Optimization of a Time-of-Arrival-Ridge Estimation Iterative Model for Ultra-Wideband Positioning in a Long Linear Area

Ultra-wideband (UWB) technology is widely used for high-precision indoor positioning due to its adaptability to various environments. However, in long linear areas, such as tunnels or corridors, the near-linear deployment of base stations caused by structural constraints significantly degrades UWB localization accuracy, rendering conventional algorithms ineffective. To address this issue, this study proposes a high-precision UWB+TOA-R positioning algorithm that incorporates Ridge estimation as a constraint condition. The algorithm introduces equivalent weights to refine the iterative computation of Ridge estimation, establishing an iteratively computed TOA-RR solution model. Experiments were conducted in a long linear corridor to compare the performance of three UWB localization models: the TOA-Least Squares (TOA-LS) model, the TOA-Ridge estimation (TOA-R) model, and the proposed TOA-Ridge estimation iterative (TOA-RR) model. The results indicate that the TOA-LS model suffers from significant coordinate distortions due to abnormalities in the inverse matrix of the coefficient matrix, regardless of the initial tag coordinates. The TOA-R model demonstrates improved accuracy and stability, particularly in cases of significant initial deviations, but still exhibits residual errors. In contrast, the TOA-RR model achieves enhanced stability and accuracy, with a positioning error of approximately 0.5 m. This study resolves the challenge of inaccurate UWB localization in long linear areas, providing a robust solution for such environments.