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.

可靠的整数模糊度分辨率 (IAR) 对于使用全球导航卫星系统 (GNSS) 进行基于载波相位的厘米级精确定位至关重要。在所有 IAR 方法中，最佳整数等变 (BIE) 估计器在最小化均方误差的意义上是最优的。然而，BIE估计器包括模糊度整数空间中的枚举，并且其复杂度随着模糊度的数量呈指数增长。而且，在复杂的城市环境中，BIE估计器的定位性能也会因较大的观测误差甚至异常值而降低。为了解决这个问题，本文提出了一种高效可靠的 IAR 方法，该方法包括两个主要步骤。首先，我们应用向量整数自举（VIB）（Teunissen et al. in J Geod 95(9):1–14, 2021），通过在每个连续的逐块整数估计中实现 BIE 来提高计算效率，即表示为VIB-BIE。其次，定义了一种称为可接受概率（ACP）的度量来控制 VIB-BIE 估计的可靠性。使用模拟和真实的多 GNSS 数据来评估所提出的方法和传统 BIE 的性能。结果表明，VIB-BIE 提高了 IAR 的灵活性和效率。在复杂的城市环境中，基于ACP的VIB-BIE在可靠性和定位精度方面均优于BIE。与BIE相比，东、北、向上方向的定位精度分别提高了42.4%、34.2%和31.8%。