一种改进的GPS整周模糊度降相关LLL算法

A modified LLL algorithm for GPS integer ambiguity decorrelation

摘要:

针对GPS整周模糊度降相关LLL(A.K.Lenstra,H.W.Lenstra,L.Lovasz)算法中存在的病态Z变换的缺陷问题,提出了一种改进的LLL算法．利用修正Gram-Schmidt正交化和行向量内积降序调整矩阵,对模糊度协方差矩阵进行降相关处理,改善LLL算法对低维矩阵的降相关效果,实现对高维矩阵的降相关．以谱条件数作为评判矩阵相关程度的准则,分别利用LLL算法和改进LLL算法对200个随机模拟的模糊度协方差矩阵进行仿真分析和比较,结果表明:改进LLL算法能更有效地减小模糊度协方差阵的谱条件数,降低矩阵的相关性,更有利于整周模糊度的搜索和解算．

Abstract:

According to the ill-conditioned Z transformation disadvantage of the LLL algorithm(A.K.Lenstra,H.W.Lenstra,L.Lovasz)for GPS integer ambiguity decorrelation,a modified LLL algorithm is proposed in the paper. The modified LLL algorithm applies the repaired Gram-Schmidt orthogonalization and row vector inner product adjustment matrixes to decorrelate integer ambiguity covariance matrixes, improve the performance of the low-dimension matrixes decorrelation applying the LLL algorithm and achieve high-dimension matrixes decorrelation.Taken the condition number as the criterion for judging the degree of matrix correlation,the performance of the LLL algorithm and the modified LLL algorithm are compared by applying 200 integer ambiguity covariance matrixes derived from random simulation. Results show that the modified LLL algorithm has better performance in decreasing the condition numbers of integer ambiguity covariance matrixes and reducing the correlations of covariance matrixes. Thus,the modified LLL algorithm is better for searching and solving GPS integer ambiguity.