A practical methodology for $\Lambda$ global polarization extraction in fixed-target experiments
Non-central heavy-ion collisions generate large orbital angular momentum in the created medium, which leads to polarization of final-state particles via spin-orbit coupling, known as global spin polarization. The observation of significant global polarization of $\Lambda$ hyperon in heavy-ion collisions indicates that the quark-gluon plasma is the most vortical fluid known in nature. Exploring $\Lambda$ global polarization at lower energies is important for understanding spin dynamics across different regions of the quantum chromodynamics (QCD) phase diagram. Low-energy nuclear experiments are typically conducted with asymmetric detector acceptance, as in fixed-target collisions at RHIC-STAR, and at facilities such as FAIR, NICA, HIAF and HIRFL-CSR. The asymmetric rapidity coverage in these experiments enhances the coupling between directed flow and detector inefficiencies, creating significant bias in $\Lambda$ global polarization measurements. In this paper, we propose a methodology to eliminate such bias arising from asymmetric detector acceptance. The method is validated using realistic detector simulations based on the STAR fixed-target configuration.