A modified LLL algorithm for GPS integer ambiguity decorrelation

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.