A new practical approach to GNSS high-dimensional ambiguity decorrelation

Based on both the lower and the upper triangular Cholesky decomposition algorithms, the (inverse) lower triangular Cholesky integer transformation and the (inverse) upper triangular Cholesky integer transformation are defined, and the (inverse) paired Cholesky integer transformation is proposed. Then, for the case of high-correlation ambiguity, a multi-time (inverse) paired Cholesky integer transformation is given. In addition, a simple and practical criterion is presented to solve the uniqueness problem of the integer transformation. It is verified by an example that (1) the (inverse) paired Cholesky integer transformation is very convenient and very efficient in practical computation; (2) the (inverse) paired Cholesky integer transformation is better than both the (inverse) lower triangular Cholesky integer transformation and the (inverse) upper triangular Cholesky integer transformation; and that (3) the inverse paired Cholesky integer transformation outperforms the paired Cholesky integer transformation slightly in the most cases.