对GPS模糊度解相关方法的一种改进

在双差载波相位模型中,整数-实数混合平差是无法避免的.通常的参数估计方法如加权最小二乘,只能给出浮点解,包括模糊度向量也只是实数解.为了加速整周模糊度的搜索过程,解相关的方法得到了应用,并被证明是行之有效的.在此,主要讨论了LLL方法.为了对该解相关方法的分析尽可能地具有现实和统计意义,利用随机模拟方法得到了没有任何先验信息的对称正定矩陈,作为模糊度向量的方差-协方差矩阵.针对现有方法中的不足,提出了改进后的LLL方法,并利用条件数作为评判解相关程度的准则,证明其是切实可行的.

One Modified LLL Algorithm in GPS Decorrelation

Within the mode of double difference carrier phase, the fundamental mixed integerreal valued adjustment problem is unavoidable. Through standard parameter estimation like weighted least squares 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 the A. K. Lenstra,H. W. Lenstra and L. Lovacs (LLL) algorithm. The analysis of this decorrelation method 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 condition number is used as a criterion for the performance of this decorrelation method. The results show that the modified LLL Algorithm works better.