GPS integer ambiguity resolution by various decorrelation methods
GPS integer ambiguity resolution by various decorrelation methods
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发表时间：
2003-06
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通讯作者：
L. Lou;E. Grafarend
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作者：
L. Lou;E. Grafarend
为了从GPS测量中获得尽可能高的精度，特别是变形分析所需的精度，使用了载波相位观测值。在双差载波相位模式下，满足基本的整数-实值混合平差问题。通过标准参数估计，如加权最小二乘法或替代鲁棒目标函数，只能给出»浮点解« -包括模糊度向量。为了加快整周模糊度值的搜索过程，应用了去相关方法，该方法在实践中工作得足够好。在这里，我们评估了用于模糊度解算的浮点解的去相关的三个建议，即（i）由P. Xu（2001）提出的逆整数Cholesky去相关（CHOL），（ii）由P. Teunissen（1997）提出的整数高斯去相关（GAUSS）和（iii）A. K.伦斯特拉，H。W. Lenstra和L. Lovacs（LLL）算法，该算法是由A. Hassibi，S. Boyd（1998）和E. Grafarend（2000年）。对不同去相关方法的分析尽可能真实和具有统计意义：已经实施了随机模拟方法，该方法保证从双差观测方差协方差矩阵导出的模糊度向量的对称、正定方差协方差矩阵（»浮点解«）。谱条件数被用作三种去相关方法的性能的标准。最后对三组模拟数据进行了对比评价。
Summary In order to obtain the highest possible accuracy from GPS measurements, in particular needed for deformation analysis, carrier phase observations are used. Within the mode of double difference carrier phase, the fundamental mixed integer-real valued adjustment problem is met. Through standard parameter estimation like weighted least squares or alternative robust objective functions only the »floating solution« – including the vector of ambiguity – can be given. In order to speed up the searching process for the integer values of ambiguity, the method of decorrelation is applied which works »in practice« sufficiently well. Here we evaluate three proposals for the decorrelation of float solutions for ambiguity resolution, namely (i) the inverse integer Cholesky decorrelation (CHOL) as proposed by P. Xu (2001) (ii) the integer Gauss decorrelation (GAUSS) initiated by P. Teunissen (1997) and (iii) the A. K. Lenstra, H. W. Lenstra, and L. Lovacs (LLL) algorithm as proposed by A. Hassibi, S. Boyd (1998), and E. Grafarend (2000). The analysis of different decorrelation methods is made as realistic and as statistically meaningful as possible: a random simulation approach has been implemented which guarantees a symmetric, positive definite variance covariance matrix of the ambiguity vector (»float solution«) derived from the double difference observation variance covariance matrix. The spectral condition number is used as a criterion for the performance of the three decorrelation methods. Three sets of simulated data are finally comparatively evaluated.