Improved GNSS integer ambiguity resolution method based on the column oriented Cholesky decomposition

Abstract

AbstractBecause the traditional Cholesky decomposition algorithm still has some problems such as computational complexity and scattered structure among matrices when solving the GNSS ambiguity,  it is the key problem to further improve the computational efficiency of the least squares ambiguity reduction correlation process in the carrier phase integer ambiguity solution. But the traditional matrix decomposition calculation is more complex and time-consuming, to improve the efficiency of the matrix decomposition, in this paper, the decomposition process of traditional matrix elements is divided into two steps: multiplication update and column reduction of square root calculation. The column reduction step is used to perform square root calculation and column division calculation, while the update step is used for the update task of multiplication. Based on the above ideas, the existing Cholesky decomposition algorithm is improved, and a column oriented Cholesky (C-Cholesky) algorithm is proposed to further improve the efficiency of matrix decomposition, so as to shorten the calculation time of integer ambiguity reduction correlation. The results show that this method is effective and superior, and can improve the data processing efficiency by about 12.34% on average without changing the integer ambiguity accuracy of the traditional Cholesky algorithm.