ($\pm$30~MeV per unit of $\pm$0.0007, the current uncertainty on this quantity), and from the knowledge of the beam-energy spectrum:  a 20\% uncertainty of the RMS width of the main luminosity peak would result in top mass uncertainties of approximately 75~MeV, far in excess of the statistical uncertainty~\cite{cite:1303.3758}.

The expected TLEP statistical uncertainties are summarized in Table~\ref{tab:TopMass}. In addition to the ten-fold increase in the number of $\ttbar$ events at TLEP, which reduces the statistical uncertainties by a factor of three, the much better knowledge of the beam-energy spectrum, and the precise measurement of the strong coupling constant with TeraZ and OkuW are bound to reduce the main experimental systematic uncertainties by one order of magnitude, hence below the statistical uncertainties. The starting design study plans to demonstrate fully the TLEP potential in this respect. A specific effort to reduce the theoretical Electroweak uncertainties on the cross section by one order of magnitude will also be needed.

\begin{table}
\begin{center}
\caption{Expected statistical uncertainties for $m_{\rm top}$, $\Gamma_{\rm top}$ and $\lambda_{\rm top}$  for TLEP, obtained from a five-years scan of $\ttbar$ threshold at $\sqrt{s} \sim 350$ GeV. The dominant experimental systematic uncertainties on the top quark mass are expected to be of the order of or smaller than the statistical uncertainties for TLEP. Also indicated is the baseline ILC potential for these measurements.\label{tab:TopMass}}
\begin{tabular}{|l|r|r|r|}
\hline  &  $m_{\rm top}$ & $\Gamma_{\rm top}$ & $\lambda_{\rm top}$ \\ \hline \hline
TLEP & {\bf 10~MeV} & {\bf 11~MeV} & ${\bf 13\%}$\\ \hline
ILC  & 31~MeV & 34~MeV & $40\%$ \\ \hline
\end{tabular}
\end{center}
\end{table}

\noindent\textbf{\textit{An overall experimental uncertainty of 10 to 20~MeV is therefore considered to be a reasonable target for the top-quark mass measurement at TLEP.}}