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Although the spatial curvature has been measured with very high precision, itstill suffers from the well known cosmic curvature tension. In this paper, wepropose an improved method to determine the cosmic curvature, by using thesimulated data of binary neutron star mergers observed by the second generationspace-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO).By applying the Hubble parameter observations of cosmic chronometers to theDECIGO standard sirens, we explore different possibilities of makingmeasurements of the cosmic curvature referring to a distant past: one is toreconstruct the Hubble parameters through the Gaussian process without theinfluence of hypothetical models, and the other is deriving constraints on$\Omega_K$ in the framework of non-flat $\Lambda$ cold dark matter model. It isshown that in the improved method DECIGO could provide a reliable and stringentconstraint on the cosmic curvature ($\Omega_{K} = -0.007\pm0.016$), while wecould only expect the zero cosmic curvature to be established at the precisionof $\Delta \Omega_K=0.12$ in the second model-dependent method. Therefore, ourresults indicate that in the framework of methodology proposed in this paper,the increasing number of well-measured standard sirens in DECIGO couldsignificantly reduce the bias of estimations for cosmic curvature. Suchconstraint is also comparable to the precision of Planck 2018 results with thenewest cosmic microwave background (CMB) observations ($\Delta \Omega_{K}\approx 0.018$), based on the concordance $\Lambda$CDM model.

High precision measurement of cosmic curvature: from gravitational waves and cosmic chronometer