PPP-RTK extends the precise point positioning (PPP) concept by incorporating the idea of integer ambiguity resolution underlying the real-time kinematic (RTK) technique, making rapid initialization and high accuracy attainable with a standalone receiver. While PPP-RTK has been well achieved by using global navigation satellite system code division multiple access observables, GLONASS PPP-RTK is nonetheless challenging due to the nature of frequency division multiple access (FDMA) observables. In this work, we present a GLONASS PPP-RTK concept that takes advantage of the integer-estimable FDMA (IE-FDMA) model recently proposed in Teunissen (in GPS Solut 23(4):1–19, 2019. https://doi.org/10.1007/s10291-019-0889-0) to guarantee rigorous integer ambiguity resolution and simultaneously takes care of the presence of the inter-frequency biases (IFBs) in homogeneous and heterogeneous network configurations. When conducting GLONASS PPP-RTK based on a network of homogeneous receivers, code and phase observation equations are used to construct the IE-FDMA model, in which the IFBs are implicitly eliminated through reparameterization. For a network consisting of heterogeneous receivers, we exclude the code observables and develop a phase-only IE-FDMA model instead, thereby circumventing the adverse effects of IFBs. For verification purposes, we collect a set of five-day global positioning system (GPS) and GLONASS data from two regional networks: one equipped with homogeneous receivers and another with heterogeneous receivers. The results show that the GLONASS-specific network corrections, including satellite clocks, satellite phase biases, and ionospheric delays estimated by the two networks, are as precise as those of their GPS-specific counterparts. Via satellite clock and phase bias corrections, we succeed in fixing both GPS and GLONASS ambiguities, shortening the convergence time to 5 (12) min, compared to 11 (18) min of ambiguity-float positioning in the case of a homogeneous (heterogeneous) network with a data sampling rate of 30 s. For ambiguity-fixed positioning, the convergence time defined in this work also indicates the time to first fix since the positioning error converges to the centimeter level once successful integer ambiguity resolution is achieved. Adding ionospheric corrections further speeds up the initialization in the two networks, with the convergence time being reduced to 0.5 (3) min. Compared with GPS-only positioning, the integration of GPS and GLONASS yields an improvement of 8–34% in accuracy and leads to a reduction of 25–50% in convergence.

PPP-RTK 扩展了精确点定位 (PPP) 概念，将整数模糊度分辨率的思想融入实​​时运动学 (RTK) 技术的基础上，使独立接收器可实现快速初始化和高精度。虽然通过使用全球导航卫星系统码分多址可观测​​量已经很好地实现了 PPP-RTK，但由于频分多址 (FDMA) 可观测量的性质，GLONASS PPP-RTK 仍然具有挑战性。在这项工作中，我们提出了 GLONASS PPP-RTK 概念，该概念利用了 Teunissen 最近提出的整数可估计 FDMA (IE-FDMA) 模型（在 GPS Solut 23(4):1–19, 2019 中。https:// doi.org/10。1007/s10291-019-0889-0) 以保证严格的整数模糊度分辨率，并同时处理同构和异构网络配置中频间偏差 (IFB) 的存在。在基于同构接收器网络进行 GLONASS PPP-RTK 时，使用代码和相位观测方程来构建 IE-FDMA 模型，其中通过重新参数化隐式消除 IFB。对于由异构接收器组成的网络，我们排除了代码可观察量，而是开发了仅相位的 IE-FDMA 模型，从而规避了 IFB 的不利影响。出于验证目的，我们从两个区域网络收集了一组为期五天的全球定位系统 (GPS) 和 GLONASS 数据：一个配备同质接收器，另一个配备异构接收器。结果表明，GLONASS 特定的网络校正，包括由两个网络估计的卫星时钟、卫星相位偏差和电离层延迟，与它们的 GPS 特定对应物一样精确。通过卫星时钟和相位偏差校正，我们成功地修复了 GPS 和 GLONASS 模糊度，将收敛时间缩短至 5 (12) 分钟，而在同质（异质）情况下，模糊度浮动定位为 11 (18) 分钟数据采样率为 30 s 的网络。对于模糊度固定定位，这项工作中定义的收敛时间也表示首次定位的时间，因为一旦成功实现整数模糊度分辨率，定位误差就会收敛到厘米级。添加电离层校正进一步加速了两个网络的初始化，收敛时间减少到 0.5 (3) 分钟。与仅使用 GPS 定位相比，GPS 和 GLONASS 的集成使精度提高了 8-34%，收敛性降低了 25-50%。