Ultra-wideband (UWB) ranging techniques can provide accurate distance measurement in line-of-sight (LOS) conditions. However, various walls and obstacles in indoor non-line-of-sight (NLOS) environments, which obstruct the direct propagation of UWB signals, can generate significant ranging errors. Due to the complex through-wall UWB signal propagation, most conventional studies simplify the ranging error model by assuming that the incidence angle is zero or the relative permittivities for different walls are the same to improve the through-wall UWB localization performance. Considering walls are different in realistic settings, this paper presents a through-multiple-wall NLOS mitigation method for UWB indoor positioning. First, spatial geometric equilibrium equations of UWB through-wall propagation and a numerical method are developed for the precise modeling of UWB through-wall ranging errors. Then, calculated error maps are determined numerically without field measurements. Finally, the determined error maps are combined with a gray wolf optimization algorithm for localization. The proposed method is evaluated via field experiments with four rooms, three walls, and six penetration cases. The results demonstrate that the method can strongly mitigate the multi-wall NLOS effects on the performance of UWB positioning systems. This solution can reduce project costs and number of power supplies for UWB indoor positioning applications.
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