Integer Ambiguity Baseline Rectifying for GNSS Augmentation Services by Linear Programming Method

The advent of the global navigation satellite system has greatly enhanced satellite positioning technology, with precise point positioning (PPP) emerging as a prominent technique. Despite the advantages of PPP, such as flexibility and reduced operational costs, it faces challenges from phase noise and atmospheric delays, which necessitate reliable ambiguity resolution. Our study introduces a novel nonstatistical estimation method—baseline rectification for integer ambiguities. This approach employs integer linear programming, integrated with sparse statistics, to formulate the problem. It establishes a theoretical foundation for the method's effectiveness, facilitating the verification and, crucially, the rectification of integer ambiguities to their true values. Real-world data testing has empirically proven that during times of moderate ionospheric activity [as indicated by rate of total electron content index], our method can effectively restore baseline ambiguities, thereby increasing the number of usable satellites in correction service and ultimately enhancing positioning accuracy (root mean squared error decreases 87.57%). This article explores the foundational theoretical concepts and mathematical modeling involved in our study. The efficacy of our proposed method has been substantiated through simulations, demonstrating its effectiveness. Furthermore, the application of our method to real-world data has shown significant improvements in positioning accuracy