On the measurement of the speed of gravitational wave

Strict measurement of the speed of gravitational wave (GW) is very important for fundamental physics. In this paper, taking cosmological effect into account, we derive a more precise formula for calculating the speed of GW based on GW 170817-like events. We find that in the case of high redshift, the usual luminosity distance needs to be replaced by co-moving distance. We consider some possible electromagnetic signals which can be significantly reduce the intrinsic uncertainty between the emission times of the gravitational and electromagnetic signals. Hopefully, the measurement accuracy will be improved to $\sim 10^{-18}\;\rm m\; s^{-1}$.