引用本文: 郭迎庆, 詹洋, 张琰, 王译那, 徐赵东, 李今保. 基于PSO与AFSA的GNSS整周模糊度种群融合优化算法[J]. 工程科学学报.
GUO Yingqing, ZHAN Yang, ZHANG Yan, WANG Yina, XU Zhaodong, LI Jinbao. Population fusion optimization algorithm for GNSS integer ambiguity resolution based on PSO and AFSA[J]. Chinese Journal of Engineering.
 Citation: GUO Yingqing, ZHAN Yang, ZHANG Yan, WANG Yina, XU Zhaodong, LI Jinbao. Population fusion optimization algorithm for GNSS integer ambiguity resolution based on PSO and AFSA[J]. Chinese Journal of Engineering.

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

• 摘要: 载波相位测量是实现全球导航卫星系统(Global navigation satellite system, GNSS)快速高精度定位的重要途径，而准确解算整周模糊度是其中的关键步骤之一. 粒子群算法(Particle swarm optimization, PSO)收敛速度快但易陷入局部最优，人工鱼群算法(Artificial fish swarm algorithm, AFSA )全局优化性能好但收敛速度慢，因此融合两种算法的优点，提出一种GNSS整周模糊度种群融合优化算法（PSOAF）. 首先，通过载波相位双差方程求解整周模糊度的浮点解和对应的协方差矩阵. 然后，采用反整数Cholesky算法对模糊度浮点解作降相关处理. 其次，针对整数最小二乘估计的不足通过优化适应度函数来提高算法的收敛性和搜索性能. 最后，通过PSOAF算法对整周模糊度进行解算. 通过经典算例和试验研究表明：PSOAF算法可以更快地收敛于最优解，搜索效率也更为出色，解算的基线精度可以控制在10 mm以内，在短基线的实际情况下具有较高的应用价值.

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 PSA’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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