Vectorial integer bootstrapping of best integer equivariant estimation (VIB-BIE) for efficient and reliable GNSS ambiguity resolution

Reliable integer ambiguity resolution (IAR) is essential for carrier phase-based centimeter-level accurate positioning using global navigation satellite systems (GNSSs). In all IAR methods, the best integer equivariant (BIE) estimator is optimal in the sense of minimizing the mean-squared errors. However, the BIE estimator comprises an enumeration in the integer space of ambiguities, and its complexity grows exponentially with the number of ambiguities. Moreover, in a complex urban environment, the positioning performance of the BIE estimator is also reduced due to larger observation errors and even outliers. To address this problem, an efficient and reliable IAR method is proposed in this paper, which consists of two major steps. First, we apply the vectorial integer bootstrapping (VIB) (Teunissen et al. in J Geod 95(9):1–14, 2021) by implementing BIE in each sequential block-by-block integer estimation to improve computation efficiency, which is denoted as VIB-BIE. Second, a measure, named the acceptable probability (ACP), is defined to control the reliability of VIB-BIE estimation. Both simulated and real multi-GNSS data are employed to evaluate the performance of the proposed method and conventional BIE. The results show that the flexibility and efficiency of IAR are both improved by VIB-BIE. In a complex urban environment, the ACP-based VIB-BIE outperforms the BIE in terms of IAR reliability and positioning accuracy. Compared to the BIE, the positioning accuracies are improved by 42.4%, 34.2%, and 31.8% in the east, north, and upward directions, respectively.