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基于PSO與AFSA的GNSS整周模糊度種群融合優化算法

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

  • 摘要: 載波相位測量是實現全球導航衛星系統(Global navigation satellite system, GNSS)快速高精度定位的重要途徑,而準確解算整周模糊度是其中的關鍵步驟之一. 粒子群算法(Particle swarm optimization, PSO)收斂速度快但易陷入局部最優,人工魚群算法(Artificial fish swarm algorithm, AFSA )全局優化性能好但收斂速度慢,因此融合兩種算法的優點,提出一種GNSS整周模糊度種群融合優化算法(PSOAF). 首先,通過載波相位雙差方程求解整周模糊度的浮點解和對應的協方差矩陣. 然后,采用反整數Cholesky算法對模糊度浮點解作降相關處理. 其次,針對整數最小二乘估計的不足通過優化適應度函數來提高算法的收斂性和搜索性能. 最后,通過PSOAF算法對整周模糊度進行解算. 通過經典算例和試驗研究表明:PSOAF算法可以更快地收斂于最優解,搜索效率也更為出色,解算的基線精度可以控制在10 mm以內,在短基線的實際情況下具有較高的應用價值.

     

    Abstract: 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.

     

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