Fast Numerical Algorithm for the Calculation of Altimetric Crossovers from Satellite Ground Tracks
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摘要: 计算交叉点是卫星测高数据处理中的重要基础性工作。扩展了交叉点存在的判断条件，可用于判断任意两条卫星地面轨迹是否有交叉点。提出了一种快速计算交叉点的数值算法--矩形收缩算法。采用一个周期的Topex/Poseidon（T/P）卫星模拟轨道和一条海洋二号（HY-2）卫星实际轨迹设计了两个算例，以验证算法的精度和效率。结果表明矩形收缩法可以快速、高精度地计算出全部交叉点。以Envisat数据为例验证了算法计算近极轨道两极交叉点的适用性。该方法不仅可以计算单一卫星轨迹的交叉点，也可计算两个不同倾角卫星的轨迹交叉点，具有很强的通用性。Abstract: Numerical calculation of crossovers is important groundwork for satellite altimeter data processing. The criteria for judging the existence of crossover are extended to be applicable to any two satellite ground tracks. A fast numerical algorithm named rectangle shrinking method is proposed in order to improve the computational efficiency. Based on a cycle of simulated orbit data of Topex/Poseidon (T/P) and a pass of observations from HY-2, two experiments are performed to assess the precision and efficiency of the algorithm. The results demonstrate that the rectangle shrinking method can rapidly work out all of crossovers with high precision. Another test on Envisat data validated the applicability to near polarorbit. The proposed algorithm has strong universality, not only solving the crossovers from tracks of a single satellite, but also two satellites with different inclinations.
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Keywords:
- satellite altimetry /
- crossover /
- satellite ground track /
- fast numerical algorithm
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图 3 T/P卫星模拟轨道 (灰色) 和HY-2卫星第91号轨道 (黑色)
Figure 3. Simulated T/P Tracks (in Gray) and No. 91 Track of HY-2(in Black)
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图 4 T/P轨迹第1号升弧段和第32号降弧段的交叉点
Figure 4. Crossover of No. 1 Ascending Pass and No. 32 Descending Pass of T/P
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图 5 算例2中三种方法计算的交叉点分布
Figure 5. Distribution of Crossovers in Example 2 Derived by Three Methods
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图 6 本文方法计算的近极轨道 (Envisat卫星) 极区交叉点
Figure 6. Near Polar Crossovers of Envisat Computed by Our Method
表 1 矩形收缩法的交叉点计算精度
Table 1 Accuracy of Crossovers Computed by Rectangle Shrinking Algorithm
纬度范围 |φ| < 30° 30°≤|φ| < 60° |φ|≥60° 全球 交叉点个数 2 540 6 604 6 858 16 002 经度标准差/(°) 0 7.0×10-12 1.2×10-10 8.0×10-11 纬度标准差/(°) 2.4×10-6 8.1×10-6 1.1×10-5 8.9×10-6 
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表 2 3种计算方法的效率比较
Table 2 Comparison of the Computational Efficiency of Three Methods
本文方法 二项式拟合法 分段拟合法 算例1 交叉点个数 16 002(100%) 16 002(100%) 15 748(98.4%) 计算时间/s 34.854 35.265 35.403 算例2 交叉点个数 127(100%) 113(89%) 81(63.8%) 计算时间/s 0.522 0.554 0.560
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