We study wireless indoor positioning systems where multiple synchronized infrastructure devices simultaneously receive signals from an object of interest whose arrival times are measured. The positioning performance is degraded by unresolvable channel multipath and non-line-of-sight (NLOS) reflctions which cause a bias in the time difference of arrival (TDOA) measurements. In order to reduce the negative effect of multi-path, a Multi-Path Map (MPM) method based on spatial domain modeling principle in the reverse positioning framework with good robustness is proposed. Meanwhile, an improved non-linear iterative algorithm with height component constrained which reduces the complexity is introduced to calculate the coordinates so that the performance of the MPM can be verified. By using the MPM measurements as pre-calibration information to compensate the TDOA observed value, the accuracy of the cooperative location based on a UWB device is 6.45 cm, which achieves 63% improvement than that of none MPM used.

Sidereal filtering is an effective method for mitigating multipath error in static GPS positioning. Using accurate estimates of multipath repeat time (MRT) in sidereal filtering can further improve the performance of the filter. There are three commonly used methods for estimating the MRT: Orbit Repeat Time Method (ORTM), Aspect Repeat Time Adjustment (ARTA), and Residual Correlation Method (RCM). This study utilizes advanced sidereal filtering (ASF) adopting the MRT estimates derived by the three methods to mitigate the multipath in observation domain, then evaluates the three methods in term of multipath reduction in both coordinate and observation domain. Normally, the differences between the MRT estimates from the three methods are less than 1.2 s on average. The three methods are basically identical in multipath reduction, with RCM being slightly better than the other two methods, whereas for a satellite affected by orbit maneuver (satellite number 13 in this study), the MRT estimated by the three methods differ by up to tens of seconds, and the RCM- and ARTA-derived MRT estimates are better than ORTM-derived ones for ASF multipath reduction. The RCM shows a slight advantage in multipath mitigation, while ORTM is the one of lowest computation and ARTA is the optimal one for real-time ASF. Thus, the best MRT estimation method for practical applications depends on which criterion overweighs the others.

Advanced sidereal filtering (ASF) is an observation-domain sidereal filtering that adopts the repeat time of each individual satellite separately rather than the mean repeat time, adopted by the modified sidereal filtering (MSF). To evaluate the performance of ASF, we apply the method to filter the multipath for a short baseline based on a dual-antenna Global Navigation Satellite System (GNSS) receiver. The errors from satellite and receiver clocks, satellite orbit, troposphere, ionosphere, and antenna phase center variations are greatly eliminated by single difference between the two antennas because they are connected to the same receiver clock. The performances of ASF are compared with MSF to evaluate the gain for multipath mitigation. Comparisons indicate that ASF slightly outperforms MSF when the repeat time values of all satellites incorporated in data processing are within the normal range (86,145–86,165 s), but the difference of variance reduction rate between ASF and MSF is statistically significant. When the data of a satellite with repeat time outside the normal range are included, the performances of MSF become much worse, but ASF is almost not affected. This advantage of ASF over MSF is important because the proportion of the days on which at least one satellite’s repeat time exceeds the normal range reaches 71.19% based on the statistics on the data of 2014 and 2015. After applying ASF multipath corrections on the test days, the averages of standard deviations of north, east, and up component are reduced from 3.8 to 2.1 mm, 3.2 to 1.7 mm, and 7.6 to 4.3 mm, respectively. Comparison between applying ASF with the single-day model and with the seven-day model indicates that the former is generally more effective in multipath reduction.

Multipath hemispherical map (MHM) is a kind of multipath mitigation approach that takes advantage of the spatial repeatability of the multipath effect under an unchanged environment. This approach is not only suitable for static environments, but also for some kinematic platforms, such as a moving ship and airplane, where the dominant multipath effects come from the platform itself and the multipath effects from the surrounding environment are considered minor or negligible. Previous studies have verified the feasibility of the MHM approach in static environments. In this study, we expanded the MHM approach to a kinematic shipborne environment. Both static and kinematic tests were carried out to demonstrate the feasibility of the MHM approach. The results indicate that, after MHM multipath mitigation, the root mean square (RMS) of baseline length deviations are reduced by 10.47% and 10.57%, and the RMS of residual values are reduced by 39.89% and 21.91% for the static and kinematic tests, respectively. Power spectrum analysis has shown that the MHM approach is more effective in mitigating multipath in low-frequency bands; the high-frequency multipath effects still exist, and are indistinguishable from observation noise. Taking the observation noise into account, the residual reductions increase to 41.68% and 24.51% in static and kinematic tests, respectively. To further improve the performance of MHM for kinematic platforms, we also analyzed the influence of spatial coverage and resolution on residual reduction.

The terrestrial reference frame is a cornerstone for modern geodesy and its applications for a wide range of Earth sciences. The underlying assumption for establishing a terrestrial reference frame is that the motion of the solid Earth's figure centre relative to the mass centre of the Earth system on a multidecadal timescale is linear. However, past international terrestrial reference frames (ITRFs) showed unexpected accelerated motion in their translation parameters. Based on this underlying assumption, the inconsistency of relative origin motions of the ITRFs has been attributed to data reduction imperfection. We investigated the impact of surface mass loading from atmosphere, ocean, snow, soil moisture, ice sheet, glacier and sea level from 1983 to 2008 on the geocentre variations. The resultant geocentre time-series display notable trend acceleration from 1998 onward, in particular in the z-component. This effect is primarily driven by the hydrological mass redistribution in the continents (soil moisture, snow, ice sheet and glacier). The acceleration is statistically significant at the 99 per cent confidence level as determined using the Mann–Kendall test, and it is highly correlated with the satellite laser ranging determined translation series. Our study, based on independent geophysical and hydrological models, demonstrates that, in addition to systematic errors from analysis procedures, the observed non-linearity of the Earth-system behaviour at interannual timescales is physically driven and is able to explain 42 per cent of the disparity between the origins of ITRF2000 and ITRF2005, as well as the high level of consistency between the ITRF2005 and ITRF2008 origins.