  Accurate facial landmark detection is critical for facial analysis tasks, yet
prevailing heatmap and coordinate regression methods grapple with prohibitive
computational costs and quantization errors. Through comprehensive theoretical
analysis and experimentation, we identify and elucidate the limitations of
existing techniques. To overcome these challenges, we pioneer the application
of True-Range Multilateration, originally devised for GPS localization, to
facial landmark detection. We propose KeyPoint Positioning System (KeyPosS) -
the first framework to deduce exact landmark coordinates by triangulating
distances between points of interest and anchor points predicted by a fully
convolutional network. A key advantage of KeyPosS is its plug-and-play nature,
enabling flexible integration into diverse decoding pipelines. Extensive
experiments on four datasets demonstrate state-of-the-art performance, with
KeyPosS outperforming existing methods in low-resolution settings despite
minimal computational overhead. By spearheading the integration of
Multilateration with facial analysis, KeyPosS marks a paradigm shift in facial
landmark detection. The code is available at https://github.com/zhiqic/KeyPosS.
