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The most thorough study of the 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 measured value, the study obtained the uncertainties $\Delta m_{\rm top} = 31$ MeV, $\Delta\Gamma_{\rm top} = 34$ MeV, and a relative uncertainty on the Yukawa coupling $\lambda_{\rm top}$ of the order of $\pm 40\%$. The dominant systematic uncertainties on the mass stem from the knowledge of $\alpha_s(m_{\rm Z})$ ($\pm 30$ MeV per unit of $\pm 0.0007$), and above all the knowledge of the luminosity spectrum: a 20\% $\pm 20$\%  uncertainty of the RMS width of the main luminosity peak results in top mass uncertainties of approximately 75 $\pm 75$  MeV, far in excess the statistical uncertainty~\cite{cite:1303.3758}. In addition to the ten-fold increase in the number of $\ttbar$ events at TLEP, which reduces the statistical uncertainty 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 are bound to reduce the main systematic uncertainties by large factors, possibly below the statistical uncertainties. A dedicated study is planned to demonstrate fully the TLEP potential in the respect. The expected statistical uncertainties are summarized in Table~\ref{tab:TopMass}.