Integration of Global Navigation Satellite System Observations for Generating Network Corrections Usin g a Virtual Reference Station Method

The rapid advancement of Global Navigation Satellite Systems (GNSS) has revolutionized the field of geospatial data acquisition significantly, enhancing the accuracy and efficiency of positioning operations. This study investigates an innovative approach to improving positional accuracy by integrating observations from multiple GNSS constellations — specifically GPS (USA), Galileo (EU), and BeiDou (China) — within a Network-based Real-Time Kinematic (NRTK) positioning framework using a Virtual Reference Station (VRS) method. Traditionally, RTK positioning techniques relied on a single base station to provide corrections, which are effective only within a limited radius due to the degradation of accuracy with increasing distance from the base. The NRTK technique, and particularly the VRS method, emerged as a superior solution by establishing a network of reference stations that deliver spatially interpolated corrections to a virtual station near the user, significantly reducing the baseline length and associated atmospheric and orbital errors. This research implements a dual-frequency double-differencing observation model to mitigate receiver and satellite clock errors, followed by ambiguity resolution using the Melbourne-Wübbena combination and an ionosphere-free linear combination. These steps are vital in estimating the double-differenced integer ambiguities for each frequency, which are subsequently utilized to compute atmospheric delays with high precision. The use of the MLAMBDA algorithm for ambiguity fixing further enhances the reliability of the results.
The methodology includes the interpolation of network corrections using four distinct models: linear combination model (LCM), linear distance-based interpolation model (DIM), least squares model (LSM), and linear interpolation model (LIM). Each model offers different strategies to compute tropospheric and ionospheric corrections at the user's location based on surrounding reference station data. Notably, DIM, while computationally simpler, showed limitations due to its unidirectional approach that neglects two-dimensional spatial variability in atmospheric conditions. To assess the performance of the proposed VRS-based NRTK system, data from six permanent GNSS stations from the UNAVCO network were used, with a focus on a single baseline for clarity. The results were evaluated across multiple scenarios: single-system, dual-system, and triple-system integrations, with and without applying network corrections. The empirical data showed that the integration of multiple GNSS systems significantly reduces positional errors. For instance, without integration, GPS yielded horizontal and vertical errors of 33 cm and 52 cm, respectively, while Galileo and BeiDou had higher error margins. However, combining all three systems reduced these errors to just 6 cm horizontally and 17 cm vertically. Analysis of atmospheric corrections revealed that both ionospheric and tropospheric corrections are highly sensitive to satellite geometry, particularly around the times of satellite rise and set. These periods showed an exponential increase in correction values, indicating the need for a threshold-based correction exclusion strategy. A threshold of 15 cm for dispersive (ionospheric) and 10 cm for non-dispersive (tropospheric) corrections was found effective; for fewer systems, thresholds up to 30 cm were tested to maintain a non-singular solution matrix.
The results highlight that among all the interpolation methods, LSM, LIM, and LCM performed comparably well, while DIM often lagged, especially under multi-dimensional spatial variability. The dual-system integration of GPS and Galileo consistently outperformed GPS and BeiDou, likely due to structural similarities between GPS and Galileo and the higher noise levels in BeiDou observations. The final outcomes underscore that the optimal configuration for high-precision real-time positioning involves the integration of all three GNSS systems with a robust interpolation model that can accurately model the spatial behavior of atmospheric corrections. This integrated approach not only improves the accuracy of the mobile receiver's coordinates but also enhances the resilience and reliability of the positioning system by reducing dependency on any single GNSS constellation. In conclusion, the study demonstrates that multi-GNSS integration within a VRS-based NRTK framework significantly enhances positional accuracy. The selection of an appropriate interpolation method and the implementation of correction magnitude thresholds are crucial for optimizing performance. This methodology, when localized and adapted with native correction software, offers a promising direction for future GNSS applications in geodetic and cadastral surveying.