Gravitational waves observation with electromagnetic counterparts provides an approach to measure the Hubble constant which is also known as the bright siren method. Great hope has been put into this method to arbitrate the Hubble tension. In this study, we apply the simulation tool GW-Universe Toolbox and modeling of the aLIGO-design background to simulate the bright siren catalogues of sub-threshold double neutron star mergers with potential contamination from noise and dis-pairing between gravitational waves and electromagnetic counterparts. The Hubble constant and other cosmology parameters are thus inferred from the simulated catalogues with a Bayesian method. From our simulation study, we reach the following conclusions: 1) the measurement error of the H 0 decreases with a lower signal-to-noise ratio threshold (or equivalently the P astro ) in the region where P astro 0.1, while the inferred most probable H 0 trends to bias towards larger values; and 2) other higher order cosmological parameters such as Ω m remain unconstrained even with the sub-threshold catalogues. We also discuss adding the network of the gravitational wave detectors to the simulation tool and the electromagnetic counterparts follow-up efficiency simulation, which will improve our work in the future.