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摘要: 本文研究了卫星信号干扰下 RTK (Real-time kinematic)整周模糊度固定问题, 提出一种基于整数约束型渐进高斯滤波的 RTK 定位方法. 首先, 结合贝叶斯推理与同伦方法优势, 导出一种兼容整数、浮点状态的渐进高斯滤波框架. 其次, 构造从先验分布到后验分布的同伦路径, 以目标浮点状态与模糊度固定的迭代求解来提高信号干扰情形下的整周模糊度固定率. 特别地, 通过渐进地融合卫星双差信息来降低线性化误差, 进而提升对目标状态后验分布的逼近精度. 最后, 通过车载 RTK 实验及后处理分析, 验证了所提方法的有效性和优越性.Abstract: This paper investigates the issue of real-time kinematic (RTK) integer ambiguity resolution under satellite signal interference and proposes an RTK positioning method based on integer-constrained progressive Gaussian filtering. Firstly, by combining the advantages of Bayesian inference and homotopy methods, a progressive Gaussian filtering framework that is compatible with both integer and floating-point states is derived. Secondly, a homotopic path is constructed from the prior distribution to the posterior distribution, and the target floating-point state and ambiguity resolution is solved iteratively for improving the integer ambiguity fixed rate under signal interference conditions. Specifically, the linearization error is reduced by progressively fusing satellite double-difference information, thus enhancing the approximation accuracy of the posterior distribution of the target state. Finally, the effectiveness and superiority of the proposed method are validated through vehicle-mounted RTK experiments and post-processing analysis.
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图 9 卫星失锁后定位误差收敛速度
Fig. 9 Positioning error convergence speed after satellite signal loss
表 1 RMSE和固定率对比
Table 1 Comparison of RMSE and fixed rate
方法 EKF IREKF IEKF REKF 所提方法 提升 RMSE-水平 (m) 0.8718 1.0223 0.9600 0.9075 0.6696 23.19% RMSE-垂直 (m) 0.2959 0.6174 0.5150 0.2871 0.2062 28.18% 固定率 (%) 50.3300 61.5800 58.4800 71.1300 90.3800 19.25% 
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表 2 单个历元平均解算时间
Table 2 The average calculation time of each epoch
方法 EKF IREKF IEKF REKF 所提方法 时间 (s) 0.0821 0.1506 0.1490 0.0863 0.0899
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