An alternative approach to calculate the posterior probability of GNSS integer ambiguity resolution
An alternative approach to calculate the posterior probability of GNSS integer ambiguity resolution
复制标题
计算 GNSS 整数模糊度分辨率后验概率的另一种方法
DOI：
10.1007/s00190-016-0963-0
复制
发表时间：
2017
影响因子：
4.4
通讯作者：
Gao Wang
中科院分区：
文献类型：
--
作者：
Yu Xianwen;Wang Jinling;Gao Wang
当通过GNSS载波相位进行精确定位时，重要的是要利用每个模糊度应该是整数的属性。对于已知的浮点解，任何与模糊向量具有相同自由度的整数向量都是概率上的模糊向量。对于整数孔径估计和整数等变估计，知道后验概率都具有重要意义。然而，为了计算后验概率，我们必须面对一个棘手的问题，即方程涉及无限数量的整数向量。本文利用模糊度的浮动解及其方差矩阵，提出了一种快速准确计算后验概率的新方法。提出的方法包括四个步骤。首先，对模糊度向量进行解相关变换。其次，通过公式直接得到各分量所采用的整数的取值范围，通过组合得到有限个整数向量。第三，利用整型向量求出后验概率的主值和修正因子。最后，得到了每个整数向量的后验概率及其误差上界。本文给出了后验概率的具体计算过程及公式的推导。理论和数值算例表明，该方法具有计算量小、计算精度高、适应性强等优点。
When precise positioning is carried out via GNSS carrier phases, it is important to make use of the property that every ambiguity should be an integer. With the known float solution, any integer vector, which has the same degree of freedom as the ambiguity vector, is the ambiguity vector in probability. For both integer aperture estimation and integer equivariant estimation, it is of great significance to know the posterior probabilities. However, to calculate the posterior probability, we have to face the thorny problem that the equation involves an infinite number of integer vectors. In this paper, using the float solution of ambiguity and its variance matrix, a new approach to rapidly and accurately calculate the posterior probability is proposed. The proposed approach consists of four steps. First, the ambiguity vector is transformed via decorrelation. Second, the range of the adopted integer of every component is directly obtained via formulas, and a finite number of integer vectors are obtained via combination. Third, using the integer vectors, the principal value of posterior probability and the correction factor are worked out. Finally, the posterior probability of every integer vector and its error upper bound can be obtained. In the paper, the detailed process to calculate the posterior probability and the derivations of the formulas are presented. The theory and numerical examples indicate that the proposed approach has the advantages of small amount of computations, high calculation accuracy and strong adaptability.