Improved HLLL Lattice Basis Reduction Algorithm to Solve GNSS Integer Ambiguity

Recently, lattice theory has been widely used for integer ambiguity resolution in the Global Navigation Satellite System (GNSS). When using to deal with ambiguity, we need reduce correlation between bases ensure efficiency of solution. Lattice reduction is divided into scale and basis vector exchange. The no direct impact on subsequent search efficiency, while exchange directly impacts efficiency. Hence, Lenstra-Lenstra-Lovász (LLL) applied improve And based Householder transformation, HLLL improved method also used. Moreover, calculation speed further, a Pivoting LLL (PHLLL) orthogonal transformation rotation sorting proposed here. idea PHLLL as follows: First, sort matrix introduced process original matrix. Then, sorted transformation. After it needs be again, until diagonal elements meet ascending order. In addition, when image operator orthogonalization, old column norm modified obtain new norm, reducing number calculations. Compared algorithm algorithm, experimental results show that higher effectiveness. theoretical superiority proved.