Ruozhou Wang

The Slant Path Delay (SPD) exhibits “non-isotropy” in the horizontal direction, validated by ray-tracing. This non-isotropy can cause decimeter-level errors in SPD, yet specific models and influencing factors remain under-researched. This study aims to quantify SPD non-isotropy with the non-isotropic value (ΔN), which represents the deviation between SPD and average SPD at corresponding elevations. We analyzed the spatiotemporal characteristics of non-isotropic SPD by estimating ΔN at 77 grid points (2019–2021, 1-day interval) and 804 grid points at different altitudes (2019–2021, 90-day interval). Using the IGG-Ⅲ scheme, we developed a non-isotropic SPD model considering azimuth continuity. We validated this model by incorporating VMF1 with horizontal gradient correction and VMF1 with horizontal gradient correction combined with the non-isotropic model into static PPP, tested at 16 IGS stations. Results indicate ΔN depends on time, latitude, altitude, elevation, and azimuth. The model categorizes SPD into positive anisotropy, undetermined isotropy, or negative anisotropy. For the 16 IGS stations, the non-isotropic model reduced the STD by 7.5%, 5.8%, and 2.8% in the E, N, and U directions, respectively, and decreased convergence time by 12.8%, 25.4%, and 1.4%. This confirms the model's effectiveness, offering a valuable tool for accurate SPD estimation and improved navigation under real atmospheric conditions.

Along with the IoT technology, the importance of indoor positioning is increasing, but the accuracy of the traditional fingerprint positioning algorithm is negatively affected by the complex indoor environment. This issue of low indoor spatial geolocation localization accuracy when the signal is collected away from the present stage occurs due to the signal instability of the iBeacon in the traditional fingerprint localization algorithm, which generates a variety of factors such as object blocking and reflection, multipath effect, etc., as well as the scarcity of reference fingerprint data points. In response, this study proposes an inverse distance-weighted optimization WKNN algorithm for indoor localization based on the GM(1,1) model. By implementing GM(1,1) model pre-process leveling, the original fingerprint library was reconstructed into a large-capacity fingerprint database using the inverse distance-weighted interpolation method. The local inverse distance-weighted interpolation was used for interpolation, combined with the WKNN algorithm to complete the coordinate solution in real time. This effectively solved the issue of low localization accuracy caused by the large fluctuation of the received signal strength (RSS) sampling measurement data and the existence of few reference fingerprint datapoints in the fingerprint database. The results show that this algorithm reduced the average positioning error by 5.9% compared with ordinary kriging (OK) interpolation leveling and reduced the average positioning error by 18.2% compared with the indoor spatial location accuracy of the original fingerprint database, which can effectively improve the positioning accuracy and provide technical support for indoor location and navigation services.