Next Generation Indoor Airport Wayfinding Using Ultra-Wideband (UWB) Localization and Pedestrian Physics: A Theoretical Framework

Navigating crowded indoor environments like airport terminals is difficult because satellite GPS signals cannot pass through dense concrete and steel buildings. Additionally, current indoor navigation apps rely on static shortest-path algorithms that ignore real-time crowd congestion, often routing users directly into severe bottlenecks. To address this, this paper proposes a theoretical, mathematical navigation framework that models real-time pedestrian dynamics by integrating ultra-wideband (UWB) trilateration, traffic flow physics, and vector calculus. The terminal map was split into a spatial grid, and localized pedestrian slowdowns were modeled using Greenshields traffic mechanics to find a critical bottleneck threshold. A continuous scalar potential field was built by combining a destination potential with a crowd repulsion potential smoothed via two-dimensional Gaussian convolution. Navigation directions were then found using the negative gradient of the field, utilizing dynamic waypoints to avoid local minima traps. Real-time positioning was achieved by simplifying UWB anchor distance equations using least-squares estimation and a moving average filter. Mathematical modeling results showed that the dynamic model successfully routed users around high-density bottlenecks into open side corridors. While this model chose physically longer paths, it consistently reduced total travel time compared to traditional static algorithms.