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The observations of gravitational wave (GW) provide us a new probe to studythe universe. GW events can be used as standard sirens if their redshifts aremeasured. Normally, stardard sirens can be divided into bright/dark sirensaccording to whether the redshifts are measured by electromagnetic (EM)counterpart observations. Firstly, we investigate the capability of the2.5-meter Wide-Field Survey Telescope (WFST) to take follow-up observations ofkilonova counterparts. For binary neutron star (BNS) bright sirens, WFST isexpected to observe 10-20 kilonovae per year in the second-generation (2G) GWdetection era. As for neutron star-black hole (NSBH) mergers, when a BH spin isextremely high and the NS is stiff, the observation rate is $\sim10$ per year.Combining optical and GW observations, the bright sirens are expected toconstrain the Hubble constant $H_0$ to $\sim2.8\%$ in five years ofobservations. As for dark sirens, tidal effects of neutron stars (NSs) duringmerging time provide us a cosmological model-independent approach to measurethe redshifts of GW sources. Then we investigate the applications of tidaleffects in redshift measurements. We find in 3G era, the host galaxy groups ofaround 45\% BNS mergers at $z<0.1$ can be identified through this method, ifthe EOS is ms1, which is roughly equivalent to the results from luminositydistant constraints. Therefore, tidal effect observations provide a reliableand cosmological model-independent method of identifying BNS mergers' hostgalaxy groups. Using this method, the BNS/NSBH dark sirens can constrain $H_0$to 0.2\%/0.3\% over a five-year observation period.

Measuring the Hubble constant with coalescences of binary neutron star and neutron star-black hole: bright sirens \& dark sirens