The rate of the universe's expansion, known as the Hubble constant, remains debated. Gravitational wave standard sirens offer an independent measurement method, using signals from events like binary neutron star mergers that encode distance and redshift information from their electromagnetic (EM) counterparts. The initial measurement from GW170817 showed promise, but more data is needed for accuracy. My work focuses on the dark sirens method, using gravitational wave events without EM counterparts to refine the Hubble constant. This approach estimates potential host galaxy redshift using galaxy catalogs. With increased observations and improved techniques, we aim to reduce systematic errors and achieve precise measurements.