Fast ambiguity resolution is a major challenge for GLONASS phase-based applications. The integer-estimable frequency-division multiple-access (IE-FDMA) model succeeds in formulating a set of estimable GLONASS phase ambiguities and preserving the integer property, to which the classical integer ambiguity resolution, typically the least-squares ambiguity decorrelation adjustment (LAMBDA), becomes readily applicable. The initial assessment of the IE-FDMA model demonstrated instantaneous ambiguity resolution capability in case of short-baseline real-time kinematic (RTK) positioning based on ionosphere-fixed formulation, in which the data processing strategy is window (batch)-based least-squares estimation with window length ranging from one to a few epochs. Here, we extend the applicability of the IE-FDMA model to Kalman-filter-based, ionosphere-fixed, ionosphere-weighted, and ionosphere-free cases, which are, respectively, adoptable for short-, medium-, and long-baseline RTK positioning. To adapt the IE-FDMA model to the Kalman filter, we estimate, at each epoch, first the estimable ambiguities, then transform them into integer-estimable ones, and finally resolve them into correct integers. This enables the rigorous integer ambiguity resolution and, at the same time, eases the recursive construction of integer-estimable ambiguities. We analyze global positioning system (GPS) and GLONASS data of nine baselines with lengths varying from several meters to more than one hundred kilometers. The results demonstrate the feasibility of fast ambiguity resolution not only for the GLONASS phase-only short-baseline RTK positioning, but for the GPS + GLONASS medium- and long-baseline RTK positioning as well. In all cases, the fixed solution with faster (several-minutes) convergence and higher (centimeter-level) precision indicates the benefits from GLONASS ambiguity resolution as compared to the float solution. Moreover, the dual-system solution with decreased ambiguity dilution of precision (ADOP) and improved positioning precision confirms the advantages of integrating GLONASS with GPS in contrast to the GPS-only situation.

中文翻译：

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整数可估计的GLONASS FDMA模型应用于基于卡尔曼滤波器的短基线到长基线RTK定位

对于基于GLONASS相位的应用程序，快速的模糊度解决是一个重大挑战。整数可估计的频分多址（IE-FDMA）模型成功地制定了一组可估计的GLONASS相位模糊度并保留了整数属性，经典整数模糊度分辨率（通常是最小二乘模糊性去相关调整，LAMBDA）针对该属性），变得容易适用。IE-FDMA模型的初步评估表明，在基于电离层固定公式的短基线实时运动（RTK）定位的情况下，瞬时模糊度解析能力非常出色，其中数据处理策略是基于窗口（批量）的最小-窗口长度范围从一个到几个纪元的平方估计。在这里，我们将IE-FDMA模型的适用性扩展到基于卡尔曼滤波器，电离层固定，电离层加权和无电离层情况，分别适用于短基线，中基线和长基线RTK定位。为了使IE-FDMA模型适合卡尔曼滤波器，我们在每个时期首先估计可估计的歧义，然后将它们转换为整数可估计的模棱两可，最后将它们分解为正确的整数。这实现了严格的整数歧义解析度，同时简化了整数可估计歧义的递归构造。我们分析了九个基线的全球定位系统（GPS）和GLONASS数据，长度从几米到一百多公里不等。结果表明，不仅对于仅GLONASS相位的短基线RTK定位，快速模糊度解决方案的可行性，但也适用于GPS + GLONASS中长基线RTK定位。在所有情况下，与浮动解决方案相比，具有更快（几分钟）收敛和更高（厘米级）精度的固定解决方案表明了GLONASS模糊度解决方案的优势。而且，双系统解决方案具有降低的歧义精度稀释度（ADOP）和改进的定位精度，这证实了与仅GPS情况相比，将GLONASS与GPS集成的优势。