GNSS instantaneous attitude determination method based on multi-variable constraints
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摘要:
传统的直接定姿法或最小二乘法依赖于整周模糊度的成功固定。当卫星数目较少或存在干扰的情形下，模糊度固定成功率会大大降低，进而导致定姿结果不准确。因此，提出基于多变量约束的姿态确定方法，所提方法将整周模糊度和姿态确定视作联合问题进行解算且对基线长度没有限制。利用天线的几何信息和姿态矩阵的正交特性对观测模型进行多变量约束，能够有效提升模糊度固定成功率并实现瞬时定姿。仿真结果表明：即使在信号观测精度非常低的场景下，所提方法也能达到75.7%的模糊度固定成功率；即使只有4颗卫星，所提方法也能达到90%以上的成功率。且在使用超短基线的前提下，所提方法能够达到0.93°的定姿精度。
Abstract:The traditional direct attitude determination or least square method depends on the correct fixation of the ambiguity. When the number of satellites is small or there is interference, the success rate of ambiguity will be greatly reduced, which will lead to inaccurate attitude determination results. This study employs the multivariate constraint-based attitude determination method, which treats attitude determination and ambiguity as a single problem to be solved and does not place any strict restrictions on the baseline's length. This paper uses the geometric information of the antennas and the orthogonal characteristics of the attitude matrix to perform multivariate constraints on the observation model. It can effectively improve the success rate of ambiguity and achieve instantaneous attitude determination. The simulation results show that the multivariable constraint method can achieve 75.7% ambiguity fixed success rate even in the scene with very low signal observation accuracy. Even if there are only four satellites, the success rate of this method can reach more than 90%. Under the premise of using the ultra-short baseline, this method can achieve an attitude accuracy of 0.93°.
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图 4 4组数据对应的模糊度固定成功率
Figure 4. Ambiguity fixed success rate corresponding to the four sets of data
表 1 4组天线布局的参数
Table 1. Parameters of four antenna configurations
组别 基线1长度/m 基线2长度/m 夹角/（°） 精度因子v 第1组 1.0 2.0 100 5.2 第2组 1.5 2.0 90 12 第3组 2.0 2.0 60 16 第4组 2.0 2.0 90 21.3 
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表 2 不同卫星数目下的模糊度固定成功率
Table 2. Success rate of ambiguity under different number of satellites
% 卫星数 第1组模糊度固定成功率 第2组模糊度固定成功率 无约束 多变量约束 无约束 多变量约束 4 0.6 90.3 0.5 90.5 5 6.7 95.4 5.8 96.6 6 33.3 100 34.5 100 7 65.9 100 65.2 100 8 95.4 100 96.2 100 9 99.9 100 99.7 100
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表 3 姿态角的均值和标准差
Table 3. Mean and standard deviation of attitude angle
(°) 组别 航向角 俯仰角 横滚角 均值 标准差 均值 标准差 均值 标准差 第1组 −123.32 0.216 −0.28 0.472 −0.25 0.670 第2组 −59.51 0.212 −0.41 0.740 −0.41 0.395
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表 4 3组天线布局的参数
Table 4. Parameters of three antenna configurations
组别 基线1长度/m 基线2长度/m 夹角/（°） 精度因子v 第1组 0.73 0.35 90 0.09 第2组 0.73 0.35 60 0.07 第3组 0.73 0.22 60 0.03
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表 5 姿态角估计值的标准差
Table 5. Standard deviation of estimated attitude angle
(°) 组别 航向角 俯仰角 横滚角 第1组 0.27 0.93 0.68 第2组 0.28 1.33 1.42 第3组 0.29 1.42 1.56
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