Sky location of massive black hole binaries in the foreground of Galactic white dwarf binaries

For space-based gravitational wave (GW) detection, the main noise source for massive black hole binaries (MBHBs) is attributed to approximately 10⁷ double white dwarf binaries in the foreground. For a GW source, the amplitude of the detector response, recorded by a space-based gravitational wave detector, exhibits a modulation effect with a year period when observing the source from various orbital positions. Under the adverse conditions mentioned above, where there is a strong foreground noise and annual modulation in the signals, we employed the wavelet transform and the strong-amplitude relevant orbital position search methods, which allows the weak MBHB sources to achieve higher locating accuracy. In detail, for two MBHB sources of lower intensity, the precision of luminosity distance, represented by the ratio ΔD_L/D_L at the 95% confidence level, is enhanced by factors of ∼2. The angular resolutions, denoted by ΔΩ_s, are enhanced by a factor of ∼20. These improvements increase the number of detectable GW sources, facilitate multi-messenger follow-up observations and provide constraints on the cosmological constant.