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In this paper, we present the application of a new method measuring Hubbleparameter $H(z)$ by using the anisotropy of luminosity distance($d_{L}$) of thegravitational wave(GW) standard sirens of neutron star(NS) binary system. Themethod has never been put into practice so far due to the lack of the abilityof detecting GW. However, LIGO's success in detecting GW of black hole(BH)binary system merger announced the potential possibility of this new method. Weapply this method to several GW detecting projects, including AdvancedLIGO(aLIGO), Einstein Telescope(ET) and DECIGO, and evaluate its constraintability on cosmological parameters of $H(z)$. It turns out that the $H(z)$ byaLIGO and ET is of bad accuracy, while the $H(z)$ by DECIGO shows a good one.We simulate $H(z)$ data at every 0.1 redshift span using the error informationof $H(z)$ by DECIGO, and put the mock data into the forecasting of cosmologicalparameters. Compared with the previous data and method, we get an obviouslytighter constraint on cosmological parameters by mock data, and a concomitantlyhigher value of Figure of Merit(FoM, the reciprocal of the area enclosed by the$2\sigma$ confidence region). For a 3-year-observation by standard sirens ofDECIGO, the FoM value is as high as 170.82. If a 10-year-observation islaunched, the FoM could reach 569.42. For comparison, the FoM of 38 actualobserved $H(z)$ data(OHD) is 9.3. We also investigate the undulant universe,which shows a comparable improvement on the constraint of cosmologicalparameters. These improvement indicates that the new method has great potentialin further cosmological constraints.

The constraint ability of Hubble parameter by gravitational wave standard sirens on cosmological parameters