The terrestrial water storage anomaly (TWSA) gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO) is now a significant issue for scientific research in high-resolution time-variable gravity fields. This paper proposes the use of singular spectrum analysis (SSA) to predict the TWSA derived from GRACE. We designed a case study in six regions in China (North China Plain (NCP), Southwest China (SWC), Three-River Headwaters Region (TRHR), Tianshan Mountains Region (TSMR), Heihe River Basin (HRB), and Lishui and Wenzhou area (LSWZ)) using GRACE RL06 data from January 2003 to August 2016 for inversion, which were compared with Center for Space Research (CSR), Helmholtz-Centre Potsdam-German Research Centre for Geosciences (GFZ), Jet Propulsion Laboratory (JPL)’s Mascon (Mass Concentration) RL05, and JPL’s Mascon RL06. We evaluated the accuracy of SSA prediction on different temporal scales based on the correlation coefficient (R), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE), which were compared with that of an auto-regressive and moving average (ARMA) model. The TWSA from September 2016 to May 2019 were predicted using SSA, which was verified using Mascon RL06, the Global Land Data Assimilation System model, and GRACE-FO results. The results show that: (1) TWSA derived from GRACE agreed well with Mascon in most regions, with the highest consistency with Mascon RL06 and (2) prediction accuracy of GRACE in TRHR and SWC was higher. SSA reconstruction improved R, NSE, and RMSE compared with those of ARMA. The R values for predicting TWS in the six regions using the SSA method were 0.34–0.98, which was better than those for ARMA (0.26–0.97), and the RMSE values were 0.03–5.55 cm, which were better than the 2.29–5.11 cm RMSE for ARMA as a whole. (3) The SSA method produced better predictions for obvious periodic and trending characteristics in the TWSA in most regions, whereas the detailed signal could not be effectively predicted. (4) The predicted TWSA from September 2016 to May 2019 were basically consistent with Global Land Data Assimilation System (GLDAS) results, and the predicted TWSA during June 2018 to May 2019 agreed well with GRACE-FO results. The research method in this paper provides a reference for bridging the gap in the TWSA between GRACE and GRACE-FO.

Multipath effects in GNSS observations significantly reduce positioning accuracy and are challenging to model and mitigate. We propose three statistical tests for multipath detection using the carrier-to-noise power density ratio (C/N0). Each test has certain advantages and disadvantages: the first S1 based on the C/N0 is sensitive to an abnormal C/N0 but cannot distinguish multipath and NLOS (non-line-of-sight). The second S2 based on the differenced C/N0 between frequencies can detect multipath without being affected by NLOS, but at least two frequencies are needed. Additionally, the combination of S1 and S2 can be used to identify NLOS. The third S3 based on the epoch difference of C/N0 is preferred for kinematic mode. The best performance is achieved when all three tests are used in combination. For the static multipath detection experiment in a harsh environment, a function related to the azimuth is established to mitigate the impact of azimuthal dependence of C/N0 on multipath detection for low-cost receivers. The detection rates for a Trimble Alloy receiver with a geodetic antenna and a low-cost u-blox F9P receiver with a microstrip patch antenna were 83.67% and 73.40%, respectively, while their incorrect detection rates were 10.11% and 20.24%, respectively. For single-epoch static RTK positioning with the u-blox F9P, the proportion of horizontal position error within 0.2 m and 2 m were improved from 61.5% to 78.8% and 78.3% to 92.8%, respectively, once multipath observations were identified. For the kinematic experiment, 47.05% and 61.79% of the observations were detected as affected by multipath interference, and 70.95% and 85.27% of NLOS observations were detected via the combination of S1 and S2 for the Alloy and u-blox F9P receivers, respectively. However, due to the sensitivity of low-cost devices to multipath effects, the number of available satellites will significantly decrease during kinematic positioning. In such cases, a weighting method should be applied.

The integration of Global Navigation Satellite Systems (GNSS) and Inertial Navigation Systems (INS) is subject to severe performance degradation in urban canyons due to signal blockages. We propose a novel tightly coupled RTK/INS robust positioning framework based on factor graph optimization (FGO), which directly fuses GNSS pseudorange and carrier-phase observations with a low-cost inertial measurement unit (IMU). The framework enhances positioning accuracy through full exploitation of integer ambiguity characteristics via persistent constraints maintained by ambiguity propagation with marginalization, while systematic sliding window size optimization under the ambiguity-constant model replaces empirical heuristics by balancing accuracy against computational efficiency. Furthermore, multiple robust estimation methods, including Gaussian mixture models (GMM) and their enhanced variants, were integrated into the framework to mitigate outliers. Vehicle-based experiments conducted in urban environments using low-cost IMU demonstrate that the proposed method achieves horizontal positioning accuracy of approximately 10 cm. Although FGO-based RTK/INS demonstrating more modest improvements than standalone RTK, ambiguity propagation achieves a practically meaningful 11.2% 3D accuracy enhancement. Considering both accuracy and computational efficiency, a sliding window size of 4-s is recommended for both FGO-based RTK and tightly coupled RTK/INS. While GMM-based methods demonstrate superior accuracy in GNSS-challenged environments despite increased computational demands, M-estimation and switch constraints provides balanced accuracy and efficiency.

The presence of unmodeled errors such as multipath and non-line-of-sight (NLOS) significantly degrades the positioning performance of global navigation satellite systems (GNSS), especially in harsh environments. We propose a novel stochastic model that considers multipath effects based on carrier-to-noise-density ratio (C/N0). This model utilizes C/N0 observations and their nominal function to construct a five-segment variance shrinking factor to enable a more accurate characterization of observation precision and yields reliable posterior residuals. Subsequently, the Institute of Geodesy and Geophysics 3 (IGG3) scheme based on posterior residuals is applied for quality control to enhance the performance of the results. Three sets of real-time kinematic (RTK) positioning experiments were conducted in harsh environments such as urban canyons and shaded areas to validate the effectiveness of the proposed method. For single-epoch static RTK positioning, the proposed method improves the horizontal accuracy of the Trimble Alloy from decimeter to centimeter level and the u-blox F9P from approximately 1.5 m to 1.0 m, with improvements of 2-13% in the ambiguity success rate compared to traditional equal-weight, C/N0, and elevation models. In kinematic positioning, the proposed method significantly improves positioning accuracy by more than 20% and increases the ambiguity success rate. The Trimble Alloy achieves decimeter-level horizontal positioning accuracy in deep urban canyons, while the u-blox F9P achieves an accuracy of around 1 m.

The Precise Point Positioning/Inertial Navigation System (PPP/INS) tightly coupled navigation system achieves decimeter to centimeter level continuous positioning accuracy using only a single Global Navigation Satellite System (GNSS) receiver. However, the conventional frameworks exhibit inconsistency in error modeling: attitude errors are defined on the special orthogonal group SO(3), whereas position and velocity errors are represented in the Euclidean space. This non-unified error representation may lead to error accumulation and amplification during state propagation. This study proposes a tightly coupled PPP/INS method that integrates Lie group–based error modeling with multi-frequency ambiguity resolution to achieve unified representation of navigation state errors, thereby improving estimation consistency and accuracy. Experimental results demonstrate that the proposed method effectively improves the PPP-Ambiguity Resolution/INS (PPP-AR/INS) positioning accuracy. Under the open-sky condition, the left-invariant method reduces 3D positioning errors by 3.3% compared to the right-invariant method and by 9.3% compared to the conventional method. During partial GNSS signal blockage, the left-invariant method improved positioning accuracy, reducing 2D and 3D errors by 4.8% and 13.1%, respectively, compared with the conventional method. During GNSS signal outages, because the inertial measurement unit (IMU) maintained higher navigation accuracy before the outage, the left-invariant method further improved positioning accuracy, reducing 2D and 3D errors by 11.2% and 6.3%, respectively, and slowing the error growth compared with the conventional method. Moreover, the proposed method introduces only a 2.4% increase in computational time compared to conventional approaches, demonstrating its efficiency and suitability for computationally constrained platforms. Overall, the left-invariant Lie group method achieves better error suppression capability in dynamic environments, offering consistent and effective error modeling solutions for PPP-AR/INS tightly coupled systems.