Global Navigation Satellite System ambiguity decorrelation through diagonal elements precomputing and ordering method

Integer ambiguity decorrelation has long been an important problem for global navigation satellite system high-precision relative positioning applications for its effect of deducing search number of candidate integer ambiguities. It is difficult to design a decorrelation method with fine performance. Among those decorrelation methods based on LDL^T decomposition, direct-ordering method (DOM) is the one that follows the principle of ordering diagonal elements of variance-covariance matrix before decorrelation. In the present study, the authors propose a diagonal element precomputing and an ordering method (DEPOM) based on LDL^T. DEPOM orders diagonal elements of the matrix according to values after LDL^T decomposition, in contrast to DOM according to values before LDL^T decomposition. Thus, DEPOM is closer to the aim of arranging the larger diagonal element to the larger row before decomposition. The nodus is to determine elements in decomposed L and D matrices, which constitutes an improved LDL^T decomposition method. The above study show that DEPOM has better decorrelation degree and a higher success rate than DOM from the numerical simulation tests. The performance of DEPOM is equivalent to the united ambiguity decorrelation method. However, it is different. DEPOM is a supplement to the integer least-squares theory. The improved LDL^T decomposition is also a new form in the LDL^T decomposition family.