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The ultra-wideband (UWB) technology has been increasingly recognized as an efficacious strategy for Indoor Positioning Systems (IPSs). However, the accuracy of the UWB system can be severely degraded by non-line-of-sight (NLOS) errors. In this study, we proposed a new method to reduce the UWB positioning error in such an indoor environment. We developed a system consisting of a Robotic Total Station (RTS), four UWB base stations, a moving target (including a prism and a UWB tag), and a PC. The observed coordinates of the moving target, captured using millimeter precision from an RTS device, served as the ground truth for calculating the positioning errors of the UWB tag. In a significant NLOS scenario, the UWB's three-dimensional positioning error was identified to exceed the nominal value declared by the manufacturer by a factor of more than three. A detailed analysis revealed that each coordinate component's error distribution pattern demonstrated considerable variance. To reduce the NLOS error, we designed a combined multilayer neural network that simultaneously fits errors on all three coordinate components and three separate multilayer networks, each dedicated to optimizing errors on a single coordinate component. All networks were trained and verified by benchmark errors obtained from the RTS. The results showed that neural networks outperform the traditional methods, attributed to their strong nonlinear modelling ability, thereby significantly improving the external accuracy by an average reduction in RMSE by 61% and 72%. It is evident that the proposed separate networks would be more suitable for NLOS positioning problems than a combined network. [ABSTRACT FROM AUTHOR]

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay's accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing. [ABSTRACT FROM AUTHOR]