Integer ambiguity resolution (IAR) is one of the key techniques in GNSS high precise positioning. However, an overlooked incorrect integer ambiguity solution may cause severe biases in the positioning results. The optimal integer aperture estimator (IAE) has the largest possible success rate given a certain fail rate. An alternative approach that take advantage of ambiguity integer nature to minimize the solution’s mean squared error (MSE) is known as the best integer equivariant (BIE) estimator. Both of which are associated with the posterior probability of the GNSS integer ambiguity. It is therefore of great significance to calculate posterior probability precisely and efficiently. Due to the occurrence of infinite sums, practical calculation approaches approximate the exact value by neglecting sufficiently small terms in the sum. As a result, they can only produce posterior probability calculation result, information about the result’s accuracy cannot be produced. In this contribution, the value of the posterior probability is bounded from below and from above by dividing the infinite sum into two parts: the major finite part and the minor infinite part. They are calculated partly by enumeration and partly by algebraical bounding. The obtained upper and lower bounds are rigorous and in closed form, so that can be conveniently used. Based on both of the bounds, a method of posterior probability calculation with controllable accuracy is proposed. It not only produces posterior probability calculation result, but also calculation error, which is always smaller than the user-defined acceptable error. Numerical experiments have verified that the proposed approach has advantages on both controllable calculation accuracy and adjustable computational workload.

整数模糊度分辨率（IAR）是GNSS高精度定位的关键技术之一。然而，一个被忽视的不正确的整数模糊度解决方案可能会导致定位结果出现严重偏差。给定一定的失败率，最优整数孔径估计器 (IAE) 具有最大可能的成功率。另一种利用模糊整数性质来最小化解的均方误差 (MSE) 的替代方法称为最佳整数等变 (BIE) 估计器。两者都与 GNSS 整数模糊度的后验概率有关。因此，准确高效地计算后验概率具有重要意义。由于无限和的出现，实际计算方法通过忽略和中足够小的项来近似精确值。因此，它们只能产生后验概率计算结果，无法产生结果准确性的信息。在这个贡献中，通过将无限和分为两部分：主要有限部分和次要无限部分，后验概率的值从下方和从上方限定。它们部分通过枚举计算，部分通过代数边界计算。得到的上下界是严格且封闭的，便于使用。基于这两个界限，提出了一种精度可控的后验概率计算方法。它不仅产生后验概率计算结果，而且计算误差总是小于用户定义的可接受误差。