Coarse normal height estimation algorithm for satellite navigation receivers
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摘要: 为了将卫星导航接收机输出的导航解应用于飞行器导航和武器发射测试等应用领域，需要将导航解中的大地高数值转换为概略正常高数值，但是不同应用领域对于概略正常高的需求是不同的。为了满足不同精度的概略正常高估计需求，实现以较短的计算时间和较小的存储空间开销来支撑实际的卫星导航接收机应用，提出了一种基于简化EGM96模型的概略正常高估计算法。以基于360阶360次EGM96地球重力场模型和2190阶2159次EGM2008地球重力场模型的计算结果为基准，统计了该概略正常高估计算法的计算时间和计算精度等指标。通过在全球格网点和亚太区域格网点测试结果的比较分析可知，该概略正常高估计算法可以求解不同精度等级的概略正常高，能够满足卫星导航接收机在亚太区域以及全球范围内的概略正常高估计的精度和时效性要求。Abstract: In order to apply the navigation solution output from the satellite navigation receiver to applications such as aircraft navigation and weapon launching testing, it is necessary to convert the geodetic height of the navigation solution to coarse normal height, but the demands for the coarse normal height in different application fields are different. To meet the normal height estimation requirements of different precisions, and to support the actual satellite navigation receiver application with low running time and storage space overhead, this paper proposes a coarse normal height estimation algorithm based on the simplified EGM96 model. Adopting the 360-degree 360-order EGM96 Earth gravity field model and the 2190-degree 2159-order EGM2008 Earth gravity field model, the running time and calculation accuracy of the coarse normal height estimation algorithm are evaluated. The test and comparative analysis of the grid points in the global region and the Asia-Pacific region show that the coarse normal height estimation algorithm can obtain the coarse normal height at different levels of accuracy, meeting the accuracy and timeliness requirements of the coarse normal height estimation with the satellite navigation receiver in the Asia-Pacific region and the global region.
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图 1 正高、正常高和大地高之间的关系
Figure 1. The relationship between orthometric height, normal height and geodetic height
表 1 基于降阶次的EGM96模型计算全球区域概略高程异常相对精度统计
Table 1. Relative accuracy statistic of the height anomaly computation method with reduced order EGM96 model on the global grids
order number relative error with EGM96 (360×360) model/m relative error with EGM2008 (2190×2159) model/m 160 0.30 0.55 140 0.35 0.59 120 0.42 0.64 100 0.51 0.69 90 0.56 0.73 80 0.63 0.79 70 0.72 0.85 60 0.81 0.92 50 0.94 1.03 40 1.08 1.15 30 1.37 1.42 
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表 2 基于降阶次EGM96模型计算亚太区域概略高程异常相对精度统计
Table 2. Relative accuracy statistic of the height anomaly computation method with reduced order EGM96 model on the Aisa-Pacific grids
order number relative error with EGM96 (360×360) model/m relative error with EGM2008 (2190×2159) model/m 160 0.38 0.50 140 0.44 0.55 120 0.54 0.64 100 0.65 0.73 90 0.72 0.80 80 0.82 0.89 70 0.91 0.97 60 1.03 1.09 50 1.22 1.25 40 1.39 1.41 30 1.61 1.62
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表 3 基于不同阶次EGM96模型的全球格网高程异常计算时间
Table 3. The average computation time consumption results for height anomaly with EGM96 models of different orders on the global grids
order number average computation time consumption of each grid point/ms 160 15.7 140 15.5 120 15.4 100 15.3 90 15.3 80 15.2 70 15.8 60 15.6 50 15.0 40 14.9 30 14.7
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