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Achieving a balance between accuracy and efficiency is a critical challenge in facial landmark detection (FLD). This paper introduces Parallel Optimal Position Search (POPoS), a high-precision encoding-decoding framework designed to address the limitations of traditional FLD methods. POPoS employs three key contributions: (1) Pseudo-range multilateration is utilized to correct heatmap errors, improving landmark localization accuracy. By integrating multiple anchor points, it reduces the impact of individual heatmap inaccuracies, leading to robust overall positioning. (2) To enhance the pseudo-range accuracy of selected anchor points, a new loss function, named multilateration anchor loss, is proposed. This loss function enhances the accuracy of the distance map, mitigates the risk of local optima, and ensures optimal solutions. (3) A single-step parallel computation algorithm is introduced, boosting computational efficiency and reducing processing time. Extensive evaluations across five benchmark datasets demonstrate that POPoS consistently outperforms existing methods, particularly excelling in low-resolution heatmaps scenarios with minimal computational overhead. These advantages make POPoS a highly efficient and accurate tool for FLD, with broad applicability in real-world scenarios.