Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas).

Positioning by means of the Global Positioning System (GPS) is a traditional and widely used method. However, its performance is affected by the user environment, such as multi-path effects and poor anti-interference abilities. Therefore, an Inertial Navigation System (INS) has been integrated with GPS to overcome the disadvantages of GPS positioning. INSs do not rely on any external system information and has strong autonomy and independence from the external environment. However, the performance of GPS/INS is visibly degraded in low-observability GPS environments (tall buildings, viaducts, underground tunnels, woods, etc.). Fortunately, with the emergence of Low-Earth-Orbit (LEO) satellites in recent years, the constellation configuration can be extended with the advantages of lower orbits, greater speeds, and richer geometric structures. LEO improves the geometric structure between users and satellites and provides many more observations. Meanwhile, a robust theory approach is applied that can restrain or remove the impact of low-accuracy observations. In this study, we applied LEO data and a robust theory approach to enhance the GPS/INS tight integration. To verify the effectiveness of this method, a set of vehicles and simulated LEO data were analyzed. The results show that robust Kalman filtering (RKF) provides a visible enhancement in the positioning accuracy of GPS/INS integration. This effectively restrains the mutation error and has a smoothing effect on the positioning results. In addition, the addition of LEO data significantly improves the positioning accuracy of a sole GPS and GPS/INS integration. The GPS/LEO/INS integration has the highest positioning accuracy, with Root-Mean-Square Errors (RMSEs) of the north, east, and vertical positions of 2.38 m, 1.94 m, and 2.49 m, respectively, which corresponds to an improvement of 30.21%, 47.43%, and 34.13% compared to sole GPS-based positioning and 8.60%, 17.24%, and 12.14% when compared to the GPS/INS mode. Simultaneously, the simulation results show that LEO and INSs can improve the positioning performance of GPS under GPS-blocked conditions.

Understanding the dynamic changes in the quality of the ecological environment and its potential driving forces is essential for protecting regional ecosystems and promoting sustainable development. In this study, we developed an improved remote sensing ecological index (IRSEI) by integrating the kernel normalized difference vegetation index (kNDVI) with an abundance index (AI) and conducted a comprehensive analysis of the spatiotemporal evolution of the quality of the ecological environment in the North China Plain (NCP) from 2000 to 2020. A multistep driving analysis framework was established to identify key climatic factors via the XGBoost algorithm and to quantify the effects of climate change and human activities through partial correlation analysis and a multiple regression residual model. The results indicate the following: (1) From 2000 to 2020, the ecological quality of the NCP significantly improved, with the average IRSEI increasing from 0.41 to 0.45. The proportion of areas with “good” or “excellent” ecological quality increased, revealing a south–north gradient, with higher values in the southern part and lower values in the northern part of the NCP. (2) Among the key climatic variables, surface temperature was significantly negatively correlated with the IRSEI, whereas atmospheric pressure and evapotranspiration were significantly positively correlated. (3) Approximately 51.97% of the ecological quality changes were jointly driven by climate change and human activities, with the contribution of human activities (28.80%) exceeding that of climate change (19.23%). These findings provide a scientific basis for understanding the driving mechanisms behind ecological environment changes and support ecological restoration and coordinated human–environment development in the context of climate change.

Several global navigation satellite systems (GNSS) broadcast overlapping frequencies to enhance interoperability, allowing tight integration with only one reference satellite for every system with the same frequency. The key to realizing tight integration is estimating and utilizing differential intersystem biases, which allows the integer characteristic of the differenced ambiguity of two satellites from different systems to be retrieved. In this study, a detailed algorithm flow of a tight integration kinematic uncalibrated phase delay (UPD)-based PPP ambiguity resolution (PPP-AR) method, which includes multiple parts, is introduced. Subsequently, PPP-AR numerical experiments were conducted in a high-shade observation environment to determine the performance. In comparison with traditional methods, our results indicate that the average success fix rate improves from 83% to 100% after using the tight integration method in an environment where only three satellites are observed for each system. Moreover, for fewer than nine satellites, the tight integration method can still consistently maintain a fixed state. However, for comparison, the traditional loose integration method could no longer be implemented.

Traditional PPP-RTK algorithm research has focused on users in a reference station network. However, if a proper PPP-RTK user algorithm can be designed for out-of-network users to achieve accurate and rapid positioning, the effective service area of existing reference station networks can be markedly expanded. To address the problem of extrapolating atmospheric corrections for out-of-network users, this study presents a single-reference-station (SRS) PPP-RTK model to address atmospheric delay corrections, by ensuring that only corrections from the closest reference station are used. Several numerical experiments were designed and conducted to compare the performance of the presented model and a widely used interpolation model. The extrapolation error distribution, mean and the maximum of absolute values of errors, and standard deviation of errors were selected as indicators. The results show that the SRS PPP-RTK model is significantly more accurate than the interpolation model. Thus, for out-of-network users, we suggest that the presented SRS PPP-RTK model should be used, and the residual atmospheric delays are needed to be estimated.

Precise point positioning with ambiguity resolution (PPP-AR) has been developed to restore the integer nature of estimated ambiguities, significantly enhancing time and frequency transfer performance. Since the end of 2019, the International Bureau of Weights and Measures has adopted PPP-AR for calculating integer PPP (IPPP) results in the time links of international atomic time. Dual-frequency (DF) ambiguity resolution method has been applied to IPPP time and frequency transfer. To incorporate multi-frequency observations into IPPP time and frequency transfer, this study adopts cascaded ambiguity resolution and cascaded cycle slip detection to investigate the performance of real-time multi-frequency IPPP in time and frequency transfer. The quality and availability of multi-frequency phase bias products were first assessed. Except for the GPS L5 frequency, the standard deviation (STD) of the phase bias products remained below 0.2 ns, with 78.79% of the narrow-lane fractional part residuals falling within 0.15 cycles, and 95.13% within 0.30 cycles. The IPPP time and frequency transfer performance of DF, triple-frequency (TF), and quad-frequency (QF) was systematically analyzed. Across both zero baselines and various baseline experiments, IPPP demonstrated reduced time transfer error fluctuations compared to float solutions. Furthermore, as the averaging time increased to several hours, IPPP demonstrated improved frequency stability. Following DF ambiguity resolution, the STD value of the zero-baseline common clock difference decreased by 5.5 ps, while the TF improved from 67.53 ps to 64.13 ps. Meanwhile, the frequency stability of the QF ambiguity-fixed solution reached 9.910 × 10⁻¹⁷ at 2.84 d averaging. Furthermore, for both short and long baselines, IPPP led to a significant reduction in time transfer errors. As the averaging time increased, IPPP demonstrated further enhancement in frequency stability.