the upcoming experiments such as the E-ELT and SKA through two different means. The E-ELT will be able to observe the Lyman-$\alpha$ absorption lines of distant quasar systems to achieve the measurement of $\Delta v$ in the redshift range of $z\in[2,5]$ [@Loeb:1998bu; @Liske]. The SKA will measure the spectroscopic velocity shift $\Delta v$ by observing the neutral hydrogen emission signals of galaxies at the precision of one percent in the redshift range of $z\in[0,1]$. Obviously, the E-ELT and SKA experiments will be the ideal complements with each other, because of the explorations of different periods for the cosmic evolution.

**E-ELT mock data:** For the E-ELT data, as discussed in Ref. [@Liske:2008ph], the standard deviation on $\Delta v$ can be estimated as $$\label{4}
   \sigma_{\Delta v} = 1.35\left(\frac{2370}{S/N}\right)\left(\frac{N_{\rm QSO}}{30}\right)^{-1/2}\left(\frac{1+z_{\rm QSO}}{5}\right)^{x} ~\mathrm{cm}~\mathrm{s}^{-1},$$ where $S/N$ is the signal-to-noise ratio of the Lyman-$\alpha$ spectrum, $N_{\rm QSO}$ is the number of observed quasars at the effective redshift $z_{\rm QSO}$, and $x$ is $1.7$ for $2\leq z\leq4$ and $0.9$ for $z\geq4$. In this work, we assume $S/N=3000$ and $N_{\rm QSO}=30$. We generate 30 mock data with a uniform distribution for the E-ELT’s redshift drift observation in six redshift bins (the redshift interval $\Delta z=0.5$ for each bin), 