Population fusion optimization algorithm for GNSS integer ambiguity resolution based on PSO and AFSA

Carrier phase measurement plays a crucial role in achieving rapid and high-precision positioning within a global navigation satellite system (Global navigation satellite system, GNSS). A pivotal aspect of this process is the accurate resolution of the integer ambiguity. Although the particle swarm optimization algorithm (Particle swarm optimization, PSO) demonstrates quick convergence, it tends to become trapped in local optima, showing a relatively weak ability to fix ambiguity. Conversely, the artificial fish school algorithm (Artificial fish swarm algorithm, AFSA) excels the global optimization performance. However, its natural selection mode, which operates without a “leader,” renders the integer ambiguity resolution process more time-consuming. By integrating the strengths of PSA and AFSA, we propose an improved hybrid algorithm, termed the particle swarm and artificial fish swarm (PSOAF) algorithms, to efficiently search for integer ambiguity solutions in GNSS. The process begins by solving the floating-point solution and its corresponding covariance matrix using the carrier phase double-difference equation. Then, to address the correlation issue, the inverse integer Cholesky algorithm is used to effectively decorrelate them. Recognizing the limitations inherent in integer least squares estimation, we further refine the effectiveness of the PSOAF algorithm by optimizing the fitness function. This optimization significantly enhances the convergence speed and search performance of the algorithm, resulting in a precise resolution of the integer ambiguity. In the initial stage of integer ambiguity search, the PSO’s characteristic of rapid convergence facilitates a coarse search, yielding a suboptimal solution. This solution serves as foundational data for the AFSA, guiding the fine search required for integer ambiguity resolution. To verify the PSOAF algorithm’s effectiveness and practicality, we conducted both three-dimensional and twelve-dimensional simulation analyses based on a classical example. The results demonstrate that the PSOAF algorithm not only converges to the optimal solution at an unprecedented rate but also exhibits markedly superior search efficiency compared to single algorithms. Further validation of the PSOAF algorithm’s real-world applicability and effectiveness was sought through experiments utilizing actual Beidou data. The results from these experiments were promising, showing that the baseline resolution error mainly remained within a 10-mm range. This finding confirms the correctness of the double-difference integer ambiguity search conducted using the PSOAF algorithm. The applicability and effectiveness of the PSOAF algorithm in real scenarios are verified. In conclusion, this study underscores the PSOAF algorithm’s significant potential for practical applications, particularly in scenarios involving short baselines.